From 7176febe54cd387dea1359bc81794b6811c466f5 Mon Sep 17 00:00:00 2001 From: Minseong Gwak Date: Wed, 3 Jun 2026 09:36:52 +0900 Subject: [PATCH] teamnote history merge --- 2024fall/Teamnote(Con Forza).zip | Bin 0 -> 26049 bytes 2024fall/Teamnote_Con_Forza_ .pdf | Bin 0 -> 1186471 bytes 2024fall/main.pdf | Bin 0 -> 180518 bytes 2024fall/main.tex | 649 +++++++ 2024fall/source/DS/LiChaoTree.cpp | 102 + 2024fall/source/DS/PBDS.cpp | 19 + 2024fall/source/DS/SegmentTree.cpp | 177 ++ 2024fall/source/DS/SplayTree.cpp | 278 +++ 2024fall/source/DS/UF_QUndo.cpp | 86 + 2024fall/source/Fundemental.cpp | 22 + 2024fall/source/Geometry/Mindset.cpp | 15 + 2024fall/source/Graph/BipartiteMatching.cpp | 17 + 2024fall/source/Graph/Dinic.cpp | 85 + 2024fall/source/Graph/MCMF.cpp | 79 + 2024fall/source/Graph/TarjanSCC.cpp | 32 + 2024fall/source/Math/CRT.cpp | 14 + 2024fall/source/Math/Diophantos.cpp | 14 + 2024fall/source/Math/FFTConv.cpp | 83 + 2024fall/source/Math/FloorSum.cpp | 8 + 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2025fall/source/DS/SegmentTree_GMS.cpp | 160 ++ 2025fall/source/DS/SplayTree.cpp | 127 ++ 2025fall/source/DS/UF_QUndo.cpp | 60 + 2025fall/source/Fundemental.cpp | 22 + 2025fall/source/Geometry/Bulldozer.cpp | 60 + 2025fall/source/Geometry/Geo.cpp | 26 + 2025fall/source/Geometry/HPI.cpp | 50 + 2025fall/source/Geometry/Mindset.cpp | 47 + .../source/Geometry/PointInConvexPolygon.cpp | 16 + 2025fall/source/Geometry/geometry_kaere.cpp | 163 ++ .../source/Geometry/namespace_geometry.cpp | 109 ++ 2025fall/source/Graph/2SAT.cpp | 5 + 2025fall/source/Graph/BipartiteMatching.cpp | 13 + 2025fall/source/Graph/Dinic.cpp | 69 + 2025fall/source/Graph/DominatorTree.cpp | 51 + 2025fall/source/Graph/MCMF.cpp | 67 + 2025fall/source/Graph/Matching.cpp | 74 + 2025fall/source/Graph/TarjanSCC.cpp | 28 + .../source/Linear Algebra/BerlekampMassey.cpp | 107 ++ 2025fall/source/Linear Algebra/Matrix.cpp | 56 + 2025fall/source/Linear Algebra/XORBasis.cpp | 5 + 2025fall/source/Math/CRT.cpp | 13 + 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2025spring/source/String/std::string.cpp | 132 ++ 2025spring/source/Tree/Centroid.cpp | 34 + 2025spring/source/Tree/HLD.cpp | 76 + 2025spring/source/empty.cpp | 0 2025spring/source/qwerty.cpp | 7 + 2025spring/teamnote.sty | 110 ++ README.md | 1 + 142 files changed, 13243 insertions(+) create mode 100644 2024fall/Teamnote(Con Forza).zip create mode 100644 2024fall/Teamnote_Con_Forza_ .pdf create mode 100644 2024fall/main.pdf create mode 100644 2024fall/main.tex create mode 100644 2024fall/source/DS/LiChaoTree.cpp create mode 100644 2024fall/source/DS/PBDS.cpp create mode 100644 2024fall/source/DS/SegmentTree.cpp create mode 100644 2024fall/source/DS/SplayTree.cpp create mode 100644 2024fall/source/DS/UF_QUndo.cpp create mode 100644 2024fall/source/Fundemental.cpp create mode 100644 2024fall/source/Geometry/Mindset.cpp create mode 100644 2024fall/source/Graph/BipartiteMatching.cpp create mode 100644 2024fall/source/Graph/Dinic.cpp create mode 100644 2024fall/source/Graph/MCMF.cpp create 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+\begin{align*} +\text{ When } X \le 2^{32}, D &= \{2, 7, 61\} \text{ is sufficient; } \\ +X \le 2^{64}, D &= \{p | p \text{ is prime}, p \le 37 \} \text{ is sufficient.} +\end{align*}} +{$\mathcal O (\log^3 X)$} +{cpp} +{source/Math/MillerRabin.cpp} + +\Algorithm{Pollad Rho Algorithm} +{ \texttt{po\_rho(N)} : returns array of prime factors of X.} +{$\mathcal O (N^{1/4})$} +{cpp} +{source/Math/PolladRho.cpp} + +\Algorithm{Diopantos Equation(Extended Euclidian Algorithm)} +{\texttt{diophantos(a, b)} : return one integer solution of $ax+by=1$, satisfying $0 \le x < b$. } +{$\mathcal O \left(\log \left( \max(a, b) \right) \right)$} +{cpp} +{source/Math/Diophantos.cpp} + +\Algorithm{Chinese Remainder Theorem} +{\texttt{crt(pll p, pll q)} : return \texttt{pll r}, satisfying follows: +\begin{align*} + x &\equiv \texttt{p.fi} \mod \texttt{p.se} \\ +\text{and } x &\equiv \texttt{q.fi} \mod \texttt{q.se} \\ + \leftrightarrow x &\equiv \texttt{r.fi} \mod \texttt{r.se} +\end{align*} +If there's no such \texttt{r}, return $\{-1, -1\}$. +} +{$\mathcal O(\log A)$} +{cpp} +{source/Math/CRT.cpp} + +\Algorithm{Harmonic Lemma} +{\texttt{f(N)} : return the value +$$\sum_{i=1}^{N} \left\lfloor \frac{N}{i} \right\rfloor = \left\lfloor \frac{N}{1}\right\rfloor + \left\lfloor \frac{N}{2} \right\rfloor + \cdots + \left\lfloor \frac{N}{N}\right\rfloor $$} +{$\mathcal O(\sqrt N )$} +{cpp} +{source/Math/Harmonic.cpp} + +\Algorithm{Floor Sum (Sum of Floor of Ratinoal Arithmetic Sequence)} +{\texttt{floor\_sum(A, B, C, N)} : retun the value +$$\sum_{x=1}^{N} \left\lfloor \frac{Ax+B}{C} \right\rfloor $$} +{$\mathcal O(\log N)$} +{cpp} +{source/Math/FloorSum.cpp} + +\Algorithm{FFT - Convolution} +{} +{$\mathcal O (N\log N)$} +{cpp} +{source/Math/FFTConv.cpp} + + + +\Algorithm{NTT - Number Theoretic Transform} +{helloworld} +{} +{cpp} +{source/Math/NTT.cpp} + +\subsubsection{Good prime numbers to run NTT} +\begin{center} +\begin{adjustbox}{width=0.8\columnwidth} +\begin{tabular}{|c|c| +>{\columncolor[HTML]{C0C0C0}}l |} +\hline +595 591 169 & 71\textless{}\textless{}23|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +645 922 817 & 77\textless{}\textless{}23|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +897 581 057 & 107\textless{}\textless{}23|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +998 244 353 & 119\textless{}\textless{}23|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +1 300 234 241 & 155\textless{}\textless{}23|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +1 224 736 769 & 73\textless{}\textless{}24|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +2 130 706 433 & 127\textless{}\textless{}24|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +167 772 161 & 5\textless{}\textless{}25|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +469 762 049 & 7\textless{}\textless{}26|1 & \multirow{-9}{*}{\cellcolor[HTML]{C0C0C0}$\omega$ = 3} \\ \hline +\end{tabular} +\end{adjustbox} +\end{center} + +\Algorithm{Polynomial (Formal Power Series)} +{} +{} +{cpp} +{source/Math/Polynomial.cpp} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Linear Algebra} +\subsection{Matrix Multiplication} +\texttt{k-i-j} 순서가 가장 Cache-Friendly 함. + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Geometry} + +\Algorithm{Mindset} +{} +{$\mathcal O(N?)$} +{cpp} +{source/Geometry/Mindset.cpp} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Greedy} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{DP} + +% \Algorithm{} +% {} +% {$\mathcal O(N?)$} +% {cpp} +% {source/} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{String} + +\Algorithm{F, Z, M, SA(Suffix Array), LCP(Longest Common Prefix)} +{For string s(1-indexed) of length N; +\begin{align*} +\texttt{F[i] = }& \text{maximum } k + +#define all(v) (v).begin(), (v).end() +#define rall(v) (v).rbegin(), (v).rend() + +#define getint(n) int n; scanf("%d%*c", &n) +#define getll(n) ll n; scanf("%lld%*c", &n) +#define inta int a; scanf("%d%*c", &a) +#define intab int a,b; scanf("%d%*c%d%*c", &a,&b) + +#define forr(i, n) for(int i=1; i <= (n); i++) +#define fors(i, s, e) for(int i = (s); i<=(e); i++) +#define fore(i, e, s) for(int i = (e); i >= s; i--) + +#define pb push_back +#define fi first +#define se second + +using namespace std; + +using ll = long long; +using pii = pair; using pll = pair; +using vi = vector; using vii = vector; +struct Line +{ + ll a=0, b=(ll)2e18+7; + ll operator()(ll x){return a*x+b;} + Line():a(0),b((ll)2e18+7){} + Line(ll a, ll b):a(a), b(b){} +}; + +ll middle(ll s, ll e){return (s+e+(ll)2e18)/2-(ll)1e18;} +struct Node +{ + Node *l=0, *r=0; + Line v; + Node():l(0), r(0), v(Line()){} +}; +void insert(Node* node, Line v, ll l, ll r, ll s, ll e) +{ + ll mid=middle(s, e); + if(e < l or r < s) return; + if(s == e) + { + node->v = (node->v(s) < v(s))?node->v:v; + return; + } + if(!node->l) node->l = new Node(); + if(!node->r) node->r = new Node(); + + if(l <= s and e <= r) + { + if(node->v(s) >= v(s) and node->v(e) >= v(e)){node->v = v; return;} + if(node->v(s) <= v(s) and node->v(e) <= v(e)) return; + insert(node->l, v, l, r, s, mid); + insert(node->r, v, l, r, mid+1, e); + } + else + { + insert(node->l, v, l, r, s, mid); + insert(node->r, v, l, r, mid+1, e); + } +} +ll query(Node* node, ll x, ll s, ll e) +{ + if(!node) return (ll)2e18+7; + if(x < s or e < x) return (ll)2e18+7; + if(s == e) return node->v(x); + + ll mid = middle(s, e); + return min({query(node->l, x, s,mid), query(node->r, x, mid+1, e), node->v(x)}); +} +// 전체 구간을 미리 고정해 놓아야 함. +// (const int L = -1e9, R = 1e9); +// Insert : insert(root, Line 객체, l, r, L, R); +// Query : query(root, x, L, R); +int main() +{ + Node *root = new Node(); + getint(n); getint(Q); + forr(i, n) + { + getll(l); getll(r); getll(a); getll(b); + insert(root, Line(a,b), l,r-1,(ll)-1e9-7, (ll)1e9+7); + } + while(Q--) + { + getint(q); + if(q == 0) + { + getll(l); getll(r); getll(a); getll(b); + insert(root, Line(a,b), l,r-1,(ll)-1e9-7, (ll)1e9+7); + } + if(q == 1) + { + getll(x); + ll ans = query(root, x,(ll)-1e9-7, (ll)1e9+7); + if(ans == (ll)2e18+7) printf("INFINITY\n"); + else printf("%lld\n", ans); + } + } +} \ No newline at end of file diff --git a/2024fall/source/DS/PBDS.cpp b/2024fall/source/DS/PBDS.cpp new file mode 100644 index 0000000..b4b6c91 --- /dev/null +++ b/2024fall/source/DS/PBDS.cpp @@ -0,0 +1,19 @@ +#include +using namespace __gnu_pbds; + +template +using indexed_set = tree, rb_tree_tag, tree_order_statistics_node_update>; + +indexed_set s; +s.insert(3); s.insert(2); s.insert(3); +s.insert(9); s.insert(7); +//2 3 7 9 + +s.insert(5); //2 3 5 7 9 +s.erase(5); //2 3 7 9 + +auto x = s.find_by_order(2); // *x : 7 + +s.order_of_key(6) // 2 +s.order_of_key(7) // 2 +s.order_of_key(8) // 3 \ No newline at end of file diff --git a/2024fall/source/DS/SegmentTree.cpp b/2024fall/source/DS/SegmentTree.cpp new file mode 100644 index 0000000..6efeee2 --- /dev/null +++ b/2024fall/source/DS/SegmentTree.cpp @@ -0,0 +1,177 @@ +namespace GMS +{ + template + class Segtree + { + class Node + { + Node *l, *r; + int s,e; D v; + public: + Node(int s, int e) :l(0), r(0), s(s), e(e), v(_e){}; + ~Node(){delete l; delete r;} + + template + friend void init(Node* node, Dini arr[] = NULL) + { + int s = node->s, e=node->e, mid=(s+e)/2; + if(s == e) + { + node->v = D(arr?arr[s]:_e); + return; + } + + node->l = new Node(s, mid); + init(node->l, arr); + node->r = new Node(mid+1, e); + init(node->r, arr); + + node->v = join(node->l->v, node->r->v); + } + friend D _query(Node* node, int a, int b) + { + int s=node->s, e=node->e; + if(a <= s and e <= b) return node->v; + if(b < s or e < a) return _e; + + return join(_query(node->l, a, b), _query(node->r, a, b)); + } + friend void _update + (Node* node, int i, function upd) + { + int s=node->s, e=node->e; + if(i < s or e < i) return; + if(s == e) + { + node->v = upd(node->v); + return; + } + + _update(node->l, i, upd); + _update(node->r, i, upd); + + node->v = join(node->l->v, node->r->v); + } + }; + + Node *root; + public: + + template + Segtree(int s,int e, Dini arr[] = NULL) + { + root = new Node(s, e); + init(root, arr); + } + ~Segtree(){delete root;} + D query(int s, int e) + {return _query(root, s, e);} + void update(int i, function upd) + {_update(root, i, upd);} + }; + + + template + class LZSegtree + { + class Node + { + Node *l, *r; + int s,e; + D v; L lz; + + void prop() + { + v = apply(v, lz, e-s+1); + if(l) l->lz = give(l->lz, lz); + if(r) r->lz = give(r->lz, lz); + + lz = _l; + } + + public: + Node(int s, int e) + :l(0), r(0), s(s), e(e), v(_e), lz(_l){}; + ~Node(){delete l; delete r;} + + template + friend void init(Node* node, Dini arr[] = NULL) + { + int s = node->s, e=node->e, mid=(s+e)/2; + if(s == e) + { + node->v = D(arr?arr[s]:_e); + return; + } + + node->l = new Node(s, mid); + init(node->l, arr); + node->r = new Node(mid+1, e); + init(node->r, arr); + + node->v = join(node->l->v, node->r->v); + } + friend D _query(Node* node, int a, int b) + { + node->prop(); + int s=node->s, e=node->e; + if(a <= s and e <= b) return node->v; + if(b < s or e < a) return _e; + + return join(_query(node->l, a, b), _query(node->r, a, b)); + } + friend void _update + (Node* node, int a, int b, function upd) + { + node->prop(); + int s=node->s, e=node->e; + if(b < s or e < a) return; + if(a <= s and e <= b) + { + node->lz = upd(node->lz); + node->prop(); + return; + } + + _update(node->l, a, b, upd); + _update(node->r, a, b, upd); + + node->v = join(node->l->v, node->r->v); + } + }; + + Node *root; + public: + + template + LZSegtree(int s,int e, Dini arr[] = NULL) + { + root = new Node(s, e); + init(root, arr); + } + ~LZSegtree(){delete root;} + D query(int s, int e){return _query(root, s, e);} + void update(int s, int e, function upd){_update(root, s, e, upd);} + }; +} // namespace GMS + +////////////////////////////////////////////////////// +#define data _data + +struct data +{ + int m, m_cnt; + constexpr data(int m):m(m), m_cnt(1){} + constexpr data(int m, int m_cnt):m(m), m_cnt(m_cnt){} +}; +data join(data A, data B) +{ + if(A.m == B.m) return data(A.m, A.m_cnt+B.m_cnt); + if(A.m < B.m) return A; + else return B; +} +data apply(data A, int lz, int len) + {return {A.m+lz, A.m_cnt};} +int give(int a, int b){return a+b;} + +using Seg = GMS::LZSegtree; diff --git a/2024fall/source/DS/SplayTree.cpp b/2024fall/source/DS/SplayTree.cpp new file mode 100644 index 0000000..f76f9f9 --- /dev/null +++ b/2024fall/source/DS/SplayTree.cpp @@ -0,0 +1,278 @@ +struct Node +{ + Node *p, *l, *r; + int key, cnt; + ll val; ll m, M, sum; ll lazy; + bool flip; + + Node(int key, ll val):p(0),l(0), r(0), key(key), cnt(1), val(val), m(val), M(val), sum(val), lazy(0), flip(0){} + + void fix() + { + cnt = 1+(l?l->cnt:0)+(r?r->cnt:0); + sum = val+(l?l->sum:0)+(r?r->sum:0); + m = min({val, (l?l->m:inf), (r?r->m:inf)}); + M = max({val, (l?l->M:-1), (r?r->M:-1)}); + } + void prop() + { + if(flip) + { + swap(l, r); + if(l) l->flip = !l->flip; + if(r) r->flip = !r->flip; + + flip = false; + } + if(lazy) + { + val += lazy; sum += cnt * lazy; + if(l) l->lazy += lazy; + if(r) r->lazy += lazy; + + lazy = 0; + } + } + +} *root; +struct SplayTree +{ + Node *root = NULL, *rp = NULL; + + SplayTree(){} + SplayTree(Node *rt) + { + if(!rt) return; + + root = rt; + rp = rt->p; + } + + void mop(Node *node) + { + if(node == root) node->prop(); + else mop(node->p); + + if(node->l) node->l->prop(); + if(node->r) node->r->prop(); + } + + void rotate(Node *node) + { + if(!root) return; + + if(node->p == rp) return; + if(node->p->l == node) + { + Node *p = node->p, *g = p->p; + Node *a = node->l, *b = node->r, *c = p->r; + + p->l = b; if(b) b->p = p; + p->r = c; if(c) c->p = p; + + node->l = a; if(a) a->p = node; + node->r = p; p->p = node; + + node->p = g; if(g) (g->l == p?g->l:g->r) = node; + + p->fix(); node->fix(); + + if(p == root) root = node; + } + else + { + Node *p = node->p, *g = p->p; + Node *a = p->l, *b = node->l, *c = node->r; + + p->l = a; if(a) a->p = p; + p->r = b; if(b) b->p = p; + + node->l = p; p->p = node; + node->r = c; if(c) c->p = node; + + node->p = g; if(g) (g->l == p?g->l:g->r) = node; + + p->fix(); node->fix(); + + if(p == root) root = node; + } + + } + + void splay(Node* node) + { + if(!root) return; + assert(node); mop(node); + + while(node->p != rp) + { + Node *p, *g; + p = node->p; g = p->p; + + if(g == rp) rotate(node); + else if((p->l == node) == (g->l == p)) + rotate(p), rotate(node); + else rotate(node), rotate(node); + } + + root = node; + } + + Node* insert(int key, ll val) + { + if(!root) + { + root = new Node(key, val); + return root; + } + else + { + Node *now = root; + while(true) + { + if(now->key == key) return NULL; + else if(now->key > key) + { + if(!now->l) break; + now = now->l; + } + else + { + if(!now->r) break; + now = now->r; + } + } + + Node *ret; + if(now->key > key) + { + ret = now->l = new Node(key, val); + now->l->p = now; + splay(now->l); + } + else + { + ret = now->r = new Node(key, val); + now->r->p = now; + splay(now->r); + } + + return ret; + } + } + + /*Node* find(int key) + { + Node* now = root; + if(!now) return NULL; + while(true) + { + if(key == now->key) break; + else if(key < now->key) + { + if(!now->l) break; + now = now->l; + } + else + { + if(!now->r) break; + now = now->r; + } + } + + splay(now); + return key == now->key?now:NULL; + } + + void erase(int key) + { + if(!find(key)) return; + if(root->l and root->r) + { + Node* e = root; + root = root->l; root->p = NULL; + + Node* now = root; + while(now->r) now = now->r; + now->r = e->r; + e->r->p = now; + splay(now); + + delete e; + } + else if(root->l) + { + Node* now = root; + root = root->l; root->p = NULL; + delete now; + } + else if(root->r) + { + Node* now = root; + root = root->r; root->p = NULL; + delete now; + } + else + { + delete root; + root = NULL; + } + }*/ + + Node* find_kth(int k) // 0-indexed + { + assert(root); + assert(root->cnt > k); + Node *now = root; now->prop(); + while(true) + { + while(now->l and now->l->cnt > k) now = now->l, now->prop(); + k -= now->l?now->l->cnt:0; + + if(k == 0) break; + k--; now = now->r; + now->prop(); + } + + splay(now); + return now; + } + Node* gather(int s, int e) + { + find_kth(e+1); + SplayTree(root->l).find_kth(s-1); + + assert(root->l->r); + return root->l->r; + } + void update(int i, int j, ll val) + { + Node *node = gather(i, j); + + node->lazy += val; node->prop(); + node->p->fix(); node->p->p->fix(); + } + void reverse(int i, int j) + { + Node *node = gather(i, j); + node->flip = !node->flip; + } + + void p_vals(int n){p_vals(root, 0, false, n);} + void p_vals(Node* node, ll lz, bool flip, int n) + { + lz += node->lazy; flip ^= node->flip; + if(!flip) + { + if(node->l) p_vals(node->l, lz, flip, n); + if(!(node->key == 0 or node->key == n+1)) printf("%lld ", node->val+lz); + if(node->r) p_vals(node->r, lz, flip, n); + } + else + { + if(node->r) p_vals(node->r, lz, flip, n); + if(!(node->key == 0 or node->key == n+1)) printf("%lld ", node->val+lz); + if(node->l) p_vals(node->l, lz, flip, n); + } + } +}; \ No newline at end of file diff --git a/2024fall/source/DS/UF_QUndo.cpp b/2024fall/source/DS/UF_QUndo.cpp new file mode 100644 index 0000000..11e656e --- /dev/null +++ b/2024fall/source/DS/UF_QUndo.cpp @@ -0,0 +1,86 @@ +struct dsu_pb +{ + const int N; + vi par; stack > s; + + dsu_pb(int N):N(N), par(N) + { + fors(i, 0, N-1) par[i] = -1; + } + int root(int i) + { + if(par[i] < 0) return i; + return root(par[i]); + } + bool join(int i, int j) + { + i = root(i); j = root(j); + s.push({{i, par[i]}, {j, par[j]}}); + + if(i == j) return false; + + if(-par[i] < -par[j]) swap(i, j); + + par[i] += par[j]; par[j] = i; + return true; + } + +protected: + void unjoin() + { + assert(!s.empty()); + auto [i, j] = s.top(); s.pop(); + + par[i.fi] = i.se; + par[j.fi] = j.se; + } +}; + +struct dsu_pf : public dsu_pb +{ + vector > st; // fi==0 -> B type, fi==1 -> A type + vector > tmp[2]; + + int A=0, B=0; + + dsu_pf(int N):dsu_pb(N){} + + bool join(int i, int j) + { + st.pb({0, {i, j}}); B++; + return dsu_pb::join(i, j); + } + void pop_front() + { + assert(!st.empty()); + if(A == 0) + { + forr(i, B) unjoin(); + + A = B; B = 0; + reverse(all(st)); + for(auto &[b, p]:st) b = 1, dsu_pb::join(p.fi, p.se); + } + else if(st.back().fi == false) + { + tmp[st.back().fi].pb(st.back()); st.pop_back(); + unjoin(); + + while(tmp[0].size() != tmp[1].size() and (unsigned) A != tmp[1].size()) + { + tmp[st.back().fi].pb(st.back()); + st.pop_back(); + unjoin(); + } + + for(auto i:{0, 1}) reverse(all(tmp[i])); + for(auto i:{0, 1}) for(auto v:tmp[i]) + st.pb(v), dsu_pb::join(v.se.fi, v.se.se); + + tmp[0].clear(); tmp[1].clear(); + } + + A--; st.pop_back(); + unjoin(); + } +}; \ No newline at end of file diff --git a/2024fall/source/Fundemental.cpp b/2024fall/source/Fundemental.cpp new file mode 100644 index 0000000..1c61be6 --- /dev/null +++ b/2024fall/source/Fundemental.cpp @@ -0,0 +1,22 @@ +#include + +#define getint(n) int n; scanf("%d%*c", &n) +#define getll(n) long long n; scanf("%lld%*c", &n) +#define getchar(n) char n; scanf("%c%*c", &n); +#define intab getint(a); getint(b) + +#define forr(i, n) for(int i=1;i<=(n);i++) +#define fors(i, s, e) for(int i=(s); i<=(e); i++) +#define fore(i, e, s) for(int i=(e); i>=(s); i--) + +#define fi first +#define se second +#define all(v) (v).begin(), (v).end() +#define rall(v) (v).rbegin(), (v).rend() +#define pb push_back + +using namespace std; +using ll = long long; using lll = __int128_t; +using pii = pair; using pll = pair; +using vi = vector; using vl = vector; +using vii = vector; using vll = vector; \ No newline at end of file diff --git a/2024fall/source/Geometry/Mindset.cpp b/2024fall/source/Geometry/Mindset.cpp new file mode 100644 index 0000000..8741756 --- /dev/null +++ b/2024fall/source/Geometry/Mindset.cpp @@ -0,0 +1,15 @@ +using pii=pair; +pii operator+(pii A, pii B){return {A.fi+B.fi, A.se+B.se};} +pii operator-(pii A, pii B){return {A.fi-B.fi, A.se-B.se};} +ll operator*(pii A, pii B){return (ll)A.fi*B.fi+(ll)A.se*B.se;} // inner product +ll operator/(pii A, pii B){return (ll)A.fi*B.se-(ll)A.se*B.fi;} // outer product + +// 각도 정렬 (O = pii(0, 0)) +sort(P+1, P+1+n, [](pii A, pii B){return (A0;}); + +// 선분 : pair -> 2D-vector B from A +// 선분 교차 판정 +bool isintersect(const pii &a, const pii &b, const pii &u, const pii &v){ + if( b/v != 0 ) return sign((u-a)/b) * sign((u+v-a)/b) <= 0 && sign((a-u)/v) * sign((a+b-u)/v) <= 0; + else return (a-u)/v == 0 && (0 <= v*(a-u) && v*(a-u) <= v*v || 0 <= b*(u-a) && b*(u-a) <= b*b); +} \ No newline at end of file diff --git a/2024fall/source/Graph/BipartiteMatching.cpp b/2024fall/source/Graph/BipartiteMatching.cpp new file mode 100644 index 0000000..5776107 --- /dev/null +++ b/2024fall/source/Graph/BipartiteMatching.cpp @@ -0,0 +1,17 @@ +vector sideadj[N]; +int selby[M]; +int chk[M], c; +bool matching(int s) +{ + for(auto i : sideadj[s]) + { + if(chk[i] == c) continue; + chk[i] = c; + + if(selby[i] and !matching(selby[i])) continue; + + selby[i] = s; + return true; + } + return false; +} \ No newline at end of file diff --git a/2024fall/source/Graph/Dinic.cpp b/2024fall/source/Graph/Dinic.cpp new file mode 100644 index 0000000..ac74f7a --- /dev/null +++ b/2024fall/source/Graph/Dinic.cpp @@ -0,0 +1,85 @@ +struct Edge +{ + int to, cap, now; + Edge* rev; + Edge(int to,int cap):to(to), cap(cap), now(0){} + int left(){return cap - now;} + void flow(int f){now += f; rev->now -= f;} + void reset(){now = 0;} +}; +vector adj[N]; + +int lv[N]; bool chk[N]; +bool bfs(int S, int T) +{ + queue q; + + q.push(S); lv[S] = 0; chk[S] = true; + + while(!q.empty()) + { + int s = q.front(); q.pop(); + for(auto i : adj[s]) + { + if(i->left() and !chk[i->to]) + { + lv[i->to] = lv[s]+1; chk[i->to] = true; + q.push(i->to); + } + } + } + return chk[T]; +} + +Edge* hist[N]; int last[N]; +bool dfs(int s, int T) +{ + if(s == T) return true; + + for(int &j=last[s]; j < adj[s].size(); j++) + { + int i = adj[s][j]->to; + if(adj[s][j]->left() == 0 or lv[i] != lv[s]+1) continue; + hist[i] = adj[s][j]; + + if(dfs(i, T)) return true; + } + return false; +} + +ll flow(int S,int T) +{ + ll ans = 0; + while(bfs(S, T)) + { + while(dfs(S, T)) + { + int m = 2e9; + + int now = T; + while(S != now) + { + m = min(m, hist[now]->left()); + now = hist[now]->rev->to; + } + now = T; + while(S != now) + hist[now]->flow(m), now = hist[now]->rev->to; + ans += m; + } + + memset(last, 0, sizeof last); + memset(chk, 0, sizeof chk); + } + return ans; +} +// isDir : isDirected => 양방향 간선이면 false +void connect(int from, int to, int cap, bool isDir = true) +{ + Edge *fw, *bw; + fw = new Edge(to, cap); + bw = new Edge(from, !isDir ? cap : 0); + fw->rev = bw; bw->rev = fw; + adj[from].push_back(fw); + adj[to].push_back(bw); +} \ No newline at end of file diff --git a/2024fall/source/Graph/MCMF.cpp b/2024fall/source/Graph/MCMF.cpp new file mode 100644 index 0000000..b2dacc1 --- /dev/null +++ b/2024fall/source/Graph/MCMF.cpp @@ -0,0 +1,79 @@ +struct Edge +{ + int to, cap, now; + ll cost; + Edge* rev; + Edge(int to,int cap, ll cost) + :to(to), cap(cap), now(0), cost(cost){} + int left(){return cap - now;} + ll flow(int f) + {now += f; rev->now -= f; return cost * f;} + void reset(){now = 0;} +}; +vector adj[N]; +Edge* hist[N]; ll dist[N]; bool inQueue[N], chk[N]; +bool spfa(int s, int t) +{ + memset(dist, 0, sizeof(dist)); + memset(chk, 0, sizeof(chk)); chk[s] = true; + + queue q; + memset(inQueue, 0, sizeof(inQueue)); + q.push(s); inQueue[s] = true; + + while(!q.empty()) + { + int now = q.front(); + q.pop(); inQueue[now] = false; + + for(auto e : adj[now]) + { + int next = e->to; + if(e->left() > 0 and + (chk[next] == false + or dist[next] > dist[now] + e->cost)) + { + chk[next] = true; + dist[next] = dist[now] + e->cost; + hist[next] = e; + if(!inQueue[next]) + q.push(next), inQueue[next] = true; + } + } + } + return chk[t]; +} +// cost가 들어가면 항상 단방향만 가능하다. (양방향 : 2번 connect) +void connect(int from, int to, int cap, ll cost) +{ + Edge *fw, *bw; + fw = new Edge(to, cap, cost); + bw = new Edge(from, 0, -cost); + fw->rev = bw; bw->rev = fw; + adj[from].push_back(fw); + adj[to].push_back(bw); +} +//maximum matching & minimum cost +pair flow(int S,int T) +{ + ll ans = 0; ll cost = 0; + while(spfa(S, T)) + { + int m = 2e9; + + int now = T; + while(S != now) + { + m = min(m, hist[now]->left()); + now = hist[now]->rev->to; + } + now = T; + while(S != now) + { + cost += hist[now]->flow(m); + now = hist[now]->rev->to; + } + ans += m; + } + return {ans, cost}; +} \ No newline at end of file diff --git a/2024fall/source/Graph/TarjanSCC.cpp b/2024fall/source/Graph/TarjanSCC.cpp new file mode 100644 index 0000000..44788f7 --- /dev/null +++ b/2024fall/source/Graph/TarjanSCC.cpp @@ -0,0 +1,32 @@ +vi adj[N]; +int in[N], c = 0; +stack p; +bool fin[N]; int scn[N], nscc = 0; + +int dfs(int s) +{ + in[s] = ++c; + p.push(s); + + int m = c; + for(auto i : adj[s]) + { + if(in[i] == 0) m = min(m, dfs(i)); + else if(!fin[i]) m = min(m, in[i]); + } + + if(m == in[s]) + { + nscc++; + while(p.top() != s) + { + int i = p.top(); p.pop(); + scn[i] = nscc; fin[i] = true; + } + p.pop(); + scn[s] = nscc; fin[s] = true; + } + return m; +} + +forr(i, n) if(!fin[i]) dfs(i); \ No newline at end of file diff --git a/2024fall/source/Math/CRT.cpp b/2024fall/source/Math/CRT.cpp new file mode 100644 index 0000000..5a10def --- /dev/null +++ b/2024fall/source/Math/CRT.cpp @@ -0,0 +1,14 @@ +pll crt(pll p, pll q) +{ + if(p.fi > q.fi) swap(p, q); + auto [a, A] = p; + auto [b, B] = q; + + ll g = gcd(A, B); + if((b-a)%g != 0) return {-1, -1}; + + ll i = A, j = B, k = b-a; + i/=g; j/=g; k/=g; + auto [x, y] = diophantos(i, j); + return {(ll)((a+(lll)A*k*x)%(A*B/g)), A*B/g}; +} \ No newline at end of file diff --git a/2024fall/source/Math/Diophantos.cpp b/2024fall/source/Math/Diophantos.cpp new file mode 100644 index 0000000..016a44b --- /dev/null +++ b/2024fall/source/Math/Diophantos.cpp @@ -0,0 +1,14 @@ +pll diophantos(ll a, ll b) +{ + assert(a>0 and b>=0); + if(b == 0) return {1, 0}; + auto [y, x] = diophantos(b, a%b); y = y-(a/b)*x; + if(x < 0 or x >= b) + { + ll t = x/b; + if(x%b < 0) t--; + + x -= b*t; y += a*t; + } + return {x, y}; +} \ No newline at end of file diff --git a/2024fall/source/Math/FFTConv.cpp b/2024fall/source/Math/FFTConv.cpp new file mode 100644 index 0000000..15d8779 --- /dev/null +++ b/2024fall/source/Math/FFTConv.cpp @@ -0,0 +1,83 @@ +using cpx = complex; +using vcpx = vector; +void fft(vcpx &a, bool inv = false) +{ + int n = a.size(), j = 0; assert((n&-n) == n); + for(int i=1; i> 1); + while(j >= bit) + { + j -= bit; + bit >>= 1; + } + j += bit; + if(i < j) swap(a[i], a[j]); + } + + vcpx roots(n/2); + prec c = 2 * pi * (inv ? -1 : 1); + for(int i=0; i=c or b>=c) return n*(n-1)/2 * (a/c) + n * (b/c) + floor_sum(a%c, b%c, c, n); + if(a == 0) return b/c*n; + + ll m = (a*(n-1)+b)/c; + return m*(n-1) - floor_sum(c, c-b-1, a, m); +} \ No newline at end of file diff --git a/2024fall/source/Math/Harmonic.cpp b/2024fall/source/Math/Harmonic.cpp new file mode 100644 index 0000000..8a995d4 --- /dev/null +++ b/2024fall/source/Math/Harmonic.cpp @@ -0,0 +1,7 @@ +ll f(int n) +{ + ll ans = 0; + for(int i = 1; i <= n; i = n/(n/i)+ 1) + ans += (ll)(n/(n/i)-i+1)*(n/i); + return ans; +} \ No newline at end of file diff --git a/2024fall/source/Math/MillerRabin.cpp b/2024fall/source/Math/MillerRabin.cpp new file mode 100644 index 0000000..5d589b5 --- /dev/null +++ b/2024fall/source/Math/MillerRabin.cpp @@ -0,0 +1,31 @@ +ll pow(ll a, ll b, ll mod) +{ + ll ret = 1; + for(int st=0; (1LL< + ll pow(ll a, ll b) + { + static_assert(mod <= (ll)2e9, "mod should be less than 2e9"); + a %= mod; + ll ret = 1; + while(b != 0) + { + if(b&1) ret = ret*a%mod; + a = a*a%mod; b>>=1; + } + + return ret; + } + template + void ntt(vector &a, bool inv = false) + { + static_assert(mod <= (ll)2e9, "mod should be less than 2e9"); + int n = a.size(), j = 0; + + assert((n & -n) == n); + assert((mod-1)%n == 0); + + for(int i=1; i> 1); + while(j >= bit){ + j -= bit; + bit >>= 1; + } + j += bit; + if(i < j) swap(a[i], a[j]); + } + + static vector root[30], iroot[30]; + for(int st=1; (1<(w, (mod-1)/(1<(w, (mod-1)/(1<(t, mod-2); + + iroot[st].pb(1); + for(int i=1; i<(1<<(st-1)); i++) + iroot[st].pb(iroot[st].back()*t%mod); + } + } + + vector* r = (inv?root:iroot); + + for(int st = 1; (1<(n, mod-2); + for(int i=0; i + vl conv(vl A, vl B) + { + int n = A.size(), m = B.size(); + int t = 1; while(t < n+m-1) t*=2; + A.resize(t); B.resize(t); + + ntt(A); ntt(B); + + fors(i, 0, t-1) A[i] = A[i]*B[i]%mod; + + ntt(A, true); + A.resize(n+m-1); + + return A; + } +} // namespace GMS \ No newline at end of file diff --git a/2024fall/source/Math/PolladRho.cpp b/2024fall/source/Math/PolladRho.cpp new file mode 100644 index 0000000..f12e2b2 --- /dev/null +++ b/2024fall/source/Math/PolladRho.cpp @@ -0,0 +1,32 @@ +void fact(ll n, vl& ret) +{ + if(n == 1) return; + if(n%2 == 0) + { + ret.pb(2); + fact(n/2, ret); + return; + } + if(is_p(n)) + { + ret.pb(n); + return; + } + + ll a, b, c, g = n; + auto f = [&c, &n](ll x)->ll{return (c+(lll)x*x)%n;}; + do + { + if(g == n) a=b=rand()%(n-2)+2, c=rand()%20+1; + a=f(a); b=f(f(b)); + g = gcd(a-b, n); + }while(g == 1); + fact(g, ret); fact(n/g, ret); +} +vl po_rho(ll n) +{ + vl ret; + fact(n, ret); + sort(all(ret)); + return ret; +} \ No newline at end of file diff --git a/2024fall/source/Math/Polynomial.cpp b/2024fall/source/Math/Polynomial.cpp new file mode 100644 index 0000000..a403704 --- /dev/null +++ b/2024fall/source/Math/Polynomial.cpp @@ -0,0 +1,287 @@ +namespace GMS +{ + template + struct Qring : public vl + { + using poly = Qring; + Qring() : vl(1, 0){} + Qring(ll c) : vl(1, c){} + Qring(ll c, int n) : vl(n, c){} + Qring(const vl& cp) : vl(cp){} + + ll& operator[](ll idx) + { + if((unsigned)idx < size()) return vl::operator[](idx); + this->resize(idx+1); return vl::operator[](idx); + } + ll operator[](ll idx) const + { + if((unsigned)idx < size()) return vl::operator[](idx); + return 0LL; + } + + void adjust() + { + while(size() > T) pop_back(); + while(size() > 1 and back() == 0) pop_back(); + } + void adjust(int n){resize(n, 0);} + + ll operator()(ll x) + { + x %= mod; + ll ret = 0; + for(auto it=rbegin(); it!=rend(); it++) + ret = (ret*x+*it)%mod; + + return ret; + } + + friend poly operator%(const poly& A, int B) // remainder by x^B + { + poly ret(A); + ret.resize(B, 0); + return ret; + } + friend poly operator%(poly&& A, int B) // remainder by x^B + { + A.resize(B, 0); + return A; + } + + friend poly operator+(const poly& A, const poly& B) + { + int n = max(A.size(), B.size()); + poly ret(0, n); + fors(i, 0, n-1) ret[i] = (A[i]+B[i])%mod; + ret.adjust(); + return ret; + } + friend poly operator+(poly&& A, const poly& B) + { + int n = B.size(); + fors(i, 0, n-1) A[i] = (A[i]+B[i])%mod; + A.adjust(); + return A; + } + + friend poly operator-(const poly& A) + { + int n = A.size(); + poly ret(0, n); + fors(i, 0, n-1) ret[i] = A[i]?mod-A[i]:0; + return ret; + } + friend poly operator-(poly&& A) + { + int n = A.size(); + fors(i, 0, n-1) A[i] = A[i]?mod-A[i]:0; + return A; + } + + friend poly operator-(const poly& A, const poly& B) + { + int n = max(A.size(), B.size()); + poly ret(0, n); + fors(i, 0, n-1) ret[i] = (mod+A[i]-B[i])%mod; + ret.adjust(); + return ret; + } + friend poly operator-(poly&& A, const poly& B) + { + int n = B.size(); + fors(i, 0, n-1) A[i] = (mod+A[i]-B[i])%mod; + A.adjust(); + return A; + } + + friend poly operator*(ll x, const poly& B) + { + poly ret(B); x %= mod; + for(auto &i : ret) i = (i*x)%mod; + ret.adjust(); + return ret; + } + + friend poly operator*(const poly& A, const poly& B) + { + poly ret(conv(A, B)); + // ACL : poly ret(atcoder::convolution(A, B)); + ret.adjust(); + return ret; + } + //friend poly operator/(const poly& A, const poly& B){return A*inv(B);} + + friend poly inv(const poly& A){return inv(A, T);} + friend poly inv(const poly& A, int t) + { + assert(A[0] != 0); + poly g = pow(A[0], mod-2); + + int st=1; + while(st <= t) + { + st <<=1; + g = (-A%st*g%st+2)*g%st; + } + g.adjust(t); + return g; + } + + friend poly diff(const poly& A) + { + int n = A.size(); + poly ret(0, n-1); + forr(i, n-1) ret[i-1] = i*A[i]%mod; + return ret; + } + friend poly inte(const poly& A) + { + static ll inv[T] = {0, }; + int n = A.size(); + poly ret(0, n+1); + forr(i, n+1) if(inv[i] == 0) inv[i] = pow(i, mod-2); + forr(i, n+1) ret[i] = inv[i]*A[i-1]%mod; + return ret; + } + + friend poly log(const poly& A){return log(A, T);} + friend poly log(const poly& A, int t) + { + assert(A[0] == 1); + poly ret = inte(diff(A) * inv(A, t)%t); + ret.adjust(t); + return ret; + } + + friend poly exp(const poly& A){return exp(A, T);} + friend poly exp(const poly& A, int t) + { + assert(A[0] == 0); + + poly g = 1; + int st = 1; + while(st < t) + { + st <<= 1; + g = (A%st-log(g, st)+1)*g%st; + } + g.adjust(t); + return g; + } + + friend poly pow(const poly& A, ll b, ll t) + { + poly ret(A); ret.adjust(); + if(ret.size() == 1) + { + ret[0] = pow(ret[0], b); + ret.adjust(t); + return ret; + } + + ll idx = 0; while(ret[idx] == 0) idx++; + if((__int128_t) idx * b >= t) return poly(0, t); + + ll c = ret[idx]; ll ic = pow(ret[idx], mod-2); poly g; + int n = ret.size(); + fors(i, idx, n-1) g[i-idx] = ret[i]*ic%mod; + g.resize(t-idx*b); + + g = exp(b * log(g, t-idx*b), t-idx*b); + c = pow(c, b); + + ret = poly(0, t); + fors(i, idx*b, t-1) ret[i] = g[i-idx*b] * c % mod; + + return ret; + } + + //Only just Polynomial, not Qring + void rev() + { + int n=size(); + poly& F = *this; + for(int i=0; i(fac, mod-2)*n%mod; + fore(i, n-1, 0) C[i] = C[i]*fac%mod, fac = fac*i%mod; + + poly B = C*A; B.resize(n); + B.rev(); + + fore(i, n-1, 0) B[i] = B[i]*facc%mod, facc = facc*i%mod; + + return B; + } + friend void calcG(vector& G, int i, int l, int r, const vl& p) + { + if(l == r) + { + ll g = p[l]?mod-p[l]:0; + G[i] = vl({g, 1}); + return; + } + int mid = (l+r)/2; + calcG(G, i*2, l, mid, p); + calcG(G, i*2+1, mid+1, r, p); + + G[i] = G[i*2]*G[i*2+1]; + } + friend void eval(const vector& G, int i, int l, int r, poly&& F, vl& ret) + { + if(l == r) + { + ret[l] = F[0]; + return; + } + + int mid=(l+r)/2; + eval(G, i*2, l, mid, div_rem(F, G[i*2]), ret); + eval(G, i*2+1, mid+1, r, div_rem(F, G[i*2+1]), ret); + } + friend vl multipoint_eval(const poly& A, const vl& B) + { + int m = B.size(); + vector G(4*m); + calcG(G, 1, 0, m-1, B); + + vl ret(m, 0); + eval(G, 1, 0, m-1, div_rem(A, G[1]), ret); + + return ret; + } + }; +} // namespace GMS + +const ll mod = 998244353, w = 3, T = 1<<20; +using poly = GMS::Qring; \ No newline at end of file diff --git a/2024fall/source/Misc/FastI.cpp b/2024fall/source/Misc/FastI.cpp new file mode 100644 index 0000000..bedabba --- /dev/null +++ b/2024fall/source/Misc/FastI.cpp @@ -0,0 +1,42 @@ +#define getint(n) int n; read(n) +#define getll(n) ll n; read(n) +#define inta getint(a) +#define intab getint(a); getint(b) +char get() +{ + static char buf[100000], *S=buf, *T=buf; + if(S == T) + { + S = buf; + T = buf + fread(buf, 1, 100000, stdin); + if(S == T) return EOF; + } + return *S++; +} +void read(int& n) +{ + n = 0; + char c; bool neg = false; + for(c = get(); c < '0'; c=get()) if(c=='-') neg = true; + for(;c>='0';c=get()) n = n*10+c-'0'; + if(neg) n = -n; +} +void read(ll& n) +{ + n = 0; + char c; bool neg = false; + for(c = get(); c < '0'; c=get()) if(c=='-') neg = true; + for(;c>='0';c=get()) n = n*10+c-'0'; + if(neg) n = -n; +} +int read(char s[]) +{ + char c; int p = 0; + while((c = get()) <= ' '); + + s[p++] = c; + while((c = get()) >= ' ') s[p++] = c; + s[p] = '\0'; + + return p; +} \ No newline at end of file diff --git a/2024fall/source/Misc/mt19937.cpp b/2024fall/source/Misc/mt19937.cpp new file mode 100644 index 0000000..7a7dd80 --- /dev/null +++ b/2024fall/source/Misc/mt19937.cpp @@ -0,0 +1,5 @@ +const long long rand_L = 1; +const long long rand_R = 10; +mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count()); +uniform_int_distribution dist(rand_L, rand_R); +auto generator = bind(dist, rng); \ No newline at end of file diff --git a/2024fall/source/String/F_Z_M_SA_LCP.cpp b/2024fall/source/String/F_Z_M_SA_LCP.cpp new file mode 100644 index 0000000..f9ffd19 --- /dev/null +++ b/2024fall/source/String/F_Z_M_SA_LCP.cpp @@ -0,0 +1,102 @@ +const int N = 1e5+7; +char s[N]; + +int F[N], Z[N], M[N]; +int sa[N]; int ord[N], tmp[N], cnt[N]; +int lcp[N]; +int main() +{ + scanf("%s", s+1); + int n = strlen(s+1); + + // KMP - fail function + { + F[1] = 0; int j = 0; + for(int i=2; i<=n;i++) + { + while(j > 0 and s[i] != s[j+1]) j = F[j]; + F[i] = j+=(s[i] == s[j+1]); + } + } + + //Z - Z array + { + Z[1] = n; int j = 1, r = 0; + for(int i=2; i<=n; i++) + { + Z[i] = i 0) k--; + } + } + + printf("\nF : "); forr(i, n) printf("%d ", F[i]); + printf("\nZ : "); forr(i, n) printf("%d ", Z[i]); + printf("\nM : "); forr(i, n) printf("%d ", M[i]); + printf("\nSA : "); forr(i, n) printf("%d ", sa[i]); + printf("\nLCP : x "); fors(i, 2, n) printf("%d ", lcp[i]); + + printf("\n"); forr(i, n) printf("%s\n", s+sa[i]); +} \ No newline at end of file diff --git a/2024fall/source/Tree/HLD.cpp b/2024fall/source/Tree/HLD.cpp new file mode 100644 index 0000000..9ba3731 --- /dev/null +++ b/2024fall/source/Tree/HLD.cpp @@ -0,0 +1,89 @@ +BOJ 트리와 쿼리 1 + +//Segment Tree 코드 +const int N = 1e5+7; + +vi adj[N]; int par[N]; int sz[N]; int d[N]; +void dfs1(int s) +{ + sz[s] = 1; + for(int i=0;i sz[adj[s][0]]) swap(adj[s][0], i); + } +} +int in[N], c; int top[N]; +void dfs2(int s) +{ + //printf("%d\n", s); + in[s] = ++c; + for(auto i : adj[s]) + { + if(i == adj[s][0]) + top[i] = top[s]; + else top[i] = i; + + dfs2(i); + } +} + +Node *root; +int query(int a,int b) +{ + int ans = 0; + while(top[a] != top[b]) + { + if(d[top[a]] > d[top[b]]) swap(a, b); + ans = max(ans, query(root, in[top[b]], in[b])); + b = par[top[b]]; + } + + if(d[a] > d[b]) swap(a, b); + ans = max(ans, query(root, in[a]+1, in[b])); + + return ans; +} +map m; +int arr[N]; pii edge[N]; +int main() +{ + getint(n); + forr(i, n-1) + { + intab; adj[a].pb(b); adj[b].pb(a); + getint(c); + m[{a,b}] = m[{b, a}] = c; + edge[i] = {a,b}; + } + + dfs1(1); + dfs2(1); + forr(i, n) arr[in[i]] = m[{par[i], i}]; + root = new Node(1, n); init(root, arr); + + getint(Q); + while(Q--) + { + getint(q); + if(q == 1) + { + getint(i); getint(c); + int a = edge[i].fi; + int b = edge[i].se; + if(par[b] == a) a = b; + + update(root, in[a], c, true); + } + if(q == 2) + { + intab; + printf("%d\n", query(a, b)); + } + } +} diff --git a/2024fall/source/empty.cpp b/2024fall/source/empty.cpp new file mode 100644 index 0000000..e69de29 diff --git a/2024fall/teamnote.sty b/2024fall/teamnote.sty new file mode 100644 index 0000000..fce7852 --- /dev/null +++ b/2024fall/teamnote.sty @@ -0,0 +1,110 @@ +\ProvidesPackage{teamnote} + +\usepackage[left=1cm,right=1cm,top=2cm,bottom=1cm,a4paper]{geometry} +\usepackage{fancyhdr} +\usepackage{lastpage} +\usepackage{ifthen} +\usepackage{minted} +\usepackage{color} +\usepackage{indentfirst} +\usepackage{amssymb} +\usepackage{amsmath} +\usepackage{import} +\usepackage{caption} +\usepackage[table,xcdraw]{xcolor} +\usepackage[T1]{fontenc} +\usepackage{setspace} + +\setstretch{1} % No line-spacing + +\renewcommand{\@listI}{% No spacing on list +\leftmargin=25pt +\rightmargin=0pt +\labelsep=5pt +\labelwidth=20pt +\itemindent=0pt +\listparindent=0pt +\topsep=0pt plus 2pt minus 4pt +\partopsep=0pt plus 1pt minus 1pt +\parsep=0pt plus 1pt +\itemsep=\parsep} + +\setlength{\columnseprule}{0.4pt} +\pagenumbering{arabic} +\setminted{breaklines=true, tabsize=2, breaksymbolleft=} +\usemintedstyle{perldoc} + +\newcommand{\revised}{Should be \textcolor{red}{\textbf{revised}}.} +\newcommand{\tested}{Should be \textcolor{red}{\textbf{tested}}.} +\newcommand{\added}{Should be \textcolor{red}{\textbf{added}}.} +\newcommand{\WIP}{\textcolor{red}{\textbf{Working in progress.}}} + +\newcommand{\schoolname}{Some University} +\newcommand{\teamname}{Some Teamname} +\newcommand{\authorname}{Some Members} + +\newcommand{\maketitlepage}{\maketitle + +\tableofcontents + +\thispagestyle{fancy} + +} +\DeclareRobustCommand{\teamnote}[3]{ + \renewcommand{\schoolname}{#1} + \renewcommand{\teamname}{#2} + \renewcommand{\authorname}{#3} +} +\pagestyle{fancy} +\lhead{\schoolname{} -- \teamname} +\rhead{Page \thepage{} of +\ifthenelse{\pageref{LastPage} < 26}{\pageref{LastPage}}{\textcolor{red}{\textbf{\pageref{LastPage}}}}} +\fancyfoot{} + +\title{Team Note of \teamname} +\author{\authorname} +\date{Compiled on \today} + + + + +\newboolean{BangShowUsage} +\setboolean{BangShowUsage}{false} +\newcommand{\ShowUsage}{\setboolean{BangShowUsage}{false}} +\newcommand{\HideUsage}{\setboolean{BangShowUsage}{true}} + + +\newboolean{BangShowComplexity} +\setboolean{BangShowComplexity}{false} +\newcommand{\ShowComplexity}{\setboolean{BangShowComplexity}{false}} +\newcommand{\HideComplexity}{\setboolean{BangShowComplexity}{true}} + + +\newboolean{BangShowAuthor} +\setboolean{BangShowAuthor}{false} +\newcommand{\ShowAuthor}{\setboolean{BangShowAuthor}{false}} +\newcommand{\HideAuthor}{\setboolean{BangShowAuthor}{true}} + +\newcommand{\Algorithm}[6]{ + \subsection{#1} + + \ifthenelse{\equal{#2}{} \OR \boolean{BangShowUsage}}{}{\textbf{Usage:} #2} + + \ifthenelse{\equal{#3}{} \OR \boolean{BangShowComplexity}}{}{\textbf{Time Complexity:} #3} + + \ifthenelse{\equal{#6}{} \OR \boolean{BangShowAuthor}}{}{\textbf{Author:} #6} + + \ifthenelse{\equal{#5}{}}{}{\ifthenelse{\equal{#4}{}}{\inputminted[]{cpp}{#5}}{\inputminted[]{#4}{#5}}} +} + +\newcommand{\SubAlgorithm}[6]{ + \subsubsection{#1} + + \ifthenelse{\equal{#2}{} \OR \boolean{BangShowUsage}}{}{\textbf{Usage:} #2} + + \ifthenelse{\equal{#3}{} \OR \boolean{BangShowComplexity}}{}{\textbf{Time Complexity:} #3} + + \ifthenelse{\equal{#6}{} \OR \boolean{BangShowAuthor}}{}{\textbf{Author:} #6} + + \ifthenelse{\equal{#5}{}}{}{\ifthenelse{\equal{#4}{}}{\inputminted[]{cpp}{#5}}{\inputminted[]{#4}{#5}}} +} diff --git a/2025fall/Teamnote_GMS_.zip b/2025fall/Teamnote_GMS_.zip new file mode 100644 index 0000000000000000000000000000000000000000..80828502cf891fa43ab05520dc570061705d5381 GIT binary patch literal 289167 zcma&NQ!2>s|Mo%so7)*#+0(n4dEWThxR6Xb9e8|2rxs^`M#3ip89X8N zLIfSo>?Gq^4{YY44;I1hf)_%>QOml8fURCbZSFZv5b0^g-)k?0tu-N^@f0w886CIs zUlF6d-Ta+_dlS$#RTBt;fSz00TFo;r%M$l6Q&%@vS65S4H=D*-vlQ&K;2LpDz#Fn# zCl;|D+AXpG(ZWq8N+XAo*E3%>DTwDI<}>GFrR;&MqkUJDR6seM4P+nWK}~lQ2hA5- z!Rd6BtmVH@-Y+p72$KjACVKg-l<@TUjrYgzaPeWJBgnDWWWObp#8gMt_XUz<+(bDS z+{%}~$skTwAx&QGxVywXf@>v@lGhP(>@IDEuClO@{`Qhh&}qm` zt>zjzs5h;aVkMQ%)@p&TCkHF9>P$6w@KH%L?qQFzE04PNYToOKhD&E&npDeZ4oO|< z$#}?SAe>AT{heCkzBDUBf06h(uzI>T`gS^42X{coGR=qj8VFDps1!+wP6C~`%z&21 z1G9M@*>uTpt@5vp8C)nbInBe=PRNq8A!(p6En2WP>3<+$2~PZ!6D`JluX%SD{9G}~ z7m0{$S-?TrJPLNoac(H1M8I_%vu(h9r;)MA_Rr8JK-~$Dm8Z&$SzKB|IdYM>Igg>h zZW~_ja$ezmCBZ=h0@8km)h58VfjyS7hV1*?y?vjjY{I?^UN2!xExuU*hO$?}f|A-t zT%xpPvi8w@o&PJ_s*r`%xewkj?z!$KpthK0TAgUwqQd0tA}wjm62rNWmb!H&7%oB; 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\\ \hline + 1e5 & 9,592 & 1e9 & \textless 6e7 & 1e13 & \textless 4e11 \\ \hline + \end{tabular} +\end{center} + +\subsubsection{Prime Gap} +\begin{align*} + 2 \cdot 10^{5} \text{ 이하의 소수 간극 } &\le 100\\ + 2^{32} \text{ 이하의 소수 간극 } &\le 464 \\ + 2^{64} \text{ 이하의 소수 간극 } &\le 1550 +\end{align*} + +\Algorithm{Miller-Rabin Algorithm} +{\texttt{is\_p(X)} : returns true if $X$ is prime, otherwise false. +\begin{align*} +\text{ When } X \le 2^{32}, D &= \{2, 7, 61\} \text{ is sufficient; } \\ +X \le 2^{64}, D &= \{p | p \text{ is prime}, p \le 37 \} \text{ is sufficient.} +\end{align*}} +{$\mathcal O (\log^3 X)$} +{cpp} +{source/Math/MillerRabin.cpp} + +\Algorithm{Pollad Rho Algorithm} +{ \texttt{po\_rho(N)} : returns array of prime factors of X.} +{$\mathcal O (N^{1/4})$} +{cpp} +{source/Math/PolladRho.cpp} + +\Algorithm{Primitive Root} +{Calculate one of the primitive roots of given prime.} +{}{cpp} +{source/Math/PrimitiveRoot.cpp} + +\Algorithm{Diopantos Equation(Extended Euclidian Algorithm)} +{\texttt{diophantos(a, b)} : return one integer solution of $ax+by=1$, satisfying $0 \le x < b$. } +{$\mathcal O \left(\log \left( \max(a, b) \right) \right)$} +{cpp} +{source/Math/Diophantos.cpp} + +\Algorithm{Chinese Remainder Theorem} +{\texttt{crt(pll p, pll q)} : return \texttt{pll r}, satisfying follows: +\begin{align*} + x &\equiv \texttt{p.fi} \mod \texttt{p.se} \\ +\text{and } x &\equiv \texttt{q.fi} \mod \texttt{q.se} \\ + \leftrightarrow x &\equiv \texttt{r.fi} \mod \texttt{r.se} +\end{align*} +If there's no such \texttt{r}, return $\{-1, -1\}$. +} +{$\mathcal O(\log A)$} +{cpp} +{source/Math/CRT.cpp} + +\Algorithm{Harmonic Lemma} +{\texttt{f(N)} : return the value +$$\sum_{i=1}^{N} \left\lfloor \frac{N}{i} \right\rfloor = \left\lfloor \frac{N}{1}\right\rfloor + \left\lfloor \frac{N}{2} \right\rfloor + \cdots + \left\lfloor \frac{N}{N}\right\rfloor $$ +Using the fact that $\left\lfloor \frac{N}{x} \right\rfloor$ has $\mathcal O(\sqrt N)$ different values.} +{$\mathcal O(\sqrt N )$} +{cpp} +{source/Math/Harmonic.cpp} + +\Algorithm{Floor Sum (Sum of Floor of Rational Arithmetic Sequence)} +{\texttt{floor\_sum(A, B, C, N)} : return the value +$$\sum_{x=0}^{N-1} \left\lfloor \frac{Ax+B}{C} \right\rfloor $$} +{$\mathcal O(\log N)$} +{cpp} +{source/Math/FloorSum.cpp} + +\Algorithm{FFT - Convolution} +{} +{$\mathcal O (N\log N)$} +{cpp} +{source/Math/FFTConv.cpp} + + + +\Algorithm{NTT - Number Theoretic Transform} +{helloworld} +{} +{cpp} +{source/Math/NTT.cpp} + +\subsubsection{Good prime numbers to run NTT} +\begin{center} +\begin{adjustbox}{width=0.8\columnwidth} +\begin{tabular}{|c|c| +>{\columncolor[HTML]{C0C0C0}}l |} +\hline +595 591 169 & 71\textless{}\textless{}23|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +645 922 817 & 77\textless{}\textless{}23|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +897 581 057 & 107\textless{}\textless{}23|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +998 244 353 & 119\textless{}\textless{}23|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +1 300 234 241 & 155\textless{}\textless{}23|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +1 224 736 769 & 73\textless{}\textless{}24|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +2 130 706 433 & 127\textless{}\textless{}24|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +167 772 161 & 5\textless{}\textless{}25|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +469 762 049 & 7\textless{}\textless{}26|1 & \multirow{-9}{*}{\cellcolor[HTML]{C0C0C0}$\omega$ = 3} \\ \hline +\end{tabular} +\end{adjustbox} +\end{center} + +\Algorithm{Polynomial (Formal Power Series)} +{} +{} +{cpp} +{source/Math/Polynomial.cpp} + +\subsection{Combinatorics} +\subsubsection{Labeled Combinatorial Target} +\begin{itemize} + \item Permutation, Combination (with, w/o repetition) + \begin{itemize} + \item Permutation $_nP_r = \frac{n!}{r!(n-r)!}$ + \item Combination $_nC_r = \binom n k = \frac{n!}{r!}$ + \item Permutation with repetition $_n\Pi_r = n^r$ + \item Combination with repetition $_nH_r = _{n+r-1}C_r$ + \end{itemize} + \item Catalan Number $C_n$ : the number of regular bracket string of length $2n$. + \begin{itemize} + \item $C_n = \frac{1}{n+1}\binom {2n}n$ + \item $C_n : 1, 1, 2, 5, 14, 42, 132,429,1430,\cdots$ (from index 0) + \item OGF of $C_n$ : $c(x) = 1+xc(x)^2, c(c) = \frac{1-\sqrt{1-4x}}{2x}$ + \item Catalan's triangle $C(n, k)$ : the number of string with $n$ X's, $k$ Y's, where the number of Y's is not greater than the number of X's when written down the string. + \begin{itemize} + \item i.e. $C(4, 3)$ : XXXXYYY, XXYXYYX are OK, but XXYYYXX is not OK. + \item $C(n, k) = \binom{n+k}{k} - \binom{n+k}{k-1} = \frac{n-k+1}{n+1}\binom{n+k}{k}$ + \item We can give the condition relax : $C_m(n, k)$ : the number of string with $n$ X's, $k$ Y's, where the number of Y's is not greater than (the number of X's) + $m$ when written down the string. + \item $C_m(n, k) = \binom{n+k}{k}-\binom{n+k}{k-m}$ when $m\leqslant k \leqslant n+m-1$. + \item $C_1(n, k) = C(n, k)$ + \end{itemize} + \end{itemize} + \item Derangement(교란순열) $D_n$ : the number of permutation of length $n$ which $\forall i\;p_i \neq i$. + \begin{itemize} + \item $D_n : 1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496,1334961 \cdots$ (from index 0) + \item EGF of $D_n$ : $D(x) = \sum_{n=0} \frac{D_n}{n!}x^n = \frac{e^{-x}}{1-x}$ + \end{itemize} + \item Stirling Number of the 1st/2nd kind. + \begin{itemize} + \item Unsigned Stirling Number of the 1st kind $c(n, k) = \genfrac{[}{]}{0pt}{}{n}{k}$ : the number of permutation of length n with k disjoint cycles. + \begin{itemize} + \item $c(n+1, k) = n \times c(n, k) + c(n, k-1)$ + \item with boundary condition $c(0, 0) = 1, c(n, 0) = c(0, k) = 0 \; \forall n, k>0$ + \item $c(n, k)$ + \begin{itemize} + \item $c(0, 0) = 1$; $c(x_{\neq0}, 0) = 0$; $c(x, x) = 1$ + \item $c(x, x) = 1$ + \item $c(5, *) = \{0, 24, 50, 35, 10 1\}$ + \item $c(6, *) = \{0, 120, 274, 225, 85, 15, 1\}$ + \end{itemize} +% \begin{tabular}{| +% >{\columncolor[HTML]{ECECEC}}r | +% >{\columncolor[HTML]{F8F9FA}}r |r|r|r|l|l|l|} +% \hline +% \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} \textit{n\textbackslash{}k}} & \cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{0}} & \cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{1}} & \cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{2}} & \cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{3}} & \multicolumn{1}{r|}{\cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{4}}} & \multicolumn{1}{r|}{\cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{5}}} & \multicolumn{1}{r|}{\cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{6}}} \\ \hline +% {\color[HTML]{202122} \textbf{0}} & {\color[HTML]{202122} 1} & \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{} & & & \\ \hline +% {\color[HTML]{202122} \textbf{1}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{} & & & \\ \hline +% {\color[HTML]{202122} \textbf{2}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \multicolumn{1}{l|}{} & & & \\ \hline +% {\color[HTML]{202122} \textbf{3}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 2} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 3} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & & & \\ \hline +% {\color[HTML]{202122} \textbf{4}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 6} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 11} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 6} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1}} & & \\ \hline +% {\color[HTML]{202122} \textbf{5}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 24} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 50} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 35} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 10}} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1}} & \\ \hline +% {\color[HTML]{202122} \textbf{6}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 120} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 274} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 225} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 85}} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 15}} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1}} \\ \hline +% \end{tabular} + \item OGF of $\genfrac{[}{]}{0pt}{}{n}{k}$ : for fixed $n$, $\sum_{k=0}^n \genfrac{[}{]}{0pt}{}{n}{k} x^k = x(x+1)(x+2)\cdots(x+n-1)$ : we can calculate it by polynomial shift \& divide and conquer + \item EGF of $\genfrac{[}{]}{0pt}{}{n}{k}$ : for fixed $k$, $\sum_{n=k}^\infty \genfrac{[}{]}{0pt}{}{n}{k} \frac{x^n}{n!} = \frac{(-\log(1-z))^k}{k!} $ + \item Signed Stirling Number of the 1st kind $s(n, k) = (-1)^{n-k}c(n, k)$ + \item EGF of $s(n, k)$ : for fixed $k$, $\sum_{n=k}^\infty s(n, k) \frac{x^n}{n!} = \frac{(\log(1+z))^k}{k!} $ + \end{itemize} + \item Stirling Number of the 2nd kind $S(n, k) = \genfrac{\{}{\}}{0pt}{}{n}{k}$ : the number of partition of $n$ labeled objects into $k$ nonempty unlabelled subsets. + \begin{itemize} + \item $S(n, k) = \frac{1}{k!}\sum_{i=0}^k(-1)^{k-i}\binom{k}{i}i^n$ + \item $S(n,k)=S(n - 1,k - 1)+k\cdot S(n - 1,k)$ + \item $S(n, k)$ + \begin{itemize} + \item $S(0, 0) = 1$; $S(x_{\neq 0}, 0) = 0$; $S(x, x) = 1$ + \item $S(5, *) = \{0, 1, 15, 25, 10, 1\}$ + \item $S(6, *) = \{0, 1, 31, 90, 65, 15, 1\}$ + \end{itemize} +% \begin{tabular}{| +% >{\columncolor[HTML]{ECECEC}}r | +% >{\columncolor[HTML]{F8F9FA}}r |r|r|r|l|l|l|} +% \hline +% \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} \textit{\textbf{n\textbackslash{}k}}} & \cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{0}} & \cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{1}} & \cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{2}} & \cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{3}} & \multicolumn{1}{r|}{\cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{4}}} & \multicolumn{1}{r|}{\cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{5}}} & \multicolumn{1}{r|}{\cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{6}}} \\ \hline +% {\color[HTML]{202122} \textbf{0}} & {\color[HTML]{202122} 1} & \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{} & & & \\ \hline +% {\color[HTML]{202122} \textbf{1}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{} & & & \\ \hline +% {\color[HTML]{202122} \textbf{2}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \multicolumn{1}{l|}{} & & & \\ \hline +% {\color[HTML]{202122} \textbf{3}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 3} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & & & \\ \hline +% {\color[HTML]{202122} \textbf{4}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 7} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 6} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1}} & & \\ \hline +% {\color[HTML]{202122} \textbf{5}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 15} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 25} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 10}} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1}} & \\ \hline +% {\color[HTML]{202122} \textbf{6}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 31} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 90} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 65}} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 15}} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1}} \\ \hline +% \end{tabular} + \item OGF of $\genfrac{\{}{\}}{0pt}{}{n}{k}$ : for fixed $n$, $\sum_{k=0}^n\genfrac{\{}{\}}{0pt}{}{n}{k}x^k=T_n(x)$, where $T_n(x) = e^{-x}\sum_{k=0}^{\infty}\frac{k^n}{k!}x^k$ is Touchard Polynomials. + \item EGF of $\genfrac{\{}{\}}{0pt}{}{n}{k}$ : for fixed $k$, $\sum_{n=k}^\infty\genfrac{\{}{\}}{0pt}{}{n}{k}\frac{x^n}{n!}=\frac{(e^x-1)^k}{k!}$ + \end{itemize} + \end{itemize} + \item Bell Number $B_n$ : the number of partition of set with size $n$. + \begin{itemize} + \item i.e. partitionize $\{a, b, c\}$ is $\{\{a\}, \{b\}, \{c\}\}, \{\{a , b\}, \{c\}\}$, $\{\{b, c\}, \{a\}\}, \{\{c, a\}, \{b\}\}, \{\{a, b, c\}\}$. Therefore, $B_3 = 5$. + \item $B_n : 1,1,2,5,15,52,203,877,4140,\cdots$ (from index 0) + \item $B_n = \sum_{k=0}^n\genfrac{\{}{\}}{0pt}{}{n}{k}$ (2nd kind of stirling number) + \item EGF of $B_n$ : $B(x) = \sum_{n=0}\frac{B_n}{n!}x^n=e^{e^x-1}$ + \item Ordered Bell Number(Fubini Number) $a_n$ : the number of distinct weak ordering on a set of n elements. + \begin{itemize} + \item $a_n : 1, 1, 3, 13, 75, 541, 4683, 47293, 545835, 7087261, \cdots$ + \item $a_n = \sum_{k=0}^nk!\genfrac{\{}{\}}{0pt}{}{n}{k}$ (stirling number of the 2nd kind) + \item EGF of $a_n$ : $a(x) = \sum_{n=0}^\infty \frac{a_n}{n!}x^n = \frac{1}{2-e^x}$ + \end{itemize} + \end{itemize} + \item Integer Partition $P(n, k)$ : the number of partitions of $n$ into exactly $k$ parts. + \begin{itemize} + \item i.e. $P(4, 2) = 2$ since $4 = 1+3 = 2+2$ + \item we also say $P(n) = \sum_{k=1}^{n}P(n, k)$ + \item $P(n, k)$ + \begin{itemize} + \item $P(x, 1) = P(x, x) = 1$ + \item $P(8, *) = \{1, 4, 5, 5, 3, 2, 1, 1\}$ + \item $P(9, *) = \{1, 4, 7, 6, 5, 3, 2, 1, 1\}$ + \end{itemize} + \item $P(n) = \{1, 2, 3, 5, 7, 11, 15, 22, 30, 42\}$ + +% \begin{tabular}{| +% >{\columncolor[HTML]{EAECF0}}c | +% >{\columncolor[HTML]{F8F9FA}}l | +% >{\columncolor[HTML]{F8F9FA}}l | +% >{\columncolor[HTML]{F8F9FA}}l | +% >{\columncolor[HTML]{F8F9FA}}l | +% >{\columncolor[HTML]{F8F9FA}}l | +% >{\columncolor[HTML]{F8F9FA}}l | +% >{\columncolor[HTML]{F8F9FA}}l | +% >{\columncolor[HTML]{F8F9FA}}l | +% >{\columncolor[HTML]{F8F9FA}}l |} +% \hline +% \multicolumn{1}{|r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} \textit{\textbf{n\textbackslash{}k}}}} & \multicolumn{1}{c|}{\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{1}}} & \multicolumn{1}{c|}{\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{2}}} & \multicolumn{1}{c|}{\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{3}}} & \multicolumn{1}{c|}{\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{4}}} & \multicolumn{1}{c|}{\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{5}}} & \multicolumn{1}{c|}{\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{6}}} & \multicolumn{1}{c|}{\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{7}}} & \multicolumn{1}{c|}{\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{8}}} & \multicolumn{1}{c|}{\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{9}}} \\ \hline +% {\color[HTML]{202122} \textbf{1}} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } \\ \hline +% {\color[HTML]{202122} \textbf{2}} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } \\ \hline +% {\color[HTML]{202122} \textbf{3}} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } \\ \hline +% {\color[HTML]{202122} \textbf{4}} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 2} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } \\ \hline +% {\color[HTML]{202122} \textbf{5}} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 2} & {\color[HTML]{202122} 2} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } \\ \hline +% {\color[HTML]{202122} \textbf{6}} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 3} & {\color[HTML]{202122} 3} & {\color[HTML]{202122} 2} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } \\ \hline +% {\color[HTML]{202122} \textbf{7}} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 3} & {\color[HTML]{202122} 4} & {\color[HTML]{202122} 3} & {\color[HTML]{202122} 2} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} } & {\color[HTML]{202122} } \\ \hline +% {\color[HTML]{202122} \textbf{8}} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 4} & {\color[HTML]{202122} 5} & {\color[HTML]{202122} 5} & {\color[HTML]{202122} 3} & {\color[HTML]{202122} 2} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} } \\ \hline +% {\color[HTML]{202122} \textbf{9}} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 4} & {\color[HTML]{202122} 7} & {\color[HTML]{202122} 6} & {\color[HTML]{202122} 5} & {\color[HTML]{202122} 3} & {\color[HTML]{202122} 2} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 1} \\ \hline +% \end{tabular} + \end{itemize} + \item 12정도(the Twelvefold Way) : the number of functions \\ + (Domain $|N| = n$, Codomain $|X| = x$)\\ + \begin{tabular}{| +>{\columncolor[HTML]{F8F9FA}}c |c|c|c|} +\hline +\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textit{\textbf{$f$-class}}} & \cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{Any $f$}} & \cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{Injective}} & \cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{Surjective}} \\ \hline +{\color[HTML]{202122} \textbf{Distinct $f$}} & \textit{$_n\Pi_x$} & \textit{$_xP_n$} & $x!\genfrac{\{}{\}}{0pt}{}{n}{k}$ \\ \hline +{\color[HTML]{202122} \textit{\textbf{\begin{tabular}[c]{@{}c@{}}$S_n$ orbits\\ $f \circ S_n$\end{tabular}}}} & \textit{$_xH_n$} & \textit{$_xC_n$} & $_{n-1}C_{n-x}$ \\ \hline +{\color[HTML]{202122} \textit{\textbf{\begin{tabular}[c]{@{}c@{}}$S_x$ orbits\\ $S_x \circ f$\end{tabular}}}} & $\sum_{k=0}^x \genfrac{\{}{\}}{0pt}{}{n}{k}$ & $[n \leqslant x]$ & $\genfrac{\{}{\}}{0pt}{}{n}{k}$ \\ \hline +{\color[HTML]{202122} \textit{\textbf{\begin{tabular}[c]{@{}c@{}}$S_n\times S_x$ orbits\\ $S_x \circ f \circ S_n$\end{tabular}}}} & $P(n+x, x)$ & $[n \leqslant x]$ & $P(n, x)$ \\ \hline +\end{tabular} +\end{itemize} + +% \Algorithm{General Lucas Comb} +% {} +% {} +% {cpp} +% {source/Math/general_lucas.cpp} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Linear Algebra} + +\Algorithm{Matrix} +{} +{} +{cpp} +{"source/Linear Algebra/Matrix.cpp"} + +\Algorithm{Berlekamp Massey} +{} +{} +{cpp} +{"source/Linear Algebra/BerlekampMassey.cpp"} + +\Algorithm{XOR Basis} +{} +{} +{cpp} +{"source/Linear Algebra/XORBasis.cpp"} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Geometry} +\Algorithm{Mindset} +{} +{} +{cpp} +{source/Geometry/Mindset.cpp} + +\Algorithm{Point in Convex Polygon} +{\texttt{isunder(upper\_hull[], (length of upper\_hull), x)} : return true if $x$(point) is under upper\_hull, otherwise false; + +\texttt{isunder(lower\_hull[], (length of lower\_hull), x, true)} : return true if $x$(point) is over lower\_hull, otherwise false. + +Point in Polygon : isunder(upper, u, x) \&\& isupper(lower, u, x, true)} +{} +{cpp} +{source/Geometry/PointInConvexPolygon.cpp} + +\Algorithm{Geo} +{} +{} +{cpp} +{source/Geometry/Geo.cpp} + +\Algorithm{Half-Plane Intersection} +{} +{} +{cpp} +{source/Geometry/HPI.cpp} + +\Algorithm{Bulldozer} +{} +{} +{cpp} +{source/Geometry/Bulldozer.cpp} + + +% \Algorithm{kactl templete} +% {} +% {} +% {cpp} +% {source/Geometry/geometry_kaere.cpp} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Greedy} +\subsection{Rearrange Inequality - Extensions} +Let $A_i, B_i$ be non-decreasing sequence of length $n$, and $p$ be some permutation, and let $inc := (1, 2, \dots, n-1, n), \;dec := (n, n-1, \dots, 2, 1)$. + +\begin{align*} +S(p) &= \sum_{i=1}^n A_i B_{p_i} + && \text{ maximize } S &&&\Rightarrow p : inc&&&&\\ + & && \text{ minimize } S &&&\Rightarrow p:dec&&&&\\ +P_{max}(p) &= \max_i(A_iB_{p_i}) + && \text{ minimize } P_{max} &&&\Rightarrow p : dec&&&&\\ +P_{min}(p) &= \min_i(A_iB_{p_i}) + && \text{ maximize } P_{min} &&&\Rightarrow p:dec&&&&\\ +A_{max}(p) &= \max_i(A_i+B_{p_i}) && \text +{ minimize } A_{max} &&& \Rightarrow p:dec&&&&\\ +A_{min}(p) &= \min_i(A_i+B_{p_i}) && \text{ maximize } A_{min} &&& \Rightarrow p:dec&&&&\\ +D_{max}(p) &= \max_i|A_i-B_{p_i}| && \text{ minimize } D_{max} &&& \Rightarrow p:inc&&&&\\ +D_{min}(p) &= \min_i|A_i-B_{p_i}| && \text{ maximize } D_{min} &&& \Rightarrow p:?&&&&\\ +\end{align*} +\begin{align*} + \text{ Permutate } A \text{ s.t.} \text{ maximize } & \sum_{i=1}^n {A_i A_{i+1}} \;(\text{Let } A_{n+1} = A_1) \\ &\Rightarrow \text{ Pendulum Arrangement } +\end{align*} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{DP} + +\Algorithm{LIS} +{}{}{cpp}{source/DP/LIS.cpp} + +\subsection{DP Optimization} + +\subsubsection{Convex Hull Optimization} +\begin{align*} + \text{ Recurrence : }& D[i] = \min_{j j \\ +0 & \text{otherwise} +\end{cases}$, with $r_{i, j}$ be the random integer in $[1, p-1]$. After construct $T$, the maximum size of $G$ is $\textrm{rank}(T)/2$ with high probability. + +If we want the result of matching, use:} +{$O(n^3)$} +{cpp} +{source/Graph/Matching.cpp} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Tree} + +\Algorithm{HLD(Heavy Light Decomposition)} +{} +{} +{cpp} +{source/Tree/HLD.cpp} + +\Algorithm{Centroid Tree} +{} +{} +{cpp} +{source/Tree/Centroid.cpp} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Data Structure} + +\Algorithm{PBDS - Policy-Based Data Structure} +{} +{Equivalent to std::set} +{cpp} +{source/DS/PBDS.cpp} + +% \Algorithm{rope}{}{}{cpp}{} + +\Algorithm{Union and Find - Queue Undoing} +{} +{$\mathcal O(\log^2N)$} +{cpp} +{source/DS/UF_QUndo.cpp} + +\Algorithm{Fenwick Tree}{}{}{cpp} +{source/DS/Fenwick.cpp} + +\Algorithm{Segment Tree} +{} +{$\mathcal O(\log N)$} +{cpp} +{source/DS/SegmentTree.cpp} + +% \Algorithm{Segment Tree Generalization} +% {} +% {$\mathcal O(\log N)$} +% {cpp} +% {source/DS/SegmentTree.cpp} + +\Algorithm{Segment Tree Beats} +{} +{$\mathcal O(\log N)$ on updating and querying} +{cpp} +{source/DS/STBeats.cpp} + +\Algorithm{Li-Chao Tree} +{} +{} +{cpp} +{source/DS/LiChaoTree.cpp} + +\Algorithm{Splay Tree} +{} +{} +{cpp} +{source/DS/SplayTree.cpp} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Numerical Analysis} + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\section{Technic} +\Algorithm{Cartesian Tree} +{} +{} +{cpp} +{source/Technic/CartesianTree.cpp} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Misc} +\Algorithm{Negative Division on C/C++} +{Procedure : (1) make both dividend and divisor positive, and calc the quotient (2) decide the sign of quotient, and calc $r$ as $a-b \times q$. Following shows the floored division, not the truncated division.} +{} +{cpp} +{source/Misc/NegDiv.cpp} + + + +\Algorithm{Fast Input} +{Fast Input with fread. Do not use with scanf, cin, or other input function. Use \texttt{forr(i, n) read(arr[i]);} instead of \texttt{forr(i, n) scanf("\%d", arr+i);}. Use \texttt{read(s+1)} instead of \texttt{scanf("\%s", s+1);}.} +{} +{cpp} +{source/Misc/FastI.cpp} + +\Algorithm{MT19937 Random Number} +{} +{} +{cpp} +{source/Misc/mt19937.cpp} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\begin{center} +\bigskip +--- Document end --- +\end{center} + +\end{multicols} + +\end{document} diff --git a/2025fall/source/DP/DnC.cpp b/2025fall/source/DP/DnC.cpp new file mode 100644 index 0000000..81918c9 --- /dev/null +++ b/2025fall/source/DP/DnC.cpp @@ -0,0 +1,12 @@ +//D[t][s...e]를 구해야 하고, j의 탐색 범위는 [l, r] +void f(int t, int s, int e, int l, int r){ + if(s > e) return; + int m = s + e >> 1; + int opt = l; + for(int i=l; i<=r; i++){ + if(D[t-1][opt] + C[opt][m] > D[t-1][i] + C[i][m]) opt = i; + } + D[t][m] = D[t-1][opt] + C[opt][m]; + f(t, s, m-1, l, opt); + f(t, m+1, e, opt, r); +} \ No newline at end of file diff --git a/2025fall/source/DP/LIS.cpp b/2025fall/source/DP/LIS.cpp new file mode 100644 index 0000000..a59118a --- /dev/null +++ b/2025fall/source/DP/LIS.cpp @@ -0,0 +1,17 @@ +template vi lis(const vector& S) { + if (S.empty()) return {}; + vi prev(sz(S)); + typedef pair p; + vector

res; + rep(i,0,sz(S)) { + // change 0 -> i for longest non-decreasing subsequence + auto it = lower_bound(all(res), p{S[i], 0}); + if (it == res.end()) res.emplace_back(), it = res.end()-1; + *it = {S[i], i}; + prev[i] = it == res.begin() ? 0 : (it-1)->second; + } + int L = sz(res), cur = res.back().second; + vi ans(L); + while (L--) ans[L] = cur, cur = prev[cur]; + return ans; +} \ No newline at end of file diff --git a/2025fall/source/DP/LineContainer.cpp b/2025fall/source/DP/LineContainer.cpp new file mode 100644 index 0000000..9f510ad --- /dev/null +++ b/2025fall/source/DP/LineContainer.cpp @@ -0,0 +1,30 @@ +struct Line { + mutable ll k, m, p; + bool operator<(const Line& o) const { return k < o.k; } + bool operator<(ll x) const { return p < x; } +}; + +struct LineContainer : multiset> { + // (for doubles, use inf = 1/.0, div(a,b) = a/b) + static const ll inf = LLONG_MAX; + ll div(ll a, ll b) { // floored division + return a / b - ((a ^ b) < 0 && a % b); } + bool isect(iterator x, iterator y) { + if (y == end()) return x->p = inf, 0; + if (x->k == y->k) x->p = x->m > y->m ? inf : -inf; + else x->p = div(y->m - x->m, x->k - y->k); + return x->p >= y->p; + } + void add(ll k, ll m) { + auto z = insert({k, m, 0}), y = z++, x = y; + while (isect(y, z)) z = erase(z); + if (x != begin() && isect(--x, y)) isect(x, y = erase(y)); + while ((y = x) != begin() && (--x)->p >= y->p) + isect(x, erase(y)); + } + ll query(ll x) { + assert(!empty()); + auto l = *lower_bound(x); + return l.k * x + l.m; + } +}; \ No newline at end of file diff --git a/2025fall/source/DP/LineContainerGMS.cpp b/2025fall/source/DP/LineContainerGMS.cpp new file mode 100644 index 0000000..f2ca023 --- /dev/null +++ b/2025fall/source/DP/LineContainerGMS.cpp @@ -0,0 +1,38 @@ +namespace LC +{ + +vll line; +int getline(ll c) +{ + int k = 0, st = 20; + while(st+1) + { + int now = k+(1<= line.size()) continue; + + if(line[now].fi*c+line[now].se < line[now-1].fi*c+line[now-1].se) k = now; + } + return k; +} +void pushline(pll C) +{ + while(line.size() >= 2) + { + pll A = line[line.size()-2]; + pll B = line.back(); + + A = {A.fi-C.fi, A.se-C.se}; + B = {B.fi-C.fi, B.se-C.se}; + A.se = -A.se; B.se = -B.se; + + if(A.fi<0) A = {-A.fi, -A.se}; + if(B.fi<0) B = {-B.fi, -B.se}; + + + if(A.se*B.fi >= B.se*A.fi) line.pop_back(); + else break; + } + line.pb(C); +} + +} // namespace LC \ No newline at end of file diff --git a/2025fall/source/DP/SlopeTrick.cpp b/2025fall/source/DP/SlopeTrick.cpp new file mode 100644 index 0000000..0358db9 --- /dev/null +++ b/2025fall/source/DP/SlopeTrick.cpp @@ -0,0 +1,52 @@ +const int N = 1e6+7; +int arr[N]; +priority_queue pq; +ll ans = 0; +int main() +{ + getint(n); + forr(i, n) scanf("%d", arr+i); + + pq.push(arr[1]); int t=0; ll val = 0; + fors(i, 2, n) + { + t++; + int r = t + pq.top(); + if(r <= arr[i]) pq.push(arr[i]-t); + else + { + pq.push(arr[i]-t); pq.push(arr[i]-t); pq.pop(); + ans += r-arr[i]; + } + } + + printf("%lld", ans); +} + + +int arr[N]; +priority_queue pq; +int ans2[N]; +int main() +{ + getint(n); + forr(i, n) scanf("%d", arr+i); + + pq.push(arr[1]); ll ans = 0; + ans2[1] = arr[1]; + fors(i, 2, n) + { + int r = (i-1) + pq.top(); + if(r <= arr[i]) pq.push(arr[i]-(i-1)); + else + { + pq.push(arr[i]-(i-1)); pq.push(arr[i]-(i-1)); pq.pop(); + ans += r-arr[i]; + } + + ans2[i] = pq.top() + (i-1); + } + + fore(i, n-1, 1) ans2[i] = min(ans2[i], ans2[i+1]-1); + forr(i, n) printf("%d\n", ans2[i]); +} \ No newline at end of file diff --git a/2025fall/source/DP/SoS.cpp b/2025fall/source/DP/SoS.cpp new file mode 100644 index 0000000..a842eb5 --- /dev/null +++ b/2025fall/source/DP/SoS.cpp @@ -0,0 +1,22 @@ +int n = 20; +vector a(1 << n); + +// keeps track of the sum over subsets +// with a certain amount of matching bits in the prefix +vector> dp(1 << n, vector(n)); + +vector sos(1 << n); +for (int mask = 0; mask < (1 << n); mask++) { + dp[mask][-1] = a[mask]; + for (int x = 0; x < n; x++) { + dp[mask][x] = dp[mask][x - 1]; + if (mask & (1 << x)) { dp[mask][x] += dp[mask - (1 << x)][x - 1]; } + } + sos[mask] = dp[mask][n - 1]; +} + +//////////////////////////////////////////// +D[i]에 미리 i에 해당하는 값을 넣어둔다 +fors(d, 0, 19) fors(i,0,(1<<20)-1) + if(i & (1< D[i] : sum of subset of mask i \ No newline at end of file diff --git a/2025fall/source/DS/Fenwick.cpp b/2025fall/source/DS/Fenwick.cpp new file mode 100644 index 0000000..42bd6ef --- /dev/null +++ b/2025fall/source/DS/Fenwick.cpp @@ -0,0 +1,9 @@ +ll tree[N]; +void update(int i,ll x) { + while(i < N) tree[i] += x, i += i&-i; +} +int query(int i) { + ll s = 0; + while(i) s += tree[i], i -= i&-i; + return s; +} \ No newline at end of file diff --git a/2025fall/source/DS/LiChaoTree.cpp b/2025fall/source/DS/LiChaoTree.cpp new file mode 100644 index 0000000..4139eb0 --- /dev/null +++ b/2025fall/source/DS/LiChaoTree.cpp @@ -0,0 +1,47 @@ +const ll L = 1e9+7, inf = 2*L*L+7; +struct Line { + ll a, b; + ll operator()(ll x){return a*x+b;} + Line():a(0),b(-inf){} + Line(ll a, ll b):a(a), b(b){} +}; +struct Node {ll l, r; Line v; Node():l(-1), r(-1), v(){}}; +using LiChao = vector; + +// add Line v in [l, r] +void update(LiChao& seg, Line v, ll l, ll r, ll s=-L, ll e=L, ll i=0) { + if(e < l or r < s) return; + if(s == e) { seg[i].v = (seg[i].v(s) > v(s))?seg[i].v:v; return; } + + ll mid=(s+e)>>1; + if(l <= s && e <= r) { + Line A = seg[i].v, B = v; if(A(s) < B(s)) swap(A, B); + if(A(e) >= B(e)) seg[i].v = A; + else if(A(mid) >= B(mid)) { + seg[i].v = A; + if(seg[i].r == -1) seg[i].r = seg.size(), seg.pb(Node()); + update(seg, B, mid+1, e, mid+1, e, seg[i].r); + } + else { + seg[i].v = B; + if(seg[i].l == -1) seg[i].l = seg.size(), seg.pb(Node()); + update(seg, A, s, mid, s, mid, seg[i].l); + } + return; + } +if(seg[i].l == -1) seg[i].l = seg.size(), seg.pb(Node()); +if(seg[i].r == -1) seg[i].r = seg.size(), seg.pb(Node()); + update(seg, v, l, r, s, mid, seg[i].l); + update(seg, v, l, r, mid+1, e, seg[i].r); +} +// query max_{l_i <= x <= r_i} (a_i*x + b_i) +ll query(LiChao& seg, ll x, ll s=-L, ll e=L, ll i=0) { + if(i == -1 or x < s or e < x) return -inf; + if(s == e) return seg[i].v(x); + ll mid = (s+e)>>1; + return max({query(seg, x, s, mid, seg[i].l), query(seg, x, mid+1, e, seg[i].r), seg[i].v(x)}); +} + +// LiChao seg(1, Node()); +// update(seg, {a, b}, l, r); +// ll v = query(seg, x); \ No newline at end of file diff --git a/2025fall/source/DS/PBDS.cpp b/2025fall/source/DS/PBDS.cpp new file mode 100644 index 0000000..f869d81 --- /dev/null +++ b/2025fall/source/DS/PBDS.cpp @@ -0,0 +1,37 @@ +#include +#include +#include +#include +using namespace __gnu_pbds; +using namespace __gnu_cxx; + +template +using indexed_set = tree, rb_tree_tag, tree_order_statistics_node_update>; + +indexed_set s; +s.insert(3); s.insert(2); s.insert(3); s.insert(9); s.insert(7); //2 3 7 9 +s.insert(5); //2 3 5 7 9 +s.erase(5); //2 3 7 9 + +auto x = s.find_by_order(2); // *x : 7 + +s.order_of_key(6) // 2 +s.order_of_key(7) // 2 +s.order_of_key(8) // 3 + +///////////////////////////////////////////////////////////// +// greater_equal <- ordered_multiset / greater <- ordered_multiset +#define oset_greater tree, rb_tree_tag, tree_order_statistics_node_update> +#define oset_less tree, rb_tree_tag, tree_order_statistics_node_update> + +void oset_m_erase(ordered_set_greater &OS, ll val){ + int index = OS.order_of_key(val); + oset_greater::iterator it = OS.find_by_order(index); + if(it != OS.end() && *it == val) OS.erase(it); +} + + +///////////////////////////////////////////////////////////// +rope r; +r.insert(r.size() - t, i); //r.size()-t번째 자리에 i를 삽입 +r.substr(a, b - a + 1) // a부터 (b-a+1)개 만큼을 잘라낸다. 즉, [a, b] 선택 diff --git a/2025fall/source/DS/STBeats.cpp b/2025fall/source/DS/STBeats.cpp new file mode 100644 index 0000000..12f7fe9 --- /dev/null +++ b/2025fall/source/DS/STBeats.cpp @@ -0,0 +1,86 @@ +const int inf = 1e9+7; +#define data _data +struct data{ + ll mx, mx_cnt, mx2, sum; + + constexpr data(ll m):mx(m), mx_cnt(1), mx2(-inf), sum(m) {} + constexpr data(ll mx, ll mx_cnt, ll mx2, ll sum):mx(mx), mx_cnt(mx_cnt), mx2(mx2), sum(sum) {} +}; +data join(data A, data B) +{ + if(A.mx == B.mx) + return {A.mx, A.mx_cnt+B.mx_cnt, max(A.mx2, B.mx2), A.sum+B.sum}; + if(A.mx < B.mx) swap(A, B); + return {A.mx, A.mx_cnt, max(A.mx2, B.mx), A.sum+B.sum}; +} +using Seg = vector; + +void init(Seg& seg, int i, int s, int e, ll* A) +{ + if(s == e) { seg[i] = A[s]; return; } + int mid = (s+e)/2; + init(seg, i*2, s, mid, A); init(seg, i*2+1, mid+1, e, A); + seg[i] = join(seg[i*2], seg[i*2+1]); +} + +void prop(Seg& seg, int i, int s, int e) +{ + if(s == e) return; + + for(auto t : {i*2, i*2+1}) { + if(seg[t].mx > seg[i].mx) { + seg[t].sum -= seg[t].mx_cnt * (seg[t].mx - seg[i].mx); + seg[t].mx = seg[i].mx; + } + } +} + +void update(Seg& seg, int i, int s, int e, int a, int b, ll v) +{ + prop(seg, i, s, e); + if(e; + +void init(Seg& seg, int i, int s, int e, ll *A) { + if(s == e) {seg[i] = A[s]; return;} + int mid = (s+e)>>1; + init(seg, i*2, s, mid, A); init(seg, i*2+1, mid+1, e, A); + seg[i] = join(seg[i*2], seg[i*2+1]); +} +void prop(Seg& seg, int i, int s, int e) { + seg[i].sum += seg[i].lazy * (e-s+1); + if(s != e) for(auto t:{i*2, i*2+1}) seg[t].lazy += seg[i].lazy; + seg[i].lazy = 0; +} + +void update(Seg& seg, int i, int s, int e, int a, int b, ll v) { + prop(seg, i, s, e); + if(e>1; + update(seg, i*2, s, mid, a, b, v); update(seg, i*2+1, mid+1, e, a, b, v); + seg[i] = join(seg[i*2], seg[i*2+1]); +} + +ll query(Seg& seg, int i, int s, int e, int a, int b) { + prop(seg, i, s, e); + if(e>1; + return query(seg, i*2, s, mid, a, b) + query(seg, i*2+1, mid+1, e, a, b); +} diff --git a/2025fall/source/DS/SegmentTree_GMS.cpp b/2025fall/source/DS/SegmentTree_GMS.cpp new file mode 100644 index 0000000..c91d9c7 --- /dev/null +++ b/2025fall/source/DS/SegmentTree_GMS.cpp @@ -0,0 +1,160 @@ +namespace GMS +{ + template + class Segtree { + class Node { + Node *l, *r; + int s,e; D v; + public: + Node(int s, int e) :l(0), r(0), s(s), e(e), v(_e){}; + ~Node(){delete l; delete r;} + + template + friend void init(Node* node, Dini arr[] = NULL) { + int s = node->s, e=node->e, mid=(s+e)/2; + if(s == e) { + node->v = D(arr?arr[s]:_e); + return; + } + + node->l = new Node(s, mid); + init(node->l, arr); + node->r = new Node(mid+1, e); + init(node->r, arr); + + node->v = join(node->l->v, node->r->v); + } + friend D _query(Node* node, int a, int b) { + int s=node->s, e=node->e; + if(a <= s and e <= b) return node->v; + if(b < s or e < a) return _e; + + return join(_query(node->l, a, b), _query(node->r, a, b)); + } + friend void _update + (Node* node, int i, function upd) { + int s=node->s, e=node->e; + if(i < s or e < i) return; + if(s == e) + { + node->v = upd(node->v); + return; + } + + _update(node->l, i, upd); + _update(node->r, i, upd); + + node->v = join(node->l->v, node->r->v); + } + }; + + Node *root; + public: + template + Segtree(int s,int e, Dini arr[] = NULL) { + root = new Node(s, e); + init(root, arr); + } + ~Segtree(){delete root;} + D query(int s, int e) + {return _query(root, s, e);} + void update(int i, function upd) + {_update(root, i, upd);} + }; + + + template + class LZSegtree { + class Node { + Node *l, *r; + int s,e; + D v; L lz; + + void prop() { + v = apply(v, lz, e-s+1); + if(l) l->lz = give(l->lz, lz); + if(r) r->lz = give(r->lz, lz); + + lz = _l; + } + + public: + Node(int s, int e) + :l(0), r(0), s(s), e(e), v(_e), lz(_l){}; + ~Node(){delete l; delete r;} + + template + friend void init(Node* node, Dini arr[] = NULL) { + int s = node->s, e=node->e, mid=(s+e)/2; + if(s == e) + { + node->v = D(arr?arr[s]:_e); + return; + } + + node->l = new Node(s, mid); + init(node->l, arr); + node->r = new Node(mid+1, e); + init(node->r, arr); + + node->v = join(node->l->v, node->r->v); + } + friend D _query(Node* node, int a, int b) { + node->prop(); + int s=node->s, e=node->e; + if(a <= s and e <= b) return node->v; + if(b < s or e < a) return _e; + + return join(_query(node->l, a, b), _query(node->r, a, b)); + } + friend void _update + (Node* node, int a, int b, function upd){ + node->prop(); + int s=node->s, e=node->e; + if(b < s or e < a) return; + if(a <= s and e <= b) + { + node->lz = upd(node->lz); + node->prop(); + return; + } + + _update(node->l, a, b, upd); + _update(node->r, a, b, upd); + + node->v = join(node->l->v, node->r->v); + } + }; + + Node *root; + public: + template + LZSegtree(int s,int e, Dini arr[] = NULL) + { + root = new Node(s, e); + init(root, arr); + } + ~LZSegtree(){delete root;} + D query(int s, int e){return _query(root, s, e);} + void update(int s, int e, function upd){_update(root, s, e, upd);} + }; +} // namespace GMS + +////////////////////////////////////////////////////// +#define data _data + +struct data { + int m, m_cnt; + constexpr data(int m):m(m), m_cnt(1){} + constexpr data(int m, int m_cnt):m(m), m_cnt(m_cnt){} +}; +data join(data A, data B) { + if(A.m == B.m) return data(A.m, A.m_cnt+B.m_cnt); + if(A.m < B.m) return A; + else return B; +} +data apply(data A, int lz, int len) + {return {A.m+lz, A.m_cnt};} +int give(int a, int b){return a+b;} + +using Seg = GMS::LZSegtree; diff --git a/2025fall/source/DS/SplayTree.cpp b/2025fall/source/DS/SplayTree.cpp new file mode 100644 index 0000000..dc46b95 --- /dev/null +++ b/2025fall/source/DS/SplayTree.cpp @@ -0,0 +1,127 @@ +struct Node +{ + Node *p, *l, *r; int cnt; ll val; + ll m, M, sum; ll lazy; bool flip, dum; + Node(ll val, bool dum = false): p(0), l(0), r(0), cnt(1), val(val), m(val), M(val), sum(val), lazy(0), flip(0), dum(dum){} + void fix(){ + cnt = 1+(l?l->cnt:0)+(r?r->cnt:0); + sum = val+(l?l->sum:0)+(r?r->sum:0); + m = min({val, (l?l->m:inf), (r?r->m:inf)}); + M = max({val, (l?l->M:-1), (r?r->M:-1)}); + } + void prop(){ + if(flip){ +swap(l, r); if(l) l->flip = !l->flip; if(r) r->flip = !r->flip; flip = false; + } + if(lazy){ +val += lazy; sum += cnt * lazy; if(l) l->lazy += lazy; if(r) r->lazy += lazy; lazy = 0; + } + } + +} *root; + +// 자기보다 더 높은 노드를 루트로 하는 SplayTree를 조작하는 경우, 하위 SplayTree는 unvalid된다. +struct SplayTree{ + Node *root = NULL, *rp = NULL; + SplayTree(){} + SplayTree(Node *rt){ + if(!rt) return; + root = rt; rp = rt->p; + } + void mop(Node *node){ + if(node == root) node->prop(); + else mop(node->p); + if(node->l) node->l->prop(); + if(node->r) node->r->prop(); + } + + void rotate(Node *node){ + if(!root) return; + if(node->p == rp) return; + if(node->p->l == node){ + Node *p = node->p, *g = p->p; + Node *a = node->l, *b = node->r, *c = p->r; + p->l = b; if(b) b->p = p; + p->r = c; if(c) c->p = p; + node->l = a; if(a) a->p = node; + node->r = p; p->p = node; + node->p = g; if(g) (g->l == p?g->l:g->r) = node; + p->fix(); node->fix(); + if(p == root) root = node; + } + else{ + Node *p = node->p, *g = p->p; + Node *a = p->l, *b = node->l, *c = node->r; + p->l = a; if(a) a->p = p; + p->r = b; if(b) b->p = p; + node->l = p; p->p = node; + node->r = c; if(c) c->p = node; + node->p = g; if(g) (g->l == p?g->l:g->r) = node; + p->fix(); node->fix(); + if(p == root) root = node; + } + } + + void splay(Node* node){ + if(!root) return; assert(node); mop(node); + while(node->p != rp){ + Node *p, *g; + p = node->p; g = p->p; + if(g == rp) rotate(node); + else if((p->l == node) == (g->l == p)) rotate(p), rotate(node); + else rotate(node), rotate(node); + } + root = node; + } + + Node* insert(ll val, bool dum = false){ + if(!root) return root = new Node(val, dum); + Node *now = root; while(now->r) now = now->r; + Node* ret = now->r = new Node(val, dum); + now->r->p = now; return splay(ret), ret; + } + + Node* find_kth(int k) { // 0-indexed + assert(root); assert(root->cnt > k); + Node *now = root; now->prop(); + while(true){ + while(now->l and now->l->cnt > k) now = now->l, now->prop(); + k -= now->l?now->l->cnt:0; + if(k == 0) break; + k--; now = now->r; + now->prop(); + } + return splay(now), now; + } + // s-1, e+1번째 노드가 항상 존재해야 한다. + Node* gather(int s, int e){ + find_kth(e+1); + SplayTree(root->l).find_kth(s-1); + assert(root->l->r); return root->l->r; + } + void update(int i, int j, ll val){ + Node *node = gather(i, j); node->lazy += val; + node->prop(); node->p->fix(); node->p->p->fix(); + } + void reverse(int i, int j){ + Node *node = gather(i, j); node->flip = !node->flip; + } + void p_vals(){p_vals(root, 0, false);} + void p_vals(Node* node, ll lz, bool flip){ + lz += node->lazy; flip ^= node->flip; + if(!flip){ + if(node->l) p_vals(node->l, lz, flip); + if(!node->dum) printf("%lld ", node->val+lz); + if(node->r) p_vals(node->r, lz, flip); + } + else{ + if(node->r) p_vals(node->r, lz, flip); + if(!node->dum) printf("%lld ", node->val+lz); + if(node->l) p_vals(node->l, lz, flip); + } + } +}; +// SplayTree sp; +// fors(i, 0, n+1) arr[i] = sp.insert(i, i==0 or i == n+1); +// Node* node = sp.gather(l, r); sp.reverse(l, r); +// sp.find_kth(k); sp.splay(arr[k]); \ No newline at end of file diff --git a/2025fall/source/DS/UF_QUndo.cpp b/2025fall/source/DS/UF_QUndo.cpp new file mode 100644 index 0000000..29462d5 --- /dev/null +++ b/2025fall/source/DS/UF_QUndo.cpp @@ -0,0 +1,60 @@ +struct dsu_pb { + const int N; + vi par; stack > s; + + dsu_pb(int N):N(N), par(N) { + fors(i, 0, N-1) par[i] = -1; + } + int root(int i) { + if(par[i] < 0) return i; + return root(par[i]); + } + bool join(int i, int j) { + i = root(i); j = root(j); + s.push({{i, par[i]}, {j, par[j]}}); + if(i == j) return false; + if(-par[i] < -par[j]) swap(i, j); + par[i] += par[j]; par[j] = i; + return true; + } + +protected: + void unjoin() { + assert(!s.empty()); + auto [i, j] = s.top(); s.pop(); + par[i.fi] = i.se; par[j.fi] = j.se; + } +}; + +struct dsu_pf : public dsu_pb { + vector > st; // fi==0 -> B type, fi==1 -> A type + vector > tmp[2]; + int A=0, B=0; + dsu_pf(int N):dsu_pb(N){} + + bool join(int i, int j) { + st.pb({0, {i, j}}); B++; + return dsu_pb::join(i, j); + } + void pop_front() { + assert(!st.empty()); + if(A == 0) { + forr(i, B) unjoin(); + A = B; B = 0; reverse(all(st)); + for(auto &[b, p]:st) b = 1, dsu_pb::join(p.fi, p.se); + } + else if(st.back().fi == false) { + tmp[st.back().fi].pb(st.back()); st.pop_back(); unjoin(); + while(tmp[0].size() != tmp[1].size() and (unsigned) A != tmp[1].size()) { + tmp[st.back().fi].pb(st.back()); + st.pop_back(); + unjoin(); + } + for(auto i:{0, 1}) reverse(all(tmp[i])); + for(auto i:{0, 1}) for(auto v:tmp[i]) + st.pb(v), dsu_pb::join(v.se.fi, v.se.se); + tmp[0].clear(); tmp[1].clear(); + } + A--; st.pop_back(); unjoin(); + } +}; \ No newline at end of file diff --git a/2025fall/source/Fundemental.cpp b/2025fall/source/Fundemental.cpp new file mode 100644 index 0000000..1c61be6 --- /dev/null +++ b/2025fall/source/Fundemental.cpp @@ -0,0 +1,22 @@ +#include + +#define getint(n) int n; scanf("%d%*c", &n) +#define getll(n) long long n; scanf("%lld%*c", &n) +#define getchar(n) char n; scanf("%c%*c", &n); +#define intab getint(a); getint(b) + +#define forr(i, n) for(int i=1;i<=(n);i++) +#define fors(i, s, e) for(int i=(s); i<=(e); i++) +#define fore(i, e, s) for(int i=(e); i>=(s); i--) + +#define fi first +#define se second +#define all(v) (v).begin(), (v).end() +#define rall(v) (v).rbegin(), (v).rend() +#define pb push_back + +using namespace std; +using ll = long long; using lll = __int128_t; +using pii = pair; using pll = pair; +using vi = vector; using vl = vector; +using vii = vector; using vll = vector; \ No newline at end of file diff --git a/2025fall/source/Geometry/Bulldozer.cpp b/2025fall/source/Geometry/Bulldozer.cpp new file mode 100644 index 0000000..1fdfad6 --- /dev/null +++ b/2025fall/source/Geometry/Bulldozer.cpp @@ -0,0 +1,60 @@ +struct ray +{ + ll x, y, dx, dy; int i, j; + ray(pll A, pll B, int i = 0, int j = 0) + { + if(A.fi == B.fi && A.se > B.se) swap(A, B), swap(i, j); + + if(A.fi>B.fi) swap(A, B), swap(i, j); + this->i = i; this->j = j; + x = A.fi; y = A.se; + dx = B.fi-A.fi; dy = B.se-A.se; + } + friend bool operator<(const ray& A, const ray& B) + { + return (A.dy*B.dx == B.dy*A.dx)?A.x == B.x?A.dx > p; vector vec; +int num[N]; + +void solve() +{ + getint(n); + p.pb({{0, 0}, 0}); + forr(i, n) + { + getll(a); getll(b); getchar(c); + p.pb({{a, b}, c=='R'}); + } + sort(p.begin()+1, p.end()); + forr(i, n) num[i] = i; + + Seg s(1, n, p); + + forr(i, n) fors(j, i+1, n) vec.pb(ray(p[i].fi, p[j].fi, i, j)); + sort(all(vec)); + + ll ans = s.query(1, n).m; + for(auto r:vec) + { + int i = r.i, j = r.j; + assert(num[i]+1 == num[j]); + + int ii = p[num[i]].se; + int jj = p[num[j]].se; + //printf("%d %d %d %d\n", i, j, ii, jj); + s.update(num[j], [ii](Dta A){return Dta(ii);}); + //printf("%d\n", s.query(1, n).m); + s.update(num[i], [jj](Dta A){return Dta(jj);}); + //printf("%d\n", s.query(1, n).m); + + swap(p[num[i]], p[num[j]]); + swap(num[i], num[j]); + + ans = max(ans, (ll)s.query(1, n).m); + } + printf("%lld\n", ans); +} diff --git a/2025fall/source/Geometry/Geo.cpp b/2025fall/source/Geometry/Geo.cpp new file mode 100644 index 0000000..7af55e8 --- /dev/null +++ b/2025fall/source/Geometry/Geo.cpp @@ -0,0 +1,26 @@ +forr(i, now) vec.pb(A[i]); +sort(all(vec)); + +vll upper; +for(auto i:vec) +{ + while(upper.size() >= 2 && ccw(upper[upper.size()-2], upper.back(), i) >= 0) + upper.pop_back(); + upper.push_back(i); +} + +reverse(all(vec)); +vll lower; +for(auto i:vec) +{ + while(lower.size() >= 2 && ccw(lower[lower.size()-2], lower.back(), i) >= 0) + lower.pop_back(); + lower.push_back(i); +} + +assert(upper.front() == lower.back() && lower.front() == upper.back()); +upper.pop_back(); lower.pop_back(); + +vll hull; +hull.insert(hull.end(), all(upper)); +hull.insert(hull.end(), all(lower)); \ No newline at end of file diff --git a/2025fall/source/Geometry/HPI.cpp b/2025fall/source/Geometry/HPI.cpp new file mode 100644 index 0000000..ed4bfad --- /dev/null +++ b/2025fall/source/Geometry/HPI.cpp @@ -0,0 +1,50 @@ +using ld = long double; +using pdd = pair; +using line = pair; // half plane : left side of vector fi->se + +const ld eps = 1e-9; +pdd operator*(const pdd& a, ld s) { return {a.fi * s, a.se * s}; } +inline bool equals(ld a, ld b) { return abs(a - b) < eps; } + +bool line_intersect(line& a, line& b, pdd& v) { + ld det = (a.se - a.fi) / (b.se - b.fi); + if (equals(det, 0)) return 0; + ld t = ((b.fi - a.fi) / (b.se - b.fi)) / det; + v = a.fi + (a.se - a.fi) * t; + return 1; +} + +bool bad(line& a, line& b, line& c) { + pdd v; if(!line_intersect(a, b, v)) return 0; + return (c.se - c.fi) / (v - c.fi) <= eps; +} + +vector HPI(vector& lns) { + auto lsgn = [&](const line& a) { + if(a.fi.se == a.se.se) return a.fi.fi > a.se.fi; + return a.fi.se > a.se.se; + }; + sort(lns.begin(), lns.end(), [&](const line& a, const line& b) { + if(lsgn(a) != lsgn(b)) return lsgn(a) < lsgn(b); + return (a.se - a.fi) / (b.se - b.fi) > 0; + }); + + deque dq; + for(auto l : lns){ + while(dq.size() >= 2 && bad(dq[dq.size()-2], dq.back(), l)) dq.pop_back(); + while(dq.size() >= 2 && bad(dq[0], dq[1], l)) dq.pop_front(); + + if(dq.size() < 2 || !bad(dq.back(), l, dq[0])) dq.pb(l); + } + + vector res; + if(dq.size() >= 3) { + for(int i = 0; i < (int)dq.size(); i++) { + int j = (i + 1) % (int)dq.size(); + pdd v; + if(!line_intersect(dq[i], dq[j], v)) continue; + res.push_back(v); + } + } + return res; +} \ No newline at end of file diff --git a/2025fall/source/Geometry/Mindset.cpp b/2025fall/source/Geometry/Mindset.cpp new file mode 100644 index 0000000..77af704 --- /dev/null +++ b/2025fall/source/Geometry/Mindset.cpp @@ -0,0 +1,47 @@ +using pii=pair; +pii operator+(pii A, pii B){return {A.fi+B.fi, A.se+B.se};} +pii operator-(pii A, pii B){return {A.fi-B.fi, A.se-B.se};} +ll operator*(pii A, pii B){return (ll)A.fi*B.fi+(ll)A.se*B.se;} // inner product +ll operator/(pii A, pii B){return (ll)A.fi*B.se-(ll)A.se*B.fi;} // outer product + +// 각도 정렬 (O = pii(0, 0)) +sort(P+1, P+1+n, [](pii A, pii B) { + if(B == O) return false; + if(A == O) return true; + return (AB:A/B<0; +}); + +// 선분 교차 +// Segment : fi에서 시작하는 se 벡터 +// fi + k * se, 0 <= k <= 1 + +using Segment = pair; +int isJoin(const Segment& A, const Segment& B) { + if(B.se/A.se != 0) { + ll p = (A.fi-B.fi)/A.se; + ll q = B.se/A.se; + + if(q<0) q = -q, p = -p; + if(p < 0 or p > q) return false; + + p = (B.fi-A.fi)/B.se; + q = A.se/B.se; + + if(q<0) q = -q, p = -p; + if(p < 0 or p > q) return false; + + return true; + } + else { + if((A.fi-B.fi)/A.se != 0) return false; + + ll p = A.fi*A.se, q = (A.fi+A.se)*A.se; + ll r = B.fi*A.se, s = (B.fi+B.se)*A.se; + + if(p>q) swap(p, q); if(r>s) swap(r, s); + + if(max(p, r) > min(q, s)) return false; + + return true; + } +} diff --git a/2025fall/source/Geometry/PointInConvexPolygon.cpp b/2025fall/source/Geometry/PointInConvexPolygon.cpp new file mode 100644 index 0000000..2a5b574 --- /dev/null +++ b/2025fall/source/Geometry/PointInConvexPolygon.cpp @@ -0,0 +1,16 @@ +auto isunder = [](pii upper[], int u, pii x, bool inv = false){ // inv==true : isover + int r = inv?-1:1; + int idx = lower_bound(upper+1, upper+1+u, x, + [&r](pii a, pii b){return r*a.fi u) return false; + if(idx == 1) { + if(r*x.fi < r*upper[1].fi) return false; + else { + int h = upper[1].se; + if(upper[2].fi == upper[1].fi) h = upper[2].se; + + return r*x.se <= r*h; + } + } + return ccw(upper[idx-1], upper[idx], x) <= 0; +}; \ No newline at end of file diff --git a/2025fall/source/Geometry/geometry_kaere.cpp b/2025fall/source/Geometry/geometry_kaere.cpp new file mode 100644 index 0000000..faa4799 --- /dev/null +++ b/2025fall/source/Geometry/geometry_kaere.cpp @@ -0,0 +1,163 @@ +typedef pair pll; +#define _x first +#define _y second + +pll operator-(const pll &a, const pll &b){ + return {a._x - b._x, a._y - b._y}; +} + +ll cross(const pll &a, const pll &b){ + return a._x * b._y - b._x * a._y; +} + +ll dot(const pll &a, const pll &b){ + return a._x * b._x + a._y * b._y; +} + +int ccw(const pll &p1, const pll &p2, const pll &p3){ + ll res = cross(p2 - p1, p3 - p1); + return (res != 0) * (res < 0 ? -1 : 1); +} + +// dist of point - point +double dist(const pll &p1, const pll &p2){ + return sqrt((p1._x - p2._x) * (p1._x - p2._x) + (p1._y - p2._y) * (p1._y - p2._y)); +} + +// dist of line - point +double dist(const pll &l1, const pll &l2, const pll &p){ + ll area = abs(cross(l2 - l1, p - l1)); + return area / dist(l1, l2); +} + +// dist of seg - point +double segDist(P& s, P& e, P& p) { + if (s==e) return (p-s).dist(); + auto d = (e-s).dist2(), t = min(d,max(.0,(p-s).dot(e-s))); + return ((p-s)*d-(e-s)*t).dist()/d; +} + +P perp() const { return P(-y, x); } // rotates +90 degrees +int sgn(T x) { return (x > 0) - (x < 0); } // sign of x + +// Returns where p is as seen from s towards e. 1/0/-1 <-> left/on line/right. +int sideOf(P s, P e, P p) { return sgn(s.cross(e, p)); } + +// Returns a vector of either 0, 1, or 2 intersection points. +template +vector

circleLine(P c, double r, P a, P b) { + P ab = b - a, p = a + ab * (c-a).dot(ab) / ab.dist2(); + double s = a.cross(b, c), h2 = r*r - s*s / ab.dist2(); + if (h2 < 0) return {}; + if (h2 == 0) return {p}; + P h = ab.unit() * sqrt(h2); + return {p - h, p + h}; +} + +// Computes the pair of points at which two circles intersect. +typedef Point P; +bool circleInter(P a,P b,double r1,double r2,pair* out) { + if (a == b) { assert(r1 != r2); return false; } + P vec = b - a; + double d2 = vec.dist2(), sum = r1+r2, dif = r1-r2, + p = (d2 + r1*r1 - r2*r2)/(d2*2), h2 = r1*r1 - p*p*d2; + if (sum*sum < d2 || dif*dif > d2) return false; + P mid = a + vec*p, per = vec.perp() * sqrt(fmax(0, h2) / d2); + *out = {mid + per, mid - per}; + return true; +} + +// Returns true iff p lies on the line segment from s to e. +template bool onSegment(P s, P e, P p) { + return p.cross(s, e) == 0 && (s - p).dot(e - p) <= 0; +} + +// Circumcircle +typedef Point P; +double ccRadius(const P& A, const P& B, const P& C) { + return (B-A).dist()*(C-B).dist()*(A-C).dist()/ + abs((B-A).cross(C-A))/2; +} +P ccCenter(const P& A, const P& B, const P& C) { + P b = C-A, c = B-A; + return A + (b*c.dist2()-c*b.dist2()).perp()/b.cross(c)/2; +} + +// Minimum enclosing circle +pair mec(vector

ps) { + shuffle(all(ps), mt19937(time(0))); + P o = ps[0]; + double r = 0, EPS = 1 + 1e-8; + rep(i,0,sz(ps)) if ((o - ps[i]).dist() > r * EPS) { + o = ps[i], r = 0; + rep(j,0,i) if ((o - ps[j]).dist() > r * EPS) { + o = (ps[i] + ps[j]) / 2; + r = (o - ps[i]).dist(); + rep(k,0,j) if ((o - ps[k]).dist() > r * EPS) { + o = ccCenter(ps[i], ps[j], ps[k]); + r = (o - ps[i]).dist(); + } + } + } + return {o, r}; +} + +// point inside convex hull in logN +bool inHull(const vector

& l, P p, bool strict = true) { + int a = 1, b = sz(l) - 1, r = !strict; + if (sz(l) < 3) return r && onSegment(l[0], l.back(), p); + if (sideOf(l[0], l[a], l[b]) > 0) swap(a, b); + if (sideOf(l[0], l[a], p) >= r || sideOf(l[0], l[b], p)<= -r) + return false; + while (abs(a - b) > 1) { + int c = (a + b) / 2; + (sideOf(l[0], l[c], p) > 0 ? b : a) = c; + } + return sgn(l[a].cross(l[b], p)) < r; +} + +// convex hull +vector convex_hull(vector &arr){ + vector up, down; + for(auto p : arr){ + while(up.size() >= 2 && ccw(up[up.size() - 2], up[up.size() - 1], p) >= 0) up.pop_back(); + while(down.size() >= 2 && ccw(down[down.size() - 2], down[down.size() - 1], p) <= 0) down.pop_back(); + up.push_back(p); + down.push_back(p); + } + up.insert(up.end(), down.rbegin() + 1, down.rend()); + return up; +} + +// rotating callipers +typedef Point P; +array hullDiameter(vector

S) { + int n = sz(S), j = n < 2 ? 0 : 1; + pair> res({0, {S[0], S[0]}}); + rep(i,0,j) + for (;; j = (j + 1) % n) { + res = max(res, {(S[i] - S[j]).dist2(), {S[i], S[j]}}); + if ((S[(j + 1) % n] - S[j]).cross(S[i + 1] - S[i]) >= 0) + break; + } + return res.second; +} + +// Closest pair +typedef Point P; +pair closest(vector

v) { + assert(sz(v) > 1); + set

S; + sort(all(v), [](P a, P b) { return a.y < b.y; }); + pair> ret{LLONG_MAX, {P(), P()}}; + int j = 0; + for (P p : v) { + P d{1 + (ll)sqrt(ret.first), 0}; + while (v[j].y <= p.y - d.x) S.erase(v[j++]); + auto lo = S.lower_bound(p - d), hi = S.upper_bound(p + d); + for (; lo != hi; ++lo) + ret = min(ret, {(*lo - p).dist2(), {*lo, p}}); + S.insert(p); + } + return ret.second; +} \ No newline at end of file diff --git a/2025fall/source/Geometry/namespace_geometry.cpp b/2025fall/source/Geometry/namespace_geometry.cpp new file mode 100644 index 0000000..7cefcba --- /dev/null +++ b/2025fall/source/Geometry/namespace_geometry.cpp @@ -0,0 +1,109 @@ +template +class Point { +public: + T x, y; + Point() : x(0), y(0) {}; + Point(T _x, T _y) : x(_x), y(_y) {}; + + Point operator+(Point p2){ + return Point(x + p2.x, y + p2.y); + } + Point operator-(Point p2){ + return Point(x - p2.x, y - p2.y); + } + T operator*(Point p2){ + return x * p2.x + y * p2.y; + } + T operator/(Point p2) { + return x * p2.y - p2.x * y; + } + T operator==(Point p2) { + return (x == p2.x) && (y == p2.y); + } + T sqdist() { + return x*x + y*y; + } + bool operator<(Point p2) { + if(y == p2.y) + return x < p2.x; + return y < p2.y; + } + +}; + +namespace geometry { + template + ll ccw(Point center, Point p2, Point p3) { + ll res = (p2 - center) / (p3 - center); + return (res > 0) - (res < 0); + } + + template + double theta(Point center, Point p2, Point p3) { + return acos(p2 * p3 / sqrt(p2.sqdist() * p3.sqdist())); + } + + template + function &, Point &, Point)> cmp_point = [](Point &l, Point &r, Point O = {(T)0, (T)0}) -> bool { + return (l < O) != (r < O) ? l < r : l/r > 0; + }; + + template + T sq_dist(Point &p1, Point &p2) { + return (p2.x - p1.x)*(p2.x - p1.x) + (p2.y - p1.y)*(p2.y - p1.y); + } + + template + double dist(Point &p1, Point &p2) { + return sqrt((double)sq_dist(p1, p2)); + } + + template + double line_point_dist(pair, Point> &l, Point p) + { + Point p1 = p - l.first, p2 = l.second - l.first; + return abs(p1 / p2)/(dist(l.first, l.second)); + } + + template + double line_min_dist(pair, Point> &l1, pair, Point> &l2) { + double ans = INFINITY; + ans = min({ans, dist(l1.first, l2.first), dist(l1.first, l2.second), dist(l1.second, l2.first), dist(l1.second, l2.second)}); + + if((l1.second - l1.first)*(l2.first - l1.first) > 0 && (l1.first - l1.second)*(l2.first - l1.second) > 0) + ans = min({ans, line_point_dist(l1, l2.first)}); + if((l1.second - l1.first)*(l2.second - l1.first) > 0 && (l1.first - l1.second)*(l2.second - l1.second) > 0) + ans = min({ans, line_point_dist(l1, l2.second)}); + swap(l1, l2); + if((l1.second - l1.first)*(l2.first - l1.first) > 0 && (l1.first - l1.second)*(l2.first - l1.second) > 0) + ans = min({ans, line_point_dist(l1, l2.first)}); + if((l1.second - l1.first)*(l2.second - l1.first) > 0 && (l1.first - l1.second)*(l2.second - l1.second) > 0) + ans = min({ans, line_point_dist(l1, l2.second)}); + swap(l1, l2); + return ans; + } + + template + vector convex_hull(vector> &pts) { + assert(pts.size() >= 2); + vector> res; + + swap(pts[0], *min_element(pts.begin(), pts.end())); + sort(pts.begin()+1, pts.end(), [&pts](Point &a, Point &b){ + ll cw = ccw(pts[0], a, b); + if(cw) return cw > 0; + return sq_dist(pts[0], a) < sq_dist(pts[0], b); + }); + auto itr = pts.begin(); + res.push_back(*(itr++)); res.push_back(*(itr++)); + + while(itr != pts.end()) + { + while(res.size() >= 2 && ccw(res[res.size()-2], res[res.size()-1], *itr) <= 0) + res.pop_back(); + res.push_back(*(itr++)); + } + return res; + } +} +using namespace geometry; diff --git a/2025fall/source/Graph/2SAT.cpp b/2025fall/source/Graph/2SAT.cpp new file mode 100644 index 0000000..8744c18 --- /dev/null +++ b/2025fall/source/Graph/2SAT.cpp @@ -0,0 +1,5 @@ +ok = true; // 1<=i&&i<=n : $x$, n+1<=i&&i<=2*n : $!x$ +forr(i, n) { + if (scn[i] == scn[i+n]) ok = false; + ans[i] = (scn[i] < scn[i+n]); +} \ No newline at end of file diff --git a/2025fall/source/Graph/BipartiteMatching.cpp b/2025fall/source/Graph/BipartiteMatching.cpp new file mode 100644 index 0000000..7b4c18c --- /dev/null +++ b/2025fall/source/Graph/BipartiteMatching.cpp @@ -0,0 +1,13 @@ +vector sideadj[N]; +int selby[M]; +int chk[M], c; +bool matching(int s) { + for(auto i : sideadj[s]) { + if(chk[i] == c) continue; + chk[i] = c; + if(selby[i] and !matching(selby[i])) continue; + selby[i] = s; + return true; + } + return false; +} \ No newline at end of file diff --git a/2025fall/source/Graph/Dinic.cpp b/2025fall/source/Graph/Dinic.cpp new file mode 100644 index 0000000..b7e5fa1 --- /dev/null +++ b/2025fall/source/Graph/Dinic.cpp @@ -0,0 +1,69 @@ +struct Edge { + int to, cap, now; + Edge* rev; + Edge(int to,int cap):to(to), cap(cap), now(0){} + int left(){return cap - now;} + void flow(int f){now += f; rev->now -= f;} + void reset(){now = 0;} +}; +vector adj[N]; + +int lv[N]; bool chk[N]; +bool bfs(int S, int T) { + queue q; + q.push(S); lv[S] = 0; chk[S] = true; + while(!q.empty()) { + int s = q.front(); q.pop(); + for(auto i : adj[s]) { + if(i->left() and !chk[i->to]) { + lv[i->to] = lv[s]+1; chk[i->to] = true; + q.push(i->to); + } + } + } + return chk[T]; +} + +Edge* hist[N]; int last[N]; +bool dfs(int s, int T) { + if(s == T) return true; + + for(int &j=last[s]; j < adj[s].size(); j++) { + int i = adj[s][j]->to; + if(adj[s][j]->left() == 0 or lv[i] != lv[s]+1) continue; + hist[i] = adj[s][j]; + + if(dfs(i, T)) return true; + } + return false; +} + +ll flow(int S,int T) { + ll ans = 0; + while(bfs(S, T)) { + while(dfs(S, T)) { + int m = 2e9; + int now = T; + while(S != now) { + m = min(m, hist[now]->left()); + now = hist[now]->rev->to; + } + now = T; + while(S != now) + hist[now]->flow(m), now = hist[now]->rev->to; + ans += m; + } + memset(last, 0, sizeof last); + memset(chk, 0, sizeof chk); + } + return ans; +} +// isDir : isDirected => 양방향 간선이면 false +void connect(int from, int to, int cap, bool isDir = true) { + Edge *fw, *bw; + fw = new Edge(to, cap); + bw = new Edge(from, !isDir ? cap : 0); + fw->rev = bw; bw->rev = fw; + adj[from].push_back(fw); + adj[to].push_back(bw); +} \ No newline at end of file diff --git a/2025fall/source/Graph/DominatorTree.cpp b/2025fall/source/Graph/DominatorTree.cpp new file mode 100644 index 0000000..5063d7d --- /dev/null +++ b/2025fall/source/Graph/DominatorTree.cpp @@ -0,0 +1,51 @@ +// https://ideone.com/aO6cH4 +namespace dtree{ // by cki86201 +vector E[N], RE[N], rdom[N]; +int S[N], RS[N], cs; +int par[N], val[N], sdom[N], rp[N], dom[N]; +void clear(int n) { cs = 0; + for(int i=0;i<=n;i++) { + par[i] = val[i] = sdom[i] = rp[i] = dom[i] = S[i] = RS[i] = 0; + E[i].clear(); RE[i].clear(); rdom[i].clear(); + } +} +void add_edge(int x, int y) { E[x].push_back(y); } +void Union(int x, int y) { par[x] = y; } +int Find(int x, int c = 0) { + if(par[x] == x) return c ? -1 : x; + int p = Find(par[x], 1); + if(p == -1) return c ? par[x] : val[x]; + if(sdom[val[x]] > sdom[val[par[x]]]) val[x] = val[par[x]]; + par[x] = p; + return c ? p : val[x]; +} +void dfs(int x) { + RS[ S[x] = ++cs ] = x; + par[cs] = sdom[cs] = val[cs] = cs; + for(int e : E[x]) { + if(S[e] == 0) dfs(e), rp[S[e]] = S[x]; + RE[S[e]].push_back(S[x]); + } +} +int solve(int s, int *up) { // Calculate idoms + dfs(s); + for(int i=cs;i;i--) { + for(int e : RE[i]) sdom[i] = min(sdom[i], sdom[Find(e)]); + if(i > 1) rdom[sdom[i]].push_back(i); + for(int e : rdom[i]) { + int p = Find(e); + if(sdom[p] == i) dom[e] = i; + else dom[e] = p; + } + if(i > 1) Union(i, rp[i]); + } + for(int i=2;i<=cs;i++) if(sdom[i] != dom[i]) dom[i] = dom[dom[i]]; + for(int i=2;i<=cs;i++) up[RS[i]] = RS[dom[i]]; + return cs; +} +} // namespace dtree + +int par[N]; +dtree::add_edge(a, b); // a -> b +int cnt = dtree::solve(s, par); +// cnt : s에서 도달할 수 있는 정점, par: dominator tree의 par diff --git a/2025fall/source/Graph/MCMF.cpp b/2025fall/source/Graph/MCMF.cpp new file mode 100644 index 0000000..ce0dcb6 --- /dev/null +++ b/2025fall/source/Graph/MCMF.cpp @@ -0,0 +1,67 @@ +struct Edge { + int to, cap, now; + ll cost; + Edge* rev; + Edge(int to,int cap, ll cost) + :to(to), cap(cap), now(0), cost(cost){} + int left(){return cap - now;} + ll flow(int f) + {now += f; rev->now -= f; return cost * f;} + void reset(){now = 0;} +}; +vector adj[N]; +Edge* hist[N]; ll dist[N]; bool inQueue[N], chk[N]; +bool spfa(int s, int t) { + memset(dist, 0, sizeof(dist)); + memset(chk, 0, sizeof(chk)); chk[s] = true; + queue q; + memset(inQueue, 0, sizeof(inQueue)); + q.push(s); inQueue[s] = true; + while(!q.empty()) { + int now = q.front(); + q.pop(); inQueue[now] = false; + + for(auto e : adj[now]) { + int next = e->to; + if(e->left() > 0 and + (chk[next] == false + or dist[next] > dist[now] + e->cost)) { + chk[next] = true; + dist[next] = dist[now] + e->cost; + hist[next] = e; + if(!inQueue[next]) + q.push(next), inQueue[next] = true; + } + } + } + return chk[t]; +} +// cost가 들어가면 항상 단방향만 가능하다. (양방향 : 2번 connect) +void connect(int from, int to, int cap, ll cost) { + Edge *fw, *bw; + fw = new Edge(to, cap, cost); + bw = new Edge(from, 0, -cost); + fw->rev = bw; bw->rev = fw; + adj[from].push_back(fw); + adj[to].push_back(bw); +} +//maximum matching & minimum cost +pair flow(int S,int T) { + ll ans = 0; ll cost = 0; + while(spfa(S, T)) { + int m = 2e9; + + int now = T; + while(S != now) { + m = min(m, hist[now]->left()); + now = hist[now]->rev->to; + } + now = T; + while(S != now) { + cost += hist[now]->flow(m); + now = hist[now]->rev->to; + } + ans += m; + } + return {ans, cost}; +} \ No newline at end of file diff --git a/2025fall/source/Graph/Matching.cpp b/2025fall/source/Graph/Matching.cpp new file mode 100644 index 0000000..22eb9a6 --- /dev/null +++ b/2025fall/source/Graph/Matching.cpp @@ -0,0 +1,74 @@ +// From https://github.com/koosaga/olympiad +// matching_short.cpp +const int MAXN = 2020 + 1; +// 1-based Vertex index +int vis[MAXN], par[MAXN], orig[MAXN], match[MAXN], aux[MAXN], t, N; +vector conn[MAXN]; +queue Q; +void addEdge(int u, int v) { conn[u].push_back(v); conn[v].push_back(u); } +void init(int n) { + N = n; t = 0; + for(int i=0; i<=n; ++i) { + conn[i].clear(); + match[i] = aux[i] = par[i] = 0; + } +} +void augment(int u, int v) { + int pv = v, nv; + do { + pv = par[v]; nv = match[pv]; + match[v] = pv; match[pv] = v; + v = nv; + } while(u != pv); +} +int lca(int v, int w) { + ++t; + while(true) { + if(v) { + if(aux[v] == t) return v; aux[v] = t; + v = orig[par[match[v]]]; + } + swap(v, w); + } +} +void blossom(int v, int w, int a) { + while(orig[v] != a) { + par[v] = w; w = match[v]; + if(vis[w] == 1) Q.push(w), vis[w] = 0; + orig[v] = orig[w] = a; + v = par[w]; + } +} +bool bfs(int u) { + fill(vis+1, vis+1+N, -1); iota(orig + 1, orig + N + 1, 1); + Q = queue (); Q.push(u); vis[u] = 0; + while(!Q.empty()) { + int v = Q.front(); Q.pop(); + for(int x: conn[v]) { + if(vis[x] == -1) { + par[x] = v; vis[x] = 1; + if(!match[x]) return augment(u, x), true; + Q.push(match[x]); vis[match[x]] = 0; + } + else if(vis[x] == 0 && orig[v] != orig[x]) { + int a = lca(orig[v], orig[x]); + blossom(x, v, a); blossom(v, x, a); + } + } + } + return false; +} +int Match() { + int ans = 0; + // find random matching (not necessary, constant improvement) + vector V(N-1); iota(V.begin(), V.end(), 1); + shuffle(V.begin(), V.end(), mt19937(0x94949)); + for(auto x: V) if(!match[x]){ + for(auto y: conn[x]) if(!match[y]) { + match[x] = y, match[y] = x; + ++ans; break; + } + } + for(int i=1; i<=N; ++i) if(!match[i] && bfs(i)) ++ans; + return ans; +} \ No newline at end of file diff --git a/2025fall/source/Graph/TarjanSCC.cpp b/2025fall/source/Graph/TarjanSCC.cpp new file mode 100644 index 0000000..333ae33 --- /dev/null +++ b/2025fall/source/Graph/TarjanSCC.cpp @@ -0,0 +1,28 @@ +vi adj[N]; +int in[N], c = 0; +stack p; +bool fin[N]; int scn[N], nscc = 0; +int dfs(int s) { + in[s] = ++c; + p.push(s); + + int m = c; + for(auto i : adj[s]) { + if(in[i] == 0) m = min(m, dfs(i)); + else if(!fin[i]) m = min(m, in[i]); + } + + if(m == in[s]) { + nscc++; + while(p.top() != s) + { + int i = p.top(); p.pop(); + scn[i] = nscc; fin[i] = true; + } + p.pop(); + scn[s] = nscc; fin[s] = true; + } + return m; +} + +forr(i, n) if(!fin[i]) dfs(i); \ No newline at end of file diff --git a/2025fall/source/Linear Algebra/BerlekampMassey.cpp b/2025fall/source/Linear Algebra/BerlekampMassey.cpp new file mode 100644 index 0000000..a8661dd --- /dev/null +++ b/2025fall/source/Linear Algebra/BerlekampMassey.cpp @@ -0,0 +1,107 @@ +// https://gist.github.com/koosaga/d4afc4434dbaa348d5bef0d60ac36aa4 +vector berlekamp_massey(vector x){ + vector ls, cur; int lf, ld; + for(int i=0; i c(i-lf-1); c.push_back(k); + for(auto &j : ls) c.push_back(-j * k % mod); + if(c.size() < cur.size()) c.resize(cur.size()); + for(int j=0; j=(int)cur.size()) + tie(ls, lf, ld) = make_tuple(cur, i, (t - x[i]) % mod); + cur = c; + } + for(auto &i : cur) i = (i % mod + mod) % mod; + return cur; +} +int get_nth(vector rec, vector dp, ll n){ + int m = rec.size(); + vector s(m), t(m); + s[0] = 1; + if(m != 1) t[1] = 1; + else t[0] = rec[0]; + auto mul = [&rec](vector v, vector w){ + int m = v.size(); + vector t(2 * m); + for(int j=0; j= mod) t[j+k] -= mod; + } + } + for(int j=2*m-1; j>=m; j--){ + for(int k=1; k<=m; k++){ + t[j-k] += (ll)t[j] * rec[k-1] % mod; + if(t[j-k] >= mod) t[j-k] -= mod; + } + } + t.resize(m); + return t; + }; + while(n){ + if(n & 1) s = mul(s, t); + t = mul(t, t); + n >>= 1; + } + ll ret = 0; + for(int i=0; i get_min_poly(int n, vector M){ + // smallest poly P such that A^i = sum_{j < i} {A^j \times P_j} + vector rnd1, rnd2; + mt19937 rng(0x14004); + auto randint = [&rng](int lb, int ub){ + return uniform_int_distribution(lb, ub)(rng); + }; + fors(i, 0, n-1) rnd1.push_back(randint(1, mod - 1)); + fors(i, 0, n-1) rnd2.push_back(randint(1, mod - 1)); + vector gobs; + fors(i, 0, 2*n+1){ + int tmp = 0; + fors(j, 0, n-1){ + tmp += (ll)rnd2[j] * rnd1[j] % mod; + if(tmp >= mod) tmp -= mod; + } + gobs.push_back(tmp); + vector nxt(n); + for(auto &i : M){ + nxt[i.x] += (ll)i.v * rnd1[i.y] % mod; + if(nxt[i.x] >= mod) nxt[i.x] -= mod; + } + rnd1 = nxt; + } + auto sol = berlekamp_massey(gobs); + reverse(sol.begin(), sol.end()); + return sol; +} + +ll det(int n, vector M){ + vector rnd; + mt19937 rng(0x14004); + auto randint = [&rng](int lb, int ub){ + return uniform_int_distribution(lb, ub)(rng); + }; + fors(i, 0, n-1) rnd.push_back(randint(1, mod - 1)); + for(auto &i : M){ + i.v = (ll)i.v * rnd[i.y] % mod; + } + auto sol = get_min_poly(n, M)[0]; + if(n % 2 == 0) sol = mod - sol; + for(auto &i : rnd) sol = (ll)sol * ipow(i, mod - 2) % mod; + return sol; +} diff --git a/2025fall/source/Linear Algebra/Matrix.cpp b/2025fall/source/Linear Algebra/Matrix.cpp new file mode 100644 index 0000000..69eccc0 --- /dev/null +++ b/2025fall/source/Linear Algebra/Matrix.cpp @@ -0,0 +1,56 @@ +class Matrix { +private: + ll c, r, mod; vector> arr; + ll power(ll x, ll y, ll p) { + if (y == 0) return 1; + ll v = power(x, y/2, p) % p; + v = (v * v) % p; + return (y%2 == 0)? v : (x * v) % p; + } + ll modInverse(ll a, ll p) { return power(a, p-2, p); } +public: + Matrix(int _n, int _m, ll p) : c(_n), r(_m), mod(p), arr(_n, vl(_m, 0)){} + void setI() { assert(c == r); for(int i=0; i Inverse() { + assert(c == r); + Matrix victim = *this, retm(c, c, mod); retm.setI(); + for (int k = 0; k < c; k++) { + int t = k - 1; while (t + 1 < c && !victim[++t][k]); + if (t == c - 1 && !victim[t][k]) + return {false, Matrix(0, 0, 0)}; + victim.swaprow(k, t), retm.swaprow(k, t); + ll d = victim[k][k]; + for (int j = 0; j < c; j++) { + victim[k][j] = (victim[k][j] * modInverse(d, mod))%mod; + retm[k][j] = (retm[k][j] * modInverse(d, mod))%mod; + } + for (int i = 0; i= k) victim[i][j] = (victim[i][j] - victim[k][j] * m + mod*mod)%mod; + retm[i][j] = (retm[i][j] - retm[k][j] * m + mod*mod)%mod; + } + } + } + return {true, retm}; + } + vector GaussElimination() { + assert(c == r - 1); + vector retv(c, 0.0); + for(ll i=0; i= 0; p--) { + retv[p] = arr[p][c] / arr[p][p]; + for (q = p - 1; q >= 0; q--) + arr[q][c] = arr[q][c] - arr[q][p] * retv[p]; + } + return retv; + } +}; \ No newline at end of file diff --git a/2025fall/source/Linear Algebra/XORBasis.cpp b/2025fall/source/Linear Algebra/XORBasis.cpp new file mode 100644 index 0000000..da2fcd3 --- /dev/null +++ b/2025fall/source/Linear Algebra/XORBasis.cpp @@ -0,0 +1,5 @@ +vector basis; +void insert(ll x) { + for(auto i:basis) x = min(x, x ^ basis[i]); + if (x != 0) basis.push_back(x); +} diff --git a/2025fall/source/Math/CRT.cpp b/2025fall/source/Math/CRT.cpp new file mode 100644 index 0000000..36276b5 --- /dev/null +++ b/2025fall/source/Math/CRT.cpp @@ -0,0 +1,13 @@ +pll crt(pll p, pll q) { + if(p.fi > q.fi) swap(p, q); + auto [a, A] = p; + auto [b, B] = q; + + ll g = gcd(A, B); + if((b-a)%g != 0) return {-1, -1}; + + ll i = A, j = B, k = b-a; + i/=g; j/=g; k/=g; + auto [x, y] = diophantos(i, j); + return {(ll)((a+(lll)A*k*x)%(A*B/g)), A*B/g}; +} \ No newline at end of file diff --git a/2025fall/source/Math/Diophantos.cpp b/2025fall/source/Math/Diophantos.cpp new file mode 100644 index 0000000..ee52470 --- /dev/null +++ b/2025fall/source/Math/Diophantos.cpp @@ -0,0 +1,12 @@ +pll diophantos(ll a, ll b) { + assert(a>0 and b>=0); + if(b == 0) return {1, 0}; + auto [y, x] = diophantos(b, a%b); y = y-(a/b)*x; + if(x < 0 or x >= b) { + ll t = x/b; + if(x%b < 0) t--; + + x -= b*t; y += a*t; + } + return {x, y}; +} \ No newline at end of file diff --git a/2025fall/source/Math/FFTConv.cpp b/2025fall/source/Math/FFTConv.cpp new file mode 100644 index 0000000..5d98a61 --- /dev/null +++ b/2025fall/source/Math/FFTConv.cpp @@ -0,0 +1,61 @@ +using cpx = complex; +using vcpx = vector; +void fft(vcpx &a, bool inv = false) { + int n = a.size(), j = 0; assert((n&-n) == n); + for(int i=1; i> 1); + while(j >= bit) { + j -= bit; bit >>= 1; + } + j += bit; if(i < j) swap(a[i], a[j]); + } + vcpx roots(n/2); + prec c = 2 * pi * (inv ? -1 : 1); + for(int i=0; i=c or b>=c) return n*(n-1)/2 * (a/c) + n * (b/c) + floor_sum(a%c, b%c, c, n); + ll m = (a*(n-1)+b)/c; + return m*n - floor_sum(c, c-b+a-1, a, m); +} \ No newline at end of file diff --git a/2025fall/source/Math/Harmonic.cpp b/2025fall/source/Math/Harmonic.cpp new file mode 100644 index 0000000..e1d7190 --- /dev/null +++ b/2025fall/source/Math/Harmonic.cpp @@ -0,0 +1,12 @@ +ll harmonic(ll n) { + ll ans = 0; + for(ll i = 1; i <= n; i = n/(n/i)+ 1) { + //for j \in [i, n/(n/i)] : n/j == n/i + + ans += n/i * (n/(n/i) - i + 1); + + // \sum_{i=1}^n {f(n/i)} + // ans += f(n/i) * (n/(n/i) - i + 1) + } + return ans; +} \ No newline at end of file diff --git a/2025fall/source/Math/MillerRabin.cpp b/2025fall/source/Math/MillerRabin.cpp new file mode 100644 index 0000000..4b8dcd4 --- /dev/null +++ b/2025fall/source/Math/MillerRabin.cpp @@ -0,0 +1,26 @@ +ll pow(ll a, ll b, ll mod) { + ll ret = 1; + for(int st=0; (1LL< +ll pow(ll a, ll b) { + a %= mod; + ll ret = 1; + while(b != 0) { + if(b&1) ret = ret*a%mod; + a = a*a%mod; b>>=1; + } + return ret; +} +template +void ntt(vector &a, bool inv = false) { + static_assert(mod <= (ll)2e9, "mod should be less than 2e9"); + int n = a.size(), j = 0; + + assert((n & -n) == n && (mod-1)%n == 0); + + for(int i=1; i> 1); + while(j >= bit) { + j -= bit; + bit >>= 1; + } + j += bit; + if(i < j) swap(a[i], a[j]); + } + + static vector root[30], iroot[30]; + for(int st=1; (1<(w, (mod-1)/(1<(w, (mod-1)/(1<(t, mod-2); + + iroot[st].pb(1); + for(int i=1; i<(1<<(st-1)); i++) + iroot[st].pb(iroot[st].back()*t%mod); + } + } + + vector* r = (inv?root:iroot); + + for(int st = 1; (1<(n, mod-2); + for(int i=0; i +vl conv(vl A, vl B) { + int n = A.size(), m = B.size(); + int t = 1; while(t < n+m-1) t*=2; + A.resize(t); B.resize(t); + + ntt(A); ntt(B); + + fors(i, 0, t-1) A[i] = A[i]*B[i]%mod; + + ntt(A, true); + A.resize(n+m-1); + + return A; +} +} // namespace GMS \ No newline at end of file diff --git a/2025fall/source/Math/PolladRho.cpp b/2025fall/source/Math/PolladRho.cpp new file mode 100644 index 0000000..3128e35 --- /dev/null +++ b/2025fall/source/Math/PolladRho.cpp @@ -0,0 +1,22 @@ +void fact(ll n, vl& ret) { + if(n == 1) return; + else if(n%2 == 0) ret.pb(2), fact(n/2, ret); + else if(is_p(n)) ret.pb(n); + else { + ll a, b, c, g = n; + auto f = [&c, &n](ll x)->ll{return (c+(lll)x*x)%n;}; + + do { + if(g == n) a=b=rand()%(n-2)+2, c=rand()%20+1; + a=f(a); b=f(f(b)); + g = gcd(a-b, n); + } while(g == 1); + fact(g, ret); fact(n/g, ret); + } +} +vl po_rho(ll n) { + vl ret; + fact(n, ret); + sort(all(ret)); + return ret; +} \ No newline at end of file diff --git a/2025fall/source/Math/Polynomial.cpp b/2025fall/source/Math/Polynomial.cpp new file mode 100644 index 0000000..2111d1f --- /dev/null +++ b/2025fall/source/Math/Polynomial.cpp @@ -0,0 +1,149 @@ +namespace GMS { +template +struct Qring : public vl { + using poly = Qring; + Qring() : vl(1, 0) {} + Qring(ll c) : vl(1, c%mod) {} + Qring(ll c, int n) : vl(n, c%mod) {} + Qring(const vl& cp) : vl(cp) {for(auto &i:*this) i%=mod;} + + ll& operator[](ll idx) { + if((unsigned)idx < size()) return vl::operator[](idx); + this->resize(idx+1); return vl::operator[](idx); + } + ll operator[](ll idx) const { + if((unsigned)idx < size()) return vl::operator[](idx); + return 0LL; + } + void adjust() { while(size() > 1 and back() == 0) pop_back(); } + void adjust(int n){resize(n, 0);} + ll operator()(ll x) { + x %= mod; ll ret = 0; + for(auto it=rbegin(); it!=rend(); it++) + ret = (ret*x+*it)%mod; + return ret; + } + friend poly operator%(const poly& A, int B){ // remainder by x^B + poly ret(A); ret.resize(B, 0); + return ret; + } + friend poly operator+(const poly& A, const poly& B) { + int n = max(A.size(), B.size()); poly ret(0, n); + fors(i, 0, n-1) ret[i] = A[i]+B[i]; + for(auto&i:ret) if(i >= mod) i -= mod; + return ret.adjust(), ret; + } + friend poly operator-(const poly& A) { + int n = A.size(); poly ret(0, n); + fors(i, 0, n-1) ret[i] = A[i]?mod-A[i]:0; + return ret; + } + friend poly operator-(const poly& A, const poly& B) { + int n = max(A.size(), B.size()); + poly ret(0, n); + fors(i, 0, n-1) ret[i] = (mod+A[i]-B[i])%mod; + return ret.adjust(), ret; + } + friend poly operator*(ll x, const poly& B) { + poly ret(B); x %= mod; + for(auto &i : ret) i = (i*x)%mod; + return ret.adjust(), ret; + } + friend poly operator*(const poly& A, const poly& B) { + poly ret = conv(A, B); + // ACL : poly ret = atcoder::convolution(A, B); + return ret.adjust(), ret; + } + friend poly inv(const poly& A, int t) { assert(A[0] != 0); + poly g = pow(A[0], mod-2); int st=1; + while(st < t){st*=2; g = (-A%st*g%st+2)*g%st;} + return g.adjust(t), g; + } + friend poly diff(const poly& A) { + int n = A.size(); poly ret(0, n-1); + fors(i, 0, n-2) ret[i] = (i+1)*A[i+1]%mod; + return ret; + } + friend poly inte(const poly& A) { + static vector inv(1, 1); + int n = A.size(); poly ret(0, n+1); + inv.resize(max((int)inv.size(), n+1)); + forr(i, n) if(inv[i] == 0) inv[i] = pow(i, mod-2); + forr(i, n) ret[i] = inv[i]*A[i-1]%mod; + return ret; + } + friend poly log(const poly& A, int t) { assert(A[0] == 1); + return inte(diff(A) * inv(A, t)%t)%t; + } + friend poly exp(const poly& A, int t) { assert(A[0] == 0); + poly g = 1; int st = 1; + while(st < t) {st*=2; g = (A%st-log(g, st)+1)*g%st;} + return g.adjust(), g; + } + friend poly pow(const poly& A, ll b, ll t) { + poly ret(A); ret.adjust(); + if(ret.size() == 1) { + ret[0] = pow(ret[0], b); + return ret.adjust(t), ret; + } + ll idx = 0; while(ret[idx] == 0) idx++; + if((__int128_t) idx * b >= t) return poly(0, t); + + ll c = ret[idx]; ll ic = pow(ret[idx], mod-2); poly g; + int n = ret.size(); + fors(i, idx, n-1) g[i-idx] = ret[i]*ic%mod; + g.resize(t-idx*b); + + g = exp(b * log(g, t-idx*b), t-idx*b); + c = pow(c, b); + + ret = poly(0, t); fors(i, idx*b, t-1) ret[i] = g[i-idx*b] * c % mod; + + return ret; + } + + //Only just Polynomial, not Qring + void rev() { reverse(begin(), end()); } + friend poly div_quot(poly F, poly G) { + F.adjust(); G.adjust(); + ll df = F.size(), dg = G.size(); + if(df < dg) return poly(0); + F.rev(); G.rev(); + F = F%(df-dg+1)*inv(G, df-dg+1)%(df-dg+1); F.rev(); + return F; + } + friend poly div_rem(poly F, poly G) {return F-G*div_quot(F, G);} + friend poly shift(const poly& F, ll c) { + ll n = F.size(); c %= mod; + poly A(0, n); ll fac = 1; + fors(i, 0, n-1) A[i] = F[i]*fac%mod, fac = fac*(i+1)%mod; + A.rev(); + + poly C(1, n); fors(i, 1, n-1) C[i] = C[i-1]*c%mod; + ll facc = fac = pow(fac, mod-2)*n%mod; + fore(i, n-1, 0) C[i] = C[i]*fac%mod, fac = fac*i%mod; + + poly B = C*A; B.resize(n); B.rev(); + fore(i, n-1, 0) B[i] = B[i]*facc%mod, facc = facc*i%mod; + return B; + } + friend void calcG(vector& G, int i, int l, int r, const vl& p) { + if(l == r){ll g = p[l]?mod-p[l]:0; G[i] = vl({g, 1}); return;} + int mid = (l+r)/2; + calcG(G, i*2, l, mid, p); calcG(G, i*2+1, mid+1, r, p); + G[i] = G[i*2]*G[i*2+1]; + } + friend void eval(const vector& G, int i, int l, int r, poly&& F, vl& ret) { + if(l == r){ret[l] = F[0];return;} + int mid=(l+r)/2; + eval(G, i*2, l, mid, div_rem(F, G[i*2]), ret); + eval(G, i*2+1, mid+1, r, div_rem(F, G[i*2+1]), ret); + } + friend vl multipoint_eval(const poly& A, const vl& B) { + int m = B.size(); + vector G(4*m); calcG(G, 1, 0, m-1, B); + vl ret(m, 0); eval(G, 1, 0, m-1, div_rem(A, G[1]), ret); + return ret; + } +}; +} // namespace GMS \ No newline at end of file diff --git a/2025fall/source/Math/PrimitiveRoot.cpp b/2025fall/source/Math/PrimitiveRoot.cpp new file mode 100644 index 0000000..09b1621 --- /dev/null +++ b/2025fall/source/Math/PrimitiveRoot.cpp @@ -0,0 +1,23 @@ +ll primary_root(ll p) { + std::random_device rd; + std::mt19937 gen(rd()); + std::uniform_int_distribution distrib(1, p-1); + + //distrib(gen); + vl g = po_rho(p-1); + + while(true) { + ll c = distrib(gen); + + bool ok = true; ll u = p-1; + ll b = 1; + for(auto i:g) { + if(i != b) u = p-1; + ll x = pow(c, u/i, p); + if(x == 1) ok = false; + u /= i; b = i; + } + + if(ok) return c; + } +} \ No newline at end of file diff --git a/2025fall/source/Math/general_lucas.cpp b/2025fall/source/Math/general_lucas.cpp new file mode 100644 index 0000000..daacd68 --- /dev/null +++ b/2025fall/source/Math/general_lucas.cpp @@ -0,0 +1,56 @@ +vector euler(1000003, -1), primes; +//Generate primes and also calculate the euler number +void genprime() { + for(ll i = 2;i<=1000002;i++) { + if(euler[i]==-1) { + primes.push_back(i); + euler[i] = i-1; + for(ll j = 2*i; j<=1000002; j+=i) { + if(euler[j]==-1)euler[j] = j; + euler[j] = (euler[j]/i)*(i-1); + } + } + } +} +//Calculates x raised to the power of p % m +ll powll(ll x, ll p, ll m = 1ll<<62) +// Mod inverse +ll inverse(ll x, ll m) + +//finds (n!)_p +ll ff(ll n, ll p, ll q) +{ + ll x = 1, y = powll(p, q); + for(ll i = 2; i<=n;i++) if(i%p) + x = (x*i)%y; + return x%y; +} + +//Generalized Lucas Theorem calculates nCm mod p^q +ll lucas_pow_comb(ll n, ll m, ll p, ll q) { + ll r = n-m, x = powll(p, q); + ll e0 = 0, eq = 0; + ll mul = (p==2&&q>=3)? 1: -1; + ll cr = r, cm = m, carry = 0, cnt = 0; + while(cr||cm||carry) { + cnt++; + int rr = cr%p, rm = cm%p; + if(rr + rm + carry >= p) { + e0++; + if(cnt>=q)eq++; + } + carry = (carry+rr+rm)/p; + cr/=p; cm/=p; + } + mul = powll(p, e0)*powll(mul, eq); + ll ret = (mul % x + x) % x; + ll temp = 1; + for(ll i = 0;;i++)//This is THE line that calculates the formula { + ret = ((ret*ff((n/temp)%x, p, q)%x)%x*(inverse(ff((m/temp)%x, p, q), x)%x*inverse(ff((r/temp)%x, p, q), x)%x)%x)%x; + + if(temp>n/p && temp>m/p && temp>r/p) + break; + temp = temp*p; + } + return (ret%x+x)%x; +} \ No newline at end of file diff --git a/2025fall/source/Math/math.tex b/2025fall/source/Math/math.tex new file mode 100644 index 0000000..e222983 --- /dev/null +++ b/2025fall/source/Math/math.tex @@ -0,0 +1,167 @@ +% Written by Anders Sjoqvist and Ulf Lundstrom, 2009 +% The main sources are: tinyKACTL, Beta and Wikipedia +\subsection{Equations} +\[ax^2+bx+c=0 \Rightarrow x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\] + +The extremum is given by $x = -b/2a$. + +\[\begin{aligned}ax+by=e\\cx+dy=f\end{aligned} +\Rightarrow +\begin{aligned}x=\dfrac{ed-bf}{ad-bc}\\y=\dfrac{af-ec}{ad-bc}\end{aligned}\] + +In general, given an equation $Ax = b$, the solution to a variable $x_i$ is given by +\[x_i = \frac{\det A_i'}{\det A} \] +where $A_i'$ is $A$ with the $i$'th column replaced by $b$. + +\subsection{Inequality} +For positive $a$, $b$, $c$, $d$ with $\frac{a}{b} < \frac{c}{d}$, $\frac{a}{b} < \frac{a+c}{b+d} < \frac{c}{d}$ hold. + +Also, for positive $a$, $b$, $c$, $d$, $\min(\frac{a}{b}, \frac{c}{d}) \leqslant \frac{a+c}{b+d} \leqslant max(\frac{a}{b}, \frac{c}{d})$. + +e.g., for two sets of disjoint vertices $A$, $B$ of $G$, + +\begin{align*} + \min \left( \frac{E(G[A])}{V(G[A])}, \frac{E(G[B])}{V(G[B])} \right) & \leqslant + \frac{E(G[A\cup B])}{V(G[A\cup B])} = \frac{E(G[A]) + E(G[B])}{V(G[A]) + V(G[B])} \\& + \leqslant \max \left( \frac{E(G[A])}{V(G[A])}, \frac{E(G[B])}{V(G[B])} \right) +\end{align*} + +(therefore, the average degree of the disjoint set is larger when we divide them.) + +\subsection{Recurrences} +If $a_n = c_1 a_{n-1} + \dots + c_k a_{n-k}$, and $r_1, \dots, r_k$ are distinct roots of $x^k - c_1 x^{k-1} - \dots - c_k$, there are $d_1, \dots, d_k$ s.t. +\[a_n = d_1r_1^n + \dots + d_kr_k^n. \] +Non-distinct roots $r$ become polynomial factors, e.g. $a_n = (d_1n + d_2)r^n$. + +% \subsection{Trigonometry} +% \begin{align*} +% \sin(v+w)&{}=\sin v\cos w+\cos v\sin w\\ +% \cos(v+w)&{}=\cos v\cos w-\sin v\sin w\\ +% \tan(v+w)&{}=\dfrac{\tan v+\tan w}{1-\tan v\tan w}\\ +% \sin v+\sin w&{}=2\sin\dfrac{v+w}{2}\cos\dfrac{v-w}{2}\\ +% \cos v+\cos w&{}=2\cos\dfrac{v+w}{2}\cos\dfrac{v-w}{2}\\ +% (V+W)\tan(v-w)/2&{}=(V-W)\tan(v+w)/2 +% \end{align*} +% where $V, W$ are lengths of sides opposite angles $v, w$. +% \begin{align*} +% a\cos x+b\sin x&=r\cos(x-\phi)\\ +% a\sin x+b\cos x&=r\sin(x+\phi) +% \end{align*} +% where $r=\sqrt{a^2+b^2}, \phi=\operatorname{atan2}(b,a)$. + +\subsection{Geometry} + +\subsubsection{Triangles} +Side lengths: $a,b,c$ + +Semiperimeter: $p=\dfrac{a+b+c}{2}$ + +Area: $A=\sqrt{p(p-a)(p-b)(p-c)}$ + +Circumradius: $R=\dfrac{abc}{4A}$ + +Inradius: $r=\dfrac{A}{p}$ + +Length of the median (divides the triangle into two equal area triangles): $m_a=\tfrac{1}{2}\sqrt{2b^2+2c^2-a^2}$ + +Length of the bisector (divides angles into two): $s_a=\sqrt{bc\left[1-\left(\dfrac{a}{b+c}\right)^2\right]}$ + +Law of sines: $\dfrac{\sin\alpha}{a}=\dfrac{\sin\beta}{b}=\dfrac{\sin\gamma}{c}=\dfrac{1}{2R}$ + +Law of cosines: $a^2=b^2+c^2-2bc\cos\alpha$ + +Law of tangents: $\dfrac{a+b}{a-b}=\dfrac{\tan\dfrac{\alpha+\beta}{2}}{\tan\dfrac{\alpha-\beta}{2}}$ + + +\subsubsection{Quadrilaterals} +With side lengths $a,b,c,d$, diagonals $e, f$, diagonals angle $\theta$, area $A$ and +magic flux $F=b^2+d^2-a^2-c^2$: + +\[ 4A = 2ef \cdot \sin\theta = F\tan\theta = \sqrt{4e^2f^2-F^2} \] + + For cyclic quadrilaterals the sum of opposite angles is $180^\circ$, +$ef = ac + bd$, and $A = \sqrt{(p-a)(p-b)(p-c)(p-d)}$. + +% \subsubsection{Spherical coordinates} +% \begin{center} +% \includegraphics[width=25mm]{source/Math/sphericalCoordinates.pdf} +% \end{center} +% \[\begin{array}{cc} +% x = r\sin\theta\cos\phi & r = \sqrt{x^2+y^2+z^2}\\ +% y = r\sin\theta\sin\phi & \theta = \textrm{acos}(z/\sqrt{x^2+y^2+z^2})\\ +% z = r\cos\theta & \phi = \textrm{atan2}(y,x) +% \end{array}\] + +\subsection{Derivatives/Integrals} +\begin{align*} + \dfrac{d}{dx}\arcsin x = \dfrac{1}{\sqrt{1-x^2}} &&& \dfrac{d}{dx}\arccos x = -\dfrac{1}{\sqrt{1-x^2}} \\ + \dfrac{d}{dx}\tan x = 1+\tan^2 x &&& \dfrac{d}{dx}\arctan x = \dfrac{1}{1+x^2} \\ + \int\tan ax = -\dfrac{\ln|\cos ax|}{a} &&& \int x\sin ax = \dfrac{\sin ax-ax \cos ax}{a^2} \\ + \int e^{-x^2} = \frac{\sqrt \pi}{2} \text{erf}(x) &&& \int xe^{ax}dx = \frac{e^{ax}}{a^2}(ax-1) +\end{align*} + +Integration by parts: +\[\int_a^bf(x)g(x)dx = [F(x)g(x)]_a^b-\int_a^bF(x)g'(x)dx\] + +\subsection{Sums} +\[ c^a + c^{a+1} + \dots + c^{b} = \frac{c^{b+1} - c^a}{c-1}, c \neq 1 \] +\begin{align*} + 1 + 2 + 3 + \dots + n &= \frac{n(n+1)}{2} \\ + 1^2 + 2^2 + 3^2 + \dots + n^2 &= \frac{n(2n+1)(n+1)}{6} \\ + 1^3 + 2^3 + 3^3 + \dots + n^3 &= \frac{n^2(n+1)^2}{4} \\ + 1^4 + 2^4 + 3^4 + \dots + n^4 &= \frac{n(n+1)(2n+1)(3n^2 + 3n - 1)}{30} \\ +\end{align*} + +\subsection{Series} +$$e^x = 1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\dots,\,(-\infty0$. +\[f(x) = \left\{ +\begin{array}{cl} +\lambda e^{-\lambda x} & x\geq0\\ +0 & x<0 +\end{array}\right.\] +\[\mu=\frac{1}{\lambda},\,\sigma^2=\frac{1}{\lambda^2}\] + +% \subsubsection{Normal distribution} +% Most real random values with mean $\mu$ and variance $\sigma^2$ are well described by $\mathcal{N}(\mu,\sigma^2),\,\sigma>0$. +% \[ f(x) = \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}} \] +% If $X_1 \sim \mathcal{N}(\mu_1,\sigma_1^2)$ and $X_2 \sim \mathcal{N}(\mu_2,\sigma_2^2)$ then +% \[ aX_1 + bX_2 + c \sim \mathcal{N}(\mu_1+\mu_2+c,a^2\sigma_1^2+b^2\sigma_2^2) \] \ No newline at end of file diff --git a/2025fall/source/Math/sphericalCoordinates.pdf b/2025fall/source/Math/sphericalCoordinates.pdf new file mode 100644 index 0000000..0c9a480 --- /dev/null +++ b/2025fall/source/Math/sphericalCoordinates.pdf @@ -0,0 +1,1709 @@ +%PDF-1.4 % +1 0 obj << /Type /Catalog /Pages 2 0 R /Metadata 207 1 R >> endobj 2 0 obj << /Type /Pages /Kids [ 5 0 R ] /Count 1 >> endobj 3 0 obj << /ModDate (D:20090814202111+02'00') /CreationDate (D:20090814175526Z) /Producer (Adobe PDF library 5.00) /Creator (Adobe Illustrator 10.0) >> endobj 5 0 obj << /Type /Page /MediaBox [ 0 0 42.51953 42.51953 ] /Parent 2 0 R /PieceInfo << /Illustrator 387 1 R >> /LastModified (D:20090814202111+02'00') /ArtBox [ 0.60059 1.50391 41.80273 44.95215 ] /Group 199 1 R /TrimBox [ 0 0 42.51953 42.51953 ] /Thumb 200 1 R /Contents 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== T) { + S = buf; T = buf + fread(buf, 1, 100000, stdin); + if(S == T) return EOF; + } + return *S++; +} +void read(int& n) { + n = 0; char c; bool neg = false; + for(c = get(); c < '0'; c=get()) if(c=='-') neg = true; + for(;c>='0';c=get()) n = n*10+c-'0'; + if(neg) n = -n; +} +void read(ll& n) { + n = 0; char c; bool neg = false; + for(c = get(); c < '0'; c=get()) if(c=='-') neg = true; + for(;c>='0';c=get()) n = n*10+c-'0'; + if(neg) n = -n; +} +int read(char s[]) { + char c; int p = 0; while((c = get()) <= ' '); + s[p++] = c; while((c = get()) >= ' ') s[p++] = c; + s[p] = '\0'; return p; +} \ No newline at end of file diff --git a/2025fall/source/Misc/NegDiv.cpp b/2025fall/source/Misc/NegDiv.cpp new file mode 100644 index 0000000..e0bbf90 --- /dev/null +++ b/2025fall/source/Misc/NegDiv.cpp @@ -0,0 +1,7 @@ +#define div _div +ll div(ll A, ll B) +{ + ll q = A/B; + if(A<0) q-=(B>0)-(B<0); + return q; +} \ No newline at end of file diff --git a/2025fall/source/Misc/StressTest.sh b/2025fall/source/Misc/StressTest.sh new file mode 100644 index 0000000..e69de29 diff --git a/2025fall/source/Misc/mt19937.cpp b/2025fall/source/Misc/mt19937.cpp new file mode 100644 index 0000000..0be15b7 --- /dev/null +++ b/2025fall/source/Misc/mt19937.cpp @@ -0,0 +1,7 @@ +const long long rand_L = 1; +const long long rand_R = 10; +mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count()); +uniform_int_distribution dist(rand_L, rand_R); +auto gen = bind(dist, rng); + +gen(); gen(); gen(); \ No newline at end of file diff --git a/2025fall/source/String/AhoCorasick.cpp b/2025fall/source/String/AhoCorasick.cpp new file mode 100644 index 0000000..5daf91f --- /dev/null +++ b/2025fall/source/String/AhoCorasick.cpp @@ -0,0 +1,49 @@ +struct Node { + int next[26]; int par, int fail; bool isfin = false; + Node(){fail = 0; fors(i, 0, 25) next[i] = -1;} +}; +Node trie[N]; int c; +void insert(char s[], int i, int node) { + if(s[i] == '\0') { + trie[node].isfin = true; return; + } + if(trie[node].next[s[i]-'a'] == -1) { + trie[node].next[s[i]-'a'] = ++c; + trie[c].par = node; + } + insert(s, i+1, trie[node].next[s[i]-'a']); +} +void bfs() { + queue q; q.push({0, -1}); + while(!q.empty()) { + auto [node, x] = q.front(); q.pop(); + if(x != -1) { + int pf = trie[trie[node].par].fail; + while(pf != 0 and trie[pf].next[x] == -1) pf = trie[pf].fail; + + if(trie[node].par != 0 and trie[pf].next[x] != -1) + { + trie[node].fail = trie[pf].next[x]; + trie[node].isfin |= trie[trie[pf].next[x]].isfin; + } + else trie[node].fail = 0; + } + fors(i, 0, 25) { + if(trie[node].next[i] == -1) continue; + q.push({trie[node].next[s[i]-'a'], i}); + } + } +} + +// For char* s, insert(s+1, 0, 0); +// trie[0].fail = 0; bfs(); +// find trie from s: +int now = 0, ok = false; +for(int i = 0; s[i]; i++) { + while(now != 0 and trie[now].next[s[i]-'a'] == -1) now = trie[now].fail; + + if(trie[now].next[s[i]-'a'] != -1) { + now = trie[now].next[s[i]-'a']; + if(trie[now].isfin) ok = true; + } +} \ No newline at end of file diff --git a/2025fall/source/String/Eertree.cpp b/2025fall/source/String/Eertree.cpp new file mode 100644 index 0000000..beee3a7 --- /dev/null +++ b/2025fall/source/String/Eertree.cpp @@ -0,0 +1,38 @@ +struct Eertree { + int len[N], link[N], nxt[N][26], r[N]; + long long cnt[N]; int sz, last, n; + char s[N]; + Eertree() { + memset(nxt, 0, sizeof(nxt)); + memset(cnt, 0, sizeof(cnt)); + s[0] = -1; + n = 0; sz = 2; last = 1; + len[0] = -1; link[0] = 0; + len[1] = 0; link[1] = 0; + } + int get_link(int v) { + while (s[n-len[v]-1] != s[n]) v = link[v]; + return v; + } + void insert(char c) { + s[++n] = c; + int cur = get_link(last); + if (!nxt[cur][c-'a']) { + int now = sz++; + r[now] = n; + len[now] = len[cur] + 2; + if (len[now] == 1) link[now] = 1; + else link[now] = nxt[get_link(link[cur])][c-'a']; + nxt[cur][c-'a'] = now; + } + last = nxt[cur][c-'a']; + cnt[last]++; + } + void propagate() { fore(i, sz-1, 2) cnt[link[i]] += cnt[i]; } +}; + +Eertree et; forr(i, n) et.insert(s[i]); +int m = et.sz; et.propagate(); +fors(i, 2, m-1) ans = max(ans, et.cnt[i] * et.len[i]); +// node i : s[(et.r[i]-et.len[i]+1)~(et.r[i])] +// distinct count of pal : m-2; count of node i : et.cnt[i]; \ No newline at end of file diff --git a/2025fall/source/String/F_Z_M_SA_LCP.cpp b/2025fall/source/String/F_Z_M_SA_LCP.cpp new file mode 100644 index 0000000..3c1e4eb --- /dev/null +++ b/2025fall/source/String/F_Z_M_SA_LCP.cpp @@ -0,0 +1,92 @@ +const int N = 1e5+7; +char s[N]; +int F[N], Z[N], M[N]; +int sa[N]; int ord[N], tmp[N], cnt[N]; +int lcp[N]; +int main() { + scanf("%s", s+1); + int n = strlen(s+1); + + // KMP - fail function { + F[1] = 0; int j = 0; + for(int i=2; i<=n;i++) + { + while(j > 0 and s[i] != s[j+1]) j = F[j]; + F[i] = j+=(s[i] == s[j+1]); + } + } + + //Z - Z array { + Z[1] = n; int j = 1, r = 0; + for(int i=2; i<=n; i++) + { + Z[i] = i 0) k--; + } + } + + printf("\nF : "); forr(i, n) printf("%d ", F[i]); + printf("\nZ : "); forr(i, n) printf("%d ", Z[i]); + printf("\nM : "); forr(i, n) printf("%d ", M[i]); + printf("\nSA : "); forr(i, n) printf("%d ", sa[i]); + printf("\nLCP : x "); fors(i, 2, n) printf("%d ", lcp[i]); + + printf("\n"); forr(i, n) printf("%s\n", s+sa[i]); +} \ No newline at end of file diff --git a/2025fall/source/String/KMP.cpp b/2025fall/source/String/KMP.cpp new file mode 100644 index 0000000..dcbd99b --- /dev/null +++ b/2025fall/source/String/KMP.cpp @@ -0,0 +1,17 @@ +int fail[N]; // N : s의 최대 길이 +vi kmp(char obj[], char s[]) { + vi ret; + for(int i = 1, j = 0; s[i]; i++) { + fail[i] = 0; + while(j > 0 and s[i] != s[j]) j = fail[j-1]; + if(s[i] == s[j]) fail[i] = ++j; + } + for(int i = 0, j = 0; obj[i]; i++) { + while(j > 0 and obj[i] != s[j]) j = fail[j-1]; + if(obj[i] == s[j]) { + if(s[j+1]) j++; + else ret.push_back(i-j), j = fail[j]; + } + } + return ret; +} \ No newline at end of file diff --git a/2025fall/source/String/std::string.cpp b/2025fall/source/String/std::string.cpp new file mode 100644 index 0000000..417a0bd --- /dev/null +++ b/2025fall/source/String/std::string.cpp @@ -0,0 +1,132 @@ +///////////////////////////////////////////////////////// +string s; //변수 선언 +///////////////////////////////////////////////////////// + + +///////////////////////////////////////////////////////// +string s = "Hwan"; //output : Hwan +///////////////////////////////////////////////////////// + + +///////////////////////////////////////////////////////// +string s1("Hwan"); //output ㄷ: Hwan +string s2(4, 'A'); //output : AAAA +string s3(s1, 0, s1.length() - 2); //output : HW +string s4(s1, 2, s1.length()); //output : an +string s5(s2); //output : AAAA +string s6("ABCDE", 3); //output : ABC + +char c[] = "TEST Code!!"; +string s7(c); //output : TEST Code!! +/////////////////////////////////////////////////////////​ +string s = "ABCDE123"; + +cout << s.at(2) << endl; //output : C (범위가 맞지 않으면 예외처리를 함) +cout << s[0] << endl; //output : A +cout << s.front() << endl; //output : A +cout << s.back() << endl; //output : 3 + +const char * c = s.c_str(); //배열로써 접근이 가능하며 '\0'에 접근이 가능하다. + +cout << c << endl; //output : ABCDE123 + +cout << (c_arr == s) ? true : false; //output : 1(true) +cout << (&(c_arr[0]) == &(s[0])) ? true : false; //output : 1(true)​ + +///////////////////////////////////////////////////////// +string s = "ABCDE123"; +string::iterator iter = s.begin(); +string r_s, cp; + +for (; iter != s.end(); iter++) { + cout << *iter; + if (*iter == 'E') + break; +} //output : ABCDE + + +copy(s.rbegin(), s.rend(), back_inserter(r_s)); +copy(s.begin(), s.end(), back_inserter(cp)); + +cout << r_s << endl; //output : 321EDCBA +cout << (s == r_s) ? true : false; //output : 0(false) +cout << (s == cp) ? true : false; //output : 1(true) +cout << (&(s[0]) == &(cp[0])) ? true : false; //output : 0(false)​ +///////////////////////////////////////////////////////// +string s = "ABCDE123" + +s.insert(0, "TEST"); //output : TESTABCDE123 +s.insert(s.begin() + s.find_first_of('D') + 1, ':'); // output : TESTABCD:123(문자만 가능) + + +////////// (compare) s = TESTABCD:123 ///////////// +s.compare("TESTABCD:123"); //output : 0 +s.compare("a"); //output : -1 +s.compare("X"); //output : -1 +s.compare("BBBBBBBBBBBBBBB"); //output : 1 +s.compare("100000000000000000000000"); //output : 1 +s.compare("VVVVV"); //output : -1 + + +////////// (erase) s = TESTABCD:123 ///////////// +s.erase(0, 4); //output : ABCD:123 +s.erase(find(s.begin(), s.end(), 'D')); //output : ABC:123('D'만 지움) +s.erase(s.find(':')); //output : ABC(':'부터 뒤 문자까지 모두 지움) + + +////////// (push, pop) s = ABC ///////////// +s.push_back('S'); //output : ABCS +s.pop_back(); //output : ABC + + +////////// (append) s = ABC ///////////// +s.append("TEST"); //output : ABCTEST +s.append(1, '1'); //output : ABCTEST1 +s.append("123456789", 3, 3); //output : ABCTEST1456 + + +////////// (clear) s = ABCTEST1456 ///////////// +const char c[] = "Hwan"; +s.append(c); //output : ABCTEST1456Hwan +s += c; //output : ABCTEST1456HwanHwan(capacity() = 15 -> 31) +s.clear(); //s.size() = 0, s.capacity() = 31 + + +////////// (replace) s = '' ///////////// +s.append("ABCD123"); //output : ABCD123 +s.replace(4, 2, "Hwan"); //output : ABCDHwan3 +s.replace(s.find('H'), s.size() - s.find('H'), "WOW"); //output : ABCDWOW + + +////////// (substr) s = ABCDWOW ///////////// +string temp = s.substr(4); //output : WOW; +temp = s.substr(3, 2); //output : DW; +temp = s.substr(s.size() - 3, 50); //output : WOW; + + +////////// (copy) s = ABCDWOW ///////////// +char arr[5]{}; +s.copy(arr, sizeof arr - 1); //output : ABCD (마지막 '\n' 포함) + + +////////// (resize) s = ABCDWOW ///////////// +s.resize(100); //output : ABCDWOW, s.size() = 100, s.capacity() = 111 +s.resize(4); //output : ABCD, s.size() = 4, s.capacity() = 15 + + +////////// (swap) s = ABCD ///////////// +string sw = "AAA"; +s.swap(sw); //s = "AAA", sw = "ABCD" + + +/////////// c++ 20 /////////////////// +s = "hello Hwan"; +s.starts_with("hello"); //output : true; +s.starts_with('h'); //output : true; +s.starts_with("Hwan"); //output : false; +s.starts_with('x'); //output : false; + +s.ends_with("Hwan"); //output : true; +s.ends_with('n'); //output : true; +s.ends_with("hello"); //output : false; +s.ends_with('q'); //output : false; \ No newline at end of file diff --git a/2025fall/source/Technic/CartesianTree.cpp b/2025fall/source/Technic/CartesianTree.cpp new file mode 100644 index 0000000..78de742 --- /dev/null +++ b/2025fall/source/Technic/CartesianTree.cpp @@ -0,0 +1,13 @@ +int A[N], par[N]; +stack st; +forr(i, n) { + int l = -1; + while(!st.empty() && A[st.top()] < A[i]) + l = st.top(), st.pop(); + if(l != -1) par[l] = i; + if(!st.empty()) par[i] = st.top(); + st.push(i); +} + +while(st.size() != 1) st.pop(); +par[st.top()] = st.top(); \ No newline at end of file diff --git a/2025fall/source/Tree/Centroid.cpp b/2025fall/source/Tree/Centroid.cpp new file mode 100644 index 0000000..8386917 --- /dev/null +++ b/2025fall/source/Tree/Centroid.cpp @@ -0,0 +1,30 @@ +vi adj[N]; bool cent[N]; +int sz[N], par[N]; + +void getSz(int s){ + sz[s] = 1; + for(auto i:adj[s]){ + if(cent[i]) continue; if(par[s] == i) continue; + par[i] = s; getSz(i); par[i] = 0; + sz[s] += sz[i]; + } +} +int getCent(int s, int n){ + for(auto i:adj[s]) if(!cent[i]&&sz[i]n/2) + return getCent(i, n); + return s; +} + +int cpar[N]; +int getCentTree(int s){ + getSz(s); int C = getCent(s, sz[s]); + cent[C] = true; + for(auto i:adj[C]){ + if(cent[i]) continue; + int c = getCentTree(i); + cpar[c] = C; + } + return C; +} + +int C = getCentTree(1); cpar[C] = -1; \ No newline at end of file diff --git a/2025fall/source/Tree/HLD.cpp b/2025fall/source/Tree/HLD.cpp new file mode 100644 index 0000000..8fc6741 --- /dev/null +++ b/2025fall/source/Tree/HLD.cpp @@ -0,0 +1,40 @@ +BOJ 트리와 쿼리 1 +1 i c: i번 간선의 비용을 c로 바꾼다. +2 u v: u에서 v로 가는 단순 경로에 존재하는 비용 중에서 가장 큰 것을 출력한다. + +vi adj[N]; int par[N]; int sz[N]; int d[N]; +void dfs1(int s) { + sz[s] = 1; + for(auto it=adj[s].begin(); it!=adj[s].end(); it++) + if(*it == par[s]) {adj[s].erase(it); break;} + for(auto &i : adj[s]) { + par[i] = s; d[i] = d[s] + 1; + dfs1(i); sz[s] += sz[i]; + if(sz[i] > sz[adj[s][0]]) swap(adj[s][0], i); + } +} +int in[N], c; int top[N]; +void dfs2(int s) { + in[s] = ++c; + for(auto i : adj[s]) { + if(i == adj[s].front()) top[i] = top[s]; + else top[i] = i; + dfs2(i); + } +} + +int query(int a,int b) { + int ans = 0; + while(top[a] != top[b]) { + if(d[top[a]] > d[top[b]]) swap(a, b); + ans = max(ans, query(root, in[top[b]], in[b])); + b = par[top[b]]; + } + if(d[a] > d[b]) swap(a, b); + return max(ans, query(root, in[a]+1, in[b])); +} + +// dfs1(1); dfs2(1); +// forr(i, n) arr[in[i]] = m[{par[i], i}]; init(root, arr); +// q == 1: update(root, in[a], c); // in[a]를 c로 대체 +// q == 2: query(a, b); \ No newline at end of file diff --git a/2025fall/source/empty.cpp b/2025fall/source/empty.cpp new file mode 100644 index 0000000..e69de29 diff --git a/2025fall/source/poro.cpp b/2025fall/source/poro.cpp new file mode 100644 index 0000000..cf77aec --- /dev/null +++ b/2025fall/source/poro.cpp @@ -0,0 +1,3 @@ +mkdir {A..M} +alias solve='g++ main.cpp -o solve_exefile -g -fsanitize=undefined,address -fno-omit-frame-pointer -Wall -Wextra && echo "Compile Done" && time ./solve_exefile' +alias fast='g++ main.cpp -o solve_exefile -O2 -Wall && echo "Compile Done" && time ./solve_exefile' diff --git a/2025fall/source/qwerty.cpp b/2025fall/source/qwerty.cpp new file mode 100644 index 0000000..814825a --- /dev/null +++ b/2025fall/source/qwerty.cpp @@ -0,0 +1,7 @@ +#pragma GCC optimize("O3") +#pragma GCC optimize("Ofast") +#pragma GCC optimize("unroll-loops") + +#define endl '\n' +#define foreach(i, l, r) for(ll i=(l); i<=(r); i++) +#define forreach(i, l, r) for(ll i=l; i>=(r); i--) \ No newline at end of file diff --git a/2025fall/teamnote.sty b/2025fall/teamnote.sty new file mode 100644 index 0000000..9b2fc5d --- /dev/null +++ b/2025fall/teamnote.sty @@ -0,0 +1,114 @@ + +\ProvidesPackage{teamnote} + +\usepackage[left=1cm,right=1cm,top=2cm,bottom=1cm,a4paper]{geometry} +\usepackage{fancyhdr} +\usepackage{lastpage} +\usepackage{minted} +\usepackage{color} +\usepackage{indentfirst} +\usepackage{amssymb} +\usepackage{amsmath} +\usepackage{import} +\usepackage{caption} +\usepackage[table,xcdraw]{xcolor} +\usepackage[T1]{fontenc} +\usepackage{setspace} + +\setstretch{1} % No line-spacing + +\renewcommand{\@listI}{% No spacing on list +\leftmargin=25pt +\rightmargin=0pt +\labelsep=5pt +\labelwidth=20pt +\itemindent=0pt +\listparindent=0pt +\topsep=0pt plus 2pt minus 4pt +\partopsep=0pt plus 1pt minus 1pt +\parsep=0pt plus 1pt +\itemsep=\parsep} + +\setlength{\columnseprule}{0.4pt} +\pagenumbering{arabic} +\setminted{breaklines=true, tabsize=2, breaksymbolleft=} +\usemintedstyle{perldoc} + +\newcommand{\revised}{Should be \textcolor{red}{\textbf{revised}}.} +\newcommand{\tested}{Should be \textcolor{red}{\textbf{tested}}.} +\newcommand{\added}{Should be \textcolor{red}{\textbf{added}}.} +\newcommand{\WIP}{\textcolor{red}{\textbf{Working in progress.}}} + +\newcommand{\schoolname}{Some University} +\newcommand{\teamname}{Some Teamname} +\newcommand{\authorname}{Some Members} +\newcommand{\contestname}{Some Contest} + +\newcommand{\maketitlepage}{\maketitle + +\tableofcontents + +\thispagestyle{fancy} + +} +\DeclareRobustCommand{\teamnote}[4]{ + \renewcommand{\schoolname}{#1} + \renewcommand{\teamname}{#2} + \renewcommand{\authorname}{#3} + \renewcommand{\contestname}{#4} +} +\pagestyle{fancy} +% \lhead{\schoolname{} -- \teamname} +% \rhead{Page \thepage{} of +\rhead{\schoolname{} -- \teamname -- \contestname} +\lhead{Page \thepage{} of +\ifthenelse{\pageref{LastPage} < 26}{\pageref{LastPage}}{\textcolor{red}{\textbf{\pageref{LastPage}}}}} +\fancyfoot{} + +\title{Team Note of \teamname} +\author{\authorname} +\date{Compiled on \today} + + + + +\newboolean{BangShowUsage} +\setboolean{BangShowUsage}{false} +\newcommand{\ShowUsage}{\setboolean{BangShowUsage}{false}} +\newcommand{\HideUsage}{\setboolean{BangShowUsage}{true}} + + +\newboolean{BangShowComplexity} +\setboolean{BangShowComplexity}{false} +\newcommand{\ShowComplexity}{\setboolean{BangShowComplexity}{false}} +\newcommand{\HideComplexity}{\setboolean{BangShowComplexity}{true}} + + +\newboolean{BangShowAuthor} +\setboolean{BangShowAuthor}{false} +\newcommand{\ShowAuthor}{\setboolean{BangShowAuthor}{false}} +\newcommand{\HideAuthor}{\setboolean{BangShowAuthor}{true}} + +\newcommand{\Algorithm}[6]{ + \subsection{#1} + + \ifthenelse{\equal{#2}{} \OR \boolean{BangShowUsage}}{}{\textbf{Usage:} #2} + + \ifthenelse{\equal{#3}{} \OR \boolean{BangShowComplexity}}{}{\textbf{Time Complexity:} #3} + + \ifthenelse{\equal{#6}{} \OR \boolean{BangShowAuthor}}{}{\textbf{Author:} #6} + + \ifthenelse{\equal{#5}{}}{}{\ifthenelse{\equal{#4}{}}{\inputminted[]{cpp}{#5}}{\inputminted[]{#4}{#5}}} +} + 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-0,0 +1,939 @@ +\documentclass[landscape, 8pt, a4paper, oneside]{extarticle} +%\documentclass[portrait, 8pt, a4paper, oneside, twocolumn]{extarticle} +\usepackage{teamnote} + +\usepackage[hangul]{kotex} + +\usepackage[most]{tcolorbox} + +\usepackage{multirow} +\usepackage{adjustbox} +\usepackage{subfiles} +\usepackage{amsmath} + +\usepackage{etoolbox} +\AtBeginEnvironment{align*}{% + +\setlength{\abovedisplayskip}{0pt} +\setlength{\belowdisplayskip}{0pt} +\setlength{\abovedisplayshortskip}{0pt} +\setlength{\belowdisplayshortskip}{0pt} + +} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\usepackage{enumitem} + +\setlistdepth{9} +\newlist{IdeaNote}{enumerate}{6} +\setlist[IdeaNote]{topsep=0pt,itemsep=-1ex,partopsep=1ex,parsep=1ex} +\setlist[IdeaNote, 1]{label= \Roman*. } +\setlist[IdeaNote, 2]{label= \Alph*. } +\setlist[IdeaNote, 3]{label= \arabic*. } +\setlist[IdeaNote, 4]{label= \roman*) } +\setlist[IdeaNote, 5]{label= \alph*) } +\setlist[IdeaNote, 6]{label= \arabic*) } +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\usepackage{multicol} +\setlength\columnseprule{0.5pt} + +\teamnote{POSTECH}{ConForza}{} + +\ShowUsage +\ShowComplexity +\HideAuthor + +\begin{document} + +\begin{multicols}{3} + +\maketitlepage + +\par\noindent\rule{\columnwidth}{0.4pt} + +\section{Have you...} + +\subsection{tried...} + +\begin{itemize} + \item \textcolor{red}{\textbf{Reading the problem once more?}} + \item doubting ``obvious" things? + \item writing obivous things? + \item radical greedy approach? + \item thinking in reverse direction? + \item a greedy algorithm? + \item network flow when your greedy algorithms stuck? + \item a dynamic programming? + \item checking the range of answer? + \item random algorithm? + \item graph modeling using states? + \item inverting state only on odd indexes? + \item calculating error bound on a real number usage? +\end{itemize} + +\subsection{checked...} + +\begin{itemize} + \item \textcolor{red}{\textbf{you have read the statement correctly?}} + \item typo copying the team note? + \item initialization on multiple test case problem? + \item additional information from the problem? + \item undefined behavior? + \item overflow? + \item function without return value? + \item real number error? + \item implicit conversion? + \item comparison between signed and unsigned integer? +\end{itemize} + +% \pagebreak + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Algorithmic Idea Note} + +\begin{tcolorbox}[breakable, enhanced, sharp corners, colback=white, colframe=black, boxrule=1pt, left=0pt] + +\begin{IdeaNote} +\item Complete Search: Backtracking \& Pruning + +\item Math + \begin{IdeaNote} + \item Number Theory + \begin{IdeaNote} + \item Prime Number + \begin{IdeaNote} + \item Sieve of Eratosthenes, Prime Factorization + \item Fast Prime Verdict; Millar-Rabin + \item Fast Prime Factorization; Pollad Rho + \item Primitive Root + \end{IdeaNote} + \item Extended Euclidean Algorithm; Diophantos Equation + \item Chinese Remainder Theorem + \item Harmonic Lemma + \item Floor Sum (Sum of Rational Arithmetic Sequence) + \item Several Sieves + \end{IdeaNote} + \item Linear Programming + \begin{IdeaNote} + \item Solve (some) LP with Shortest Path + \end{IdeaNote} + \item FFT \& Polynomials + \begin{IdeaNote} + \item FFT : Convolution + \begin{IdeaNote} + \item High precision FFT with modulo 1e9+7 + \end{IdeaNote} + \item NTT : Number Theoretic Tranform + \item Quotient Ring (Formal Power Series) + \begin{IdeaNote} + \item Multiplication + \item FPS : Inverse / Division + \item Integration / Differentiation + \item FPS : Logarithm / Exponentiation + \item FPS : Power of Polynomial + \item Division - Quotient \& Remainder + \item Polynomial Taylor Shift + \item Multipoint Evaluation + \end{IdeaNote} + \end{IdeaNote} + \item Combinatorics + \begin{IdeaNote} + \item Labeled Combinatorial Target + \item The Twelvefold Way (12정도) + \item Generating Function + \begin{IdeaNote} + \item OGF(Ordinary Generating Function) + \item EGF(Exponentional Generating Function) + \item DGF?(Dirichlet Genetration Function) : Number Theory + \end{IdeaNote} + \item Umbral Calculus + \end{IdeaNote} + \end{IdeaNote} + +\item Linear Algebra + +\item Geometry + \begin{IdeaNote} + \item Basic Tools + \begin{IdeaNote} + \item Outer Product (CCW) + \item Sorting by Polar + \item Segment Intersection + \item Closest Point + \item Furthest Point + \end{IdeaNote} + \item Convex Polygon (Convex Hull) + \begin{IdeaNote} + \item Convex Hull Construction + \item Convex Layer + \item Rotating Calipers + \item Point Containment + \item Tangent to convex polygon + \item Inner and Outer Tangent of two Convex's + \end{IdeaNote} + \item General Polygon + \item Half Plane Intersection + \item Delaunay Triangulation : Voronoi diagram + \end{IdeaNote} + + +\item Greedy + \begin{IdeaNote} + \item Rearrangement Inequality + \end{IdeaNote} + +\item DP + \begin{IdeaNote} + \item DP Optimization + \begin{IdeaNote} + \item Convex Hull Trick + \item Alien's Trick (Lagrangian Relaxation) + \item Slope Trick + \end{IdeaNote} + \end{IdeaNote} + +\item String + \begin{IdeaNote} + \item KMP(Knuth-Morris-Pratt), Z, Manacher Algorithm + \item Trie + \item Aho-Corasick + \item Suffix Array \& LCP Array + \item Eertree + \item Wavelet Tree + \end{IdeaNote} + +\item Graph + \begin{IdeaNote} + \item Searching : DFS/BFS + \item DAG(Directed Acyclic Graph) : Topological Sorting + \item MST(Minimum Spanning Tree) + \begin{IdeaNote} + \item Kruskal Algorithm + \item Prim Algorithm + \item Euclidian MST + \end{IdeaNote} + \item Shortest Path + \begin{IdeaNote} + \item Dijkstra Algorithm + \item Bellman-Ford Algorithm + \item Floyd-Warshall Algorithm + \item Shortest Path DAG + \end{IdeaNote} + \item Connectivity + \begin{IdeaNote} + \item Offline Dynamic Connectivity (Odc) + \item Online Dynamic Connectivity + \begin{IdeaNote} + \item Euler Tour Tree + \item Top Tree + \end{IdeaNote} + \end{IdeaNote} + \item DFS tree + \begin{IdeaNote} + \item SCC(Strongly Connected Component) + \begin{IdeaNote} + \item Graph Compression + \item 2-SAT Problem + \item Offline Incremental SCC + \end{IdeaNote} + \item BCC (BiConnected Component) + \begin{IdeaNote} + \item Blcok Cut Tree + \item Cactus Graph + \end{IdeaNote} + \item Articulation Points and Bridges + \end{IdeaNote} + \item Network Flow + \begin{IdeaNote} + \item Ford-Fulkerson/Edmonds-Karp Algorithm + \item Dinic's Algorithm + \item Push-Relabel Algorithm + \item MCMF(Minimum Cost Maximum Flow) + \item Minimum s-t Cut = Maximum Flow + \item Bipartite Matching + \begin{IdeaNote} + \item Minimum Vertex Cover on Bipartite + \item Maximum Independent Set on Bipartite + \item Minimum Path Cover on DAG + \item Maximum Antichain on DAG + \end{IdeaNote} + \item Circulation + \item General Matching + \end{IdeaNote} + \item Treewidth + \end{IdeaNote} + +\item Tree + \begin{IdeaNote} + \item LCA(Lowest Common Ancestor) + \item Heavy-Light Decomposition + \item Centroid Decomposition + \item Link-Cut Tree + \end{IdeaNote} + +\item Data Structure + \begin{IdeaNote} + \item C++ Standard Library + \begin{IdeaNote} + \item Stack, Queue, List, Vector, Deque + \item Priority Queue; Heap + \item Set, Map : Binary Search Tree + \item Unordered Set, Unordered Map : Hashing + \item PBDS(Policy-Based Data Structure) + \item Rope (Cord) + \end{IdeaNote} + \item Disjoint Set (Unoin-Find structure) + \begin{IdeaNote} + \item Union by Rank / Path Compression + \item UF with LCA (Making Root) + \item UF with Edge Weight + \item UF with Unjoining + \begin{IdeaNote} + \item Unjoin from latest (Stack undoing) + \item Unjoin from earliest (Queue undoing) + \item Unjoin by Priority (Priority undoing) + \end{IdeaNote} + \end{IdeaNote} + \item Sparse Table + \item Range Query Structure + \begin{IdeaNote} + \item Square Root Decomposition + \item Fenwick Tree + \item Segment Tree + \begin{IdeaNote} + \item Lazy Propagation \& Generalization + \item 금광 ST (Maximum Adjacent Sum of Given Range) + \item PST (Persistent Segment Tree) + \item MST (Merge Sort Tree) + \item Segment Tree on Tree (HLD) + \item Li-Chao Tree (Segment Add Get Min) + \item ST Beats + \item Kinetic ST + \end{IdeaNote} + \item Splay Tree + \begin{IdeaNote} + \item Range Reverse / Range Shift + \end{IdeaNote} + \end{IdeaNote} + \end{IdeaNote} + +\item Sorting \& Searching + \begin{IdeaNote} + \item Sorting + \item Searching + \begin{IdeaNote} + \item Binary Search : Monotone Sequence / function + \begin{IdeaNote} + \item Lower bount / Upper bound + \item LIS (Longest Increasing Subsequence) + \item PBS (Parallel Binary Search) + \end{IdeaNote} + \item Ternary Search : Unimodal Sequence / function + \begin{IdeaNote} + \item Fibonacci Search (Golden Ratio Search) + \end{IdeaNote} + \end{IdeaNote} + \end{IdeaNote} + +\item Numerical Analysis + \begin{IdeaNote} + \item Numerical Differentiation + \item Gradient Descent + \end{IdeaNote} + +\item Technic + \begin{IdeaNote} + \item Coordinate Compression + \item Two Pointer/Sliding Window + \item Sweeping + \item Meet in the Middle + \item Bitmasking + \item Small to Large + \item Randomization + \begin{IdeaNote} + \item Verifying Matrix Multiplication + \end{IdeaNote} + \item Query Technic + \begin{IdeaNote} + \item Offline Query + \begin{IdeaNote} + \item Mo's Algorithm + \end{IdeaNote} + \end{IdeaNote} + \end{IdeaNote} + +\end{IdeaNote} + +\end{tcolorbox} + +\Algorithm{astilate} +{}{}{cpp}{source/Fundemental.cpp} + +\Algorithm{qwerty} +{}{}{cpp}{source/qwerty.cpp} + +\subsection{Tips for Inequality with Rational Number} +Let $A$, $B$, $x$, $n$ be integer, and operator `/' means floor division(quotient). +\begin{align*} + Ax \leqslant B & \Leftrightarrow x \leqslant B/A \\ + Ax < B & \Leftrightarrow x \leqslant (B-1)/A \\ + Ax \geqslant B & \Leftrightarrow x \geqslant (B+A-1)/A \\ + Ax > B & \Leftrightarrow x \geqslant B/A+1 \\ \\ + x < n & \Leftrightarrow x+1\leqslant n +\end{align*} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + +\section{Math} +\subfile{source/Math/math} +\subsection{Prime Number} + +\subsubsection{Distribution of Prime Number} + +\begin{center} + \begin{tabular}{| + >{\columncolor[HTML]{BFBFBF}}c |c| + >{\columncolor[HTML]{BFBFBF}}c |c| + >{\columncolor[HTML]{BFBFBF}}c |c|} + \hline + 1e2 & 25 & 1e6 & 78,498 & 1e10 & \textless 5e8 \\ \hline + 1e3 & 168 & 1e7 & 664,579 & 1e11 & \textless 5e9 \\ \hline + 1e4 & 1,229 & 1e8 & \textless 6e6 & 1e12 & \textless 4e10 \\ \hline + 1e5 & 9,592 & 1e9 & \textless 6e7 & 1e13 & \textless 4e11 \\ \hline + \end{tabular} +\end{center} + +\subsubsection{Prime Gap} +\begin{align*} + 2 \cdot 10^{5} \text{ 이하의 소수 간극 } &\le 100\\ + 2^{32} \text{ 이하의 소수 간극 } &\le 464 \\ + 2^{64} \text{ 이하의 소수 간극 } &\le 1550 +\end{align*} + +\Algorithm{Miller-Rabin Algorithm} +{\texttt{is\_p(X)} : returns true if $X$ is prime, otherwise false. +\begin{align*} +\text{ When } X \le 2^{32}, D &= \{2, 7, 61\} \text{ is sufficient; } \\ +X \le 2^{64}, D &= \{p | p \text{ is prime}, p \le 37 \} \text{ is sufficient.} +\end{align*}} +{$\mathcal O (\log^3 X)$} +{cpp} +{source/Math/MillerRabin.cpp} + +\Algorithm{Pollad Rho Algorithm} +{ \texttt{po\_rho(N)} : returns array of prime factors of X.} +{$\mathcal O (N^{1/4})$} +{cpp} +{source/Math/PolladRho.cpp} + +\Algorithm{Primitive Root} +{Calculate one of the primitive roots of given prime.} +{}{cpp} +{source/Math/PrimitiveRoot.cpp} + +\Algorithm{Diopantos Equation(Extended Euclidian Algorithm)} +{\texttt{diophantos(a, b)} : return one integer solution of $ax+by=1$, satisfying $0 \le x < b$. } +{$\mathcal O \left(\log \left( \max(a, b) \right) \right)$} +{cpp} +{source/Math/Diophantos.cpp} + +\Algorithm{Chinese Remainder Theorem} +{\texttt{crt(pll p, pll q)} : return \texttt{pll r}, satisfying follows: +\begin{align*} + x &\equiv \texttt{p.fi} \mod \texttt{p.se} \\ +\text{and } x &\equiv \texttt{q.fi} \mod \texttt{q.se} \\ + \leftrightarrow x &\equiv \texttt{r.fi} \mod \texttt{r.se} +\end{align*} +If there's no such \texttt{r}, return $\{-1, -1\}$. +} +{$\mathcal O(\log A)$} +{cpp} +{source/Math/CRT.cpp} + +\Algorithm{Harmonic Lemma} +{\texttt{f(N)} : return the value +$$\sum_{i=1}^{N} \left\lfloor \frac{N}{i} \right\rfloor = \left\lfloor \frac{N}{1}\right\rfloor + \left\lfloor \frac{N}{2} \right\rfloor + \cdots + \left\lfloor \frac{N}{N}\right\rfloor $$ +Using the fact that $\left\lfloor \frac{N}{x} \right\rfloor$ has $\mathcal O(\sqrt N)$ different values.} +{$\mathcal O(\sqrt N )$} +{cpp} +{source/Math/Harmonic.cpp} + +\Algorithm{Floor Sum (Sum of Floor of Rational Arithmetic Sequence)} +{\texttt{floor\_sum(A, B, C, N)} : return the value +$$\sum_{x=0}^{N-1} \left\lfloor \frac{Ax+B}{C} \right\rfloor $$} +{$\mathcal O(\log N)$} +{cpp} +{source/Math/FloorSum.cpp} + +\Algorithm{FFT - Convolution} +{} +{$\mathcal O (N\log N)$} +{cpp} +{source/Math/FFTConv.cpp} + + + +\Algorithm{NTT - Number Theoretic Transform} +{helloworld} +{} +{cpp} +{source/Math/NTT.cpp} + +\subsubsection{Good prime numbers to run NTT} +\begin{center} +\begin{adjustbox}{width=0.8\columnwidth} +\begin{tabular}{|c|c| +>{\columncolor[HTML]{C0C0C0}}l |} +\hline +595 591 169 & 71\textless{}\textless{}23|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +645 922 817 & 77\textless{}\textless{}23|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +897 581 057 & 107\textless{}\textless{}23|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +998 244 353 & 119\textless{}\textless{}23|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +1 300 234 241 & 155\textless{}\textless{}23|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +1 224 736 769 & 73\textless{}\textless{}24|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +2 130 706 433 & 127\textless{}\textless{}24|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +167 772 161 & 5\textless{}\textless{}25|1 & \cellcolor[HTML]{C0C0C0} \\ \cline{1-2} +469 762 049 & 7\textless{}\textless{}26|1 & \multirow{-9}{*}{\cellcolor[HTML]{C0C0C0}$\omega$ = 3} \\ \hline +\end{tabular} +\end{adjustbox} +\end{center} + +\Algorithm{Polynomial (Formal Power Series)} +{} +{} +{cpp} +{source/Math/Polynomial.cpp} + +\subsection{Combinatorics} +\subsubsection{Labeled Combinatorial Target} +\begin{itemize} + \item Permutation, Combination (with, w/o repetition) + \begin{itemize} + \item Permutation $_nP_r = \frac{n!}{r!(n-r)!}$ + \item Combination $_nC_r = \binom n k = \frac{n!}{r!}$ + \item Permutation with repetition $_n\Pi_r = n^r$ + \item Combination with repetition $_nH_r = _{n+r-1}C_r$ + \end{itemize} + \item Catalan Number $C_n$ : the number of regular bracket string of length $2n$. + \begin{itemize} + \item $C_n = \frac{1}{n+1}\binom {2n}n$ + \item $C_n : 1, 1, 2, 5, 14, 42, 132,429,1430,\cdots$ (from index 0) + \item OGF of $C_n$ : $c(x) = 1+xc(x)^2, c(c) = \frac{1-\sqrt{1-4x}}{2x}$ + \item Catalan's triangle $C(n, k)$ : the number of string with $n$ X's, $k$ Y's, where the number of Y's is not greater than the number of X's when written down the string. + \begin{itemize} + \item i.e. $C(4, 3)$ : XXXXYYY, XXYXYYX are OK, but XXYYYXX is not OK. + \item $C(n, k) = \binom{n+k}{k} - \binom{n+k}{k-1} = \frac{n-k+1}{n+1}\binom{n+k}{k}$ + \item We can give the condition relax : $C_m(n, k)$ : the number of string with $n$ X's, $k$ Y's, where the number of Y's is not greater than (the number of X's) + $m$ when written down the string. + \item $C_m(n, k) = \binom{n+k}{k}-\binom{n+k}{k-m}$ when $m\leqslant k \leqslant n+m-1$. + \item $C_1(n, k) = C(n, k)$ + \end{itemize} + \end{itemize} + \item Derangement(교란순열) $D_n$ : the number of permutation of length $n$ which $\forall i\;p_i \neq i$. + \begin{itemize} + \item $D_n : 1, 0, 1, 2, 9, 44, 265, 1854, 14833, 133496,1334961 \cdots$ (from index 0) + \item EGF of $D_n$ : $D(x) = \sum_{n=0} \frac{D_n}{n!}x^n = \frac{e^{-x}}{1-x}$ + \end{itemize} + \item Stirling Number of the 1st/2nd kind. + \begin{itemize} + \item Unsigned Stirling Number of the 1st kind $c(n, k) = {n \brack k}$ : the number of permutation of length n with k disjoint cycles. + \begin{itemize} + \item $c(n+1, k) = n \times c(n, k) + c(n, k-1)$ + \item with boundary condition $c(0, 0) = 1, c(n, 0) = c(0, k) = 0 \; \forall n, k>0$ + \item $c(n, k)$\\ + \begin{tabular}{| +>{\columncolor[HTML]{ECECEC}}r | +>{\columncolor[HTML]{F8F9FA}}r |r|r|r|l|l|l|} +\hline +\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} \textit{n\textbackslash{}k}} & \cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{0}} & \cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{1}} & \cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{2}} & \cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{3}} & \multicolumn{1}{r|}{\cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{4}}} & \multicolumn{1}{r|}{\cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{5}}} & \multicolumn{1}{r|}{\cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{6}}} \\ \hline +{\color[HTML]{202122} \textbf{0}} & {\color[HTML]{202122} 1} & \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{} & & & \\ \hline +{\color[HTML]{202122} \textbf{1}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{} & & & \\ \hline +{\color[HTML]{202122} \textbf{2}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \multicolumn{1}{l|}{} & & & \\ \hline +{\color[HTML]{202122} \textbf{3}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 2} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 3} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & & & \\ \hline +{\color[HTML]{202122} \textbf{4}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 6} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 11} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 6} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1}} & & \\ \hline +{\color[HTML]{202122} \textbf{5}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 24} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 50} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 35} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 10}} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1}} & \\ \hline +{\color[HTML]{202122} \textbf{6}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 120} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 274} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 225} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 85}} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 15}} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1}} \\ \hline +\end{tabular} + \item OGF of ${n \brack k}$ : for fixed $n$, $\sum_{k=0}^n {n \brack k} x^k = x(x+1)(x+2)\cdots(x+n-1)$ : we can calculate it by polynomial shift \& divide and conquer + \item EGF of ${n \brack k}$ : for fixed $k$, $\sum_{n=k}^\infty {n \brack k} \frac{x^n}{n!} = \frac{(-\log(1-z))^k}{k!} $ + \item Signed Stirling Number of the 1st kind $s(n, k) = (-1)^{n-k}c(n, k)$ + \item EGF of $s(n, k)$ : for fixed $k$, $\sum_{n=k}^\infty s(n, k) \frac{x^n}{n!} = \frac{(\log(1+z))^k}{k!} $ + \end{itemize} + \item Stirling Number of the 2nd kind $S(n, k) = {n \brace k}$ : the number of partition of $n$ labeled objects into $k$ nonempty unlabelled subsets. + \begin{itemize} + \item $S(n, k) = \frac{1}{k!}\sum_{i=0}^k(-1)^{k-i}\binom{k}{i}i^n$ + \item $S(n, k)$\\ + \begin{tabular}{| +>{\columncolor[HTML]{ECECEC}}r | +>{\columncolor[HTML]{F8F9FA}}r |r|r|r|l|l|l|} +\hline +\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} \textit{\textbf{n\textbackslash{}k}}} & \cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{0}} & \cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{1}} & \cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{2}} & \cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{3}} & \multicolumn{1}{r|}{\cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{4}}} & \multicolumn{1}{r|}{\cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{5}}} & \multicolumn{1}{r|}{\cellcolor[HTML]{ECECEC}{\color[HTML]{202122} \textbf{6}}} \\ \hline +{\color[HTML]{202122} \textbf{0}} & {\color[HTML]{202122} 1} & \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{} & & & \\ \hline +{\color[HTML]{202122} \textbf{1}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \multicolumn{1}{l|}{} & \multicolumn{1}{l|}{} & & & \\ \hline +{\color[HTML]{202122} \textbf{2}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \multicolumn{1}{l|}{} & & & \\ \hline +{\color[HTML]{202122} \textbf{3}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 3} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & & & \\ \hline +{\color[HTML]{202122} \textbf{4}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 7} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 6} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1}} & & \\ \hline +{\color[HTML]{202122} \textbf{5}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 15} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 25} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 10}} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1}} & \\ \hline +{\color[HTML]{202122} \textbf{6}} & {\color[HTML]{202122} 0} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 31} & \cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 90} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 65}} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 15}} & \multicolumn{1}{r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} 1}} \\ \hline +\end{tabular} + \item OGF of ${n \brace k}$ : for fixed $n$, $\sum_{k=0}^n{n\brace k}x^k=T_n(x)$, where $T_n(x) = e^{-x}\sum_{k=0}^{\infty}\frac{k^n}{k!}x^k$ is Touchard Polynomials. + \item EGF of ${n \brace k}$ : for fixed $k$, $\sum_{n=k}^\infty{n\brace k}x^n=\frac{(e^x-1)^k}{k!}$ + \end{itemize} + \end{itemize} + \item + \item Bell Number $B_n$ : the number of partition of set with size $n$. + \begin{itemize} + \item i.e. partitionize $\{a, b, c\}$ is $\{\{a\}, \{b\}, \{c\}\}, \{\{a , b\}, \{c\}\}$, $\{\{b, c\}, \{a\}\}, \{\{c, a\}, \{b\}\}, \{\{a, b, c\}\}$. Therefore, $B_3 = 5$. + \item $B_n : 1,1,2,5,15,52,203,877,4140,\cdots$ (from index 0) + \item $B_n = \sum_{k=0}^n{n \brace k}$ (2nd kind of stirling number) + \item EGF of $B_n$ : $B(x) = \sum_{n=0}\frac{B_n}{n!}x^n=e^{e^x-1}$ + \item Ordered Bell Number(Fubini Number) $a_n$ : the number of distinct weak ordering on a set of n elements. + \begin{itemize} + \item $a_n : 1, 1, 3, 13, 75, 541, 4683, 47293, 545835, 7087261, \cdots$ + \item $a_n = \sum_{k=0}^nk!{n \brace k}$ (stirling number of the 2nd kind) + \item EGF of $a_n$ : $a(x) = \sum_{n=0}^\infty \frac{a_n}{n!}x^n = \frac{1}{2-e^x}$ + \end{itemize} + \end{itemize} + \item Integer Partition $P(n, k)$ : the number of partitions of $n$ into exactly $k$ parts. + \begin{itemize} + \item i.e. $P(4, 2) = 2$ since $4 = 1+3 = 2+2$ + \item we also say $P(n) = \sum_{k=1}^{n}P(n, k)$ + \item $P(n, k)$\\ + \begin{tabular}{| +>{\columncolor[HTML]{EAECF0}}c | +>{\columncolor[HTML]{F8F9FA}}l | +>{\columncolor[HTML]{F8F9FA}}l | +>{\columncolor[HTML]{F8F9FA}}l | +>{\columncolor[HTML]{F8F9FA}}l | +>{\columncolor[HTML]{F8F9FA}}l | +>{\columncolor[HTML]{F8F9FA}}l | +>{\columncolor[HTML]{F8F9FA}}l | +>{\columncolor[HTML]{F8F9FA}}l | +>{\columncolor[HTML]{F8F9FA}}l |} +\hline +\multicolumn{1}{|r|}{\cellcolor[HTML]{F8F9FA}{\color[HTML]{202122} \textit{\textbf{n\textbackslash{}k}}}} & \multicolumn{1}{c|}{\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{1}}} & \multicolumn{1}{c|}{\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{2}}} & \multicolumn{1}{c|}{\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{3}}} & \multicolumn{1}{c|}{\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{4}}} & \multicolumn{1}{c|}{\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{5}}} & \multicolumn{1}{c|}{\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{6}}} & \multicolumn{1}{c|}{\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{7}}} & \multicolumn{1}{c|}{\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{8}}} & \multicolumn{1}{c|}{\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{9}}} \\ \hline +{\color[HTML]{202122} \textbf{1}} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } \\ \hline +{\color[HTML]{202122} \textbf{2}} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } \\ \hline +{\color[HTML]{202122} \textbf{3}} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } \\ \hline +{\color[HTML]{202122} \textbf{4}} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 2} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } \\ \hline +{\color[HTML]{202122} \textbf{5}} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 2} & {\color[HTML]{202122} 2} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } \\ \hline +{\color[HTML]{202122} \textbf{6}} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 3} & {\color[HTML]{202122} 3} & {\color[HTML]{202122} 2} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} } & {\color[HTML]{202122} } & {\color[HTML]{202122} } \\ \hline +{\color[HTML]{202122} \textbf{7}} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 3} & {\color[HTML]{202122} 4} & {\color[HTML]{202122} 3} & {\color[HTML]{202122} 2} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} } & {\color[HTML]{202122} } \\ \hline +{\color[HTML]{202122} \textbf{8}} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 4} & {\color[HTML]{202122} 5} & {\color[HTML]{202122} 5} & {\color[HTML]{202122} 3} & {\color[HTML]{202122} 2} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} } \\ \hline +{\color[HTML]{202122} \textbf{9}} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 4} & {\color[HTML]{202122} 7} & {\color[HTML]{202122} 6} & {\color[HTML]{202122} 5} & {\color[HTML]{202122} 3} & {\color[HTML]{202122} 2} & {\color[HTML]{202122} 1} & {\color[HTML]{202122} 1} \\ \hline +\end{tabular} + \end{itemize} + \item 12정도(the Twelvefold Way) : the number of functions \\ + (Domain $|N| = n$, Codomain $|X| = x$)\\ + \begin{tabular}{| +>{\columncolor[HTML]{F8F9FA}}c |c|c|c|} +\hline +\cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textit{\textbf{$f$-class}}} & \cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{Any $f$}} & \cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{Injective}} & \cellcolor[HTML]{EAECF0}{\color[HTML]{202122} \textbf{Surjective}} \\ \hline +{\color[HTML]{202122} \textbf{Distinct $f$}} & \textit{$_n\Pi_x$} & \textit{$_xP_n$} & $x!{x\brace n}$ \\ \hline +{\color[HTML]{202122} \textit{\textbf{\begin{tabular}[c]{@{}c@{}}$S_n$ orbits\\ $f \circ S_n$\end{tabular}}}} & \textit{$_xH_n$} & \textit{$_xC_n$} & $_{n-1}C_{n-x}$ \\ \hline +{\color[HTML]{202122} \textit{\textbf{\begin{tabular}[c]{@{}c@{}}$S_x$ orbits\\ $S_x \circ f$\end{tabular}}}} & $\sum_{k=0}^x {n \brace k}$ & $[n \leqslant x]$ & ${n \brace x}$ \\ \hline +{\color[HTML]{202122} \textit{\textbf{\begin{tabular}[c]{@{}c@{}}$S_n\times S_x$ orbits\\ $S_x \circ f \circ S_n$\end{tabular}}}} & $P(n+x, x)$ & $[n \leqslant x]$ & $P(n, x)$ \\ \hline +\end{tabular} +\end{itemize} + +\Algorithm{General Lucas Comb} +{} +{} +{cpp} +{source/Math/general_lucas.cpp} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Linear Algebra} +\Algorithm{Matrix} +{} +{} +{cpp} +{"source/Linear Algebra/Matrix.cpp"} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Geometry} +\Algorithm{Mindset} +{} +{} +{cpp} +{source/Geometry/Mindset.cpp} + +% \Algorithm{Point in Convex Polygon} +% {\texttt{isunder(upper\_hull[], (length of upper\_hull), x)} : return true if $x$(point) is under upper\_hull, otherwise false; + +% \texttt{isunder(lower\_hull[], (length of lower\_hull), x, true)} : return true if $x$(point) is over lower\_hull, otherwise false. + +% Point in Polygon : isunder(upper, u, x) \&\& isupper(lower, u, x, true)} +% {} +% {cpp} +% {source/Geometry/PointInConvexPolygon.cpp} + +\Algorithm{kactl templete} +{} +{} +{cpp} +{source/Geometry/geometry_kaere.cpp} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{Greedy} +\subsection{Rearrange Inequality - Extensions} +Let $A_i, B_i$ be non-decreasing sequence of length $n$, and $p$ be some permutation, and let $inc := (1, 2, \dots, n-1, n), \;dec := (n, n-1, \dots, 2, 1)$. + +\begin{align*} +S(p) &= \sum_{i=1}^n A_i B_{p_i} + && \text{ maximize } S &&&\Rightarrow p : inc&&&&\\ + & && \text{ minimize } S &&&\Rightarrow p:dec&&&&\\ +P_{max}(p) &= \max_i(A_iB_{p_i}) + && \text{ minimize } P_{max} &&&\Rightarrow p : dec&&&&\\ +P_{min}(p) &= \min_i(A_iB_{p_i}) + && \text{ maximize } P_{min} &&&\Rightarrow p:dec&&&&\\ +A_{max}(p) &= \max_i(A_i+B_{p_i}) && \text +{ minimize } A_{max} &&& \Rightarrow p:dec&&&&\\ +A_{min}(p) &= \min_i(A_i+B_{p_i}) && \text{ maximize } A_{min} &&& \Rightarrow p:dec&&&&\\ +D_{max}(p) &= \max_i|A_i-B_{p_i}| && \text{ minimize } D_{max} &&& \Rightarrow p:inc&&&&\\ +D_{min}(p) &= \min_i|A_i-B_{p_i}| && \text{ maximize } D_{min} &&& \Rightarrow p:?&&&&\\ +\end{align*} +\begin{align*} + \text{ Permutate } A \text{ s.t.} \text{ maximize } & \sum_{i=1}^n {A_i A_{i+1}} \;(\text{Let } A_{n+1} = A_1) \\ &\Rightarrow \text{ Pendulum Arrangement } +\end{align*} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\section{DP} + +\Algorithm{LIS} +{}{}{cpp}{source/DP/LIS.cpp} + +\subsection{DP Optimization} + +\subsubsection{Convex Hull Optimization} +\begin{align*} + \text{ Recurrence : }& D[i] = \min_{j e) return; + int m = s + e >> 1; + int opt = l; + for(int i=l; i<=r; i++){ + if(D[t-1][opt] + C[opt][m] > D[t-1][i] + C[i][m]) opt = i; + } + D[t][m] = D[t-1][opt] + C[opt][m]; + f(t, s, m-1, l, opt); + f(t, m+1, e, opt, r); +} \ No newline at end of file diff --git a/2025spring/source/DP/LIS.cpp b/2025spring/source/DP/LIS.cpp new file mode 100644 index 0000000..a59118a --- /dev/null +++ b/2025spring/source/DP/LIS.cpp @@ -0,0 +1,17 @@ +template vi lis(const vector& S) { + if (S.empty()) return {}; + vi prev(sz(S)); + typedef pair p; + vector

res; + rep(i,0,sz(S)) { + // change 0 -> i for longest non-decreasing subsequence + auto it = lower_bound(all(res), p{S[i], 0}); + if (it == res.end()) res.emplace_back(), it = res.end()-1; + *it = {S[i], i}; + prev[i] = it == res.begin() ? 0 : (it-1)->second; + } + int L = sz(res), cur = res.back().second; + vi ans(L); + while (L--) ans[L] = cur, cur = prev[cur]; + return ans; +} \ No newline at end of file diff --git a/2025spring/source/DP/LineContainer.cpp b/2025spring/source/DP/LineContainer.cpp new file mode 100644 index 0000000..9f510ad --- /dev/null +++ b/2025spring/source/DP/LineContainer.cpp @@ -0,0 +1,30 @@ +struct Line { + mutable ll k, m, p; + bool operator<(const Line& o) const { return k < o.k; } + bool operator<(ll x) const { return p < x; } +}; + +struct LineContainer : multiset> { + // (for doubles, use inf = 1/.0, div(a,b) = a/b) + static const ll inf = LLONG_MAX; + ll div(ll a, ll b) { // floored division + return a / b - ((a ^ b) < 0 && a % b); } + bool isect(iterator x, iterator y) { + if (y == end()) return x->p = inf, 0; + if (x->k == y->k) x->p = x->m > y->m ? inf : -inf; + else x->p = div(y->m - x->m, x->k - y->k); + return x->p >= y->p; + } + void add(ll k, ll m) { + auto z = insert({k, m, 0}), y = z++, x = y; + while (isect(y, z)) z = erase(z); + if (x != begin() && isect(--x, y)) isect(x, y = erase(y)); + while ((y = x) != begin() && (--x)->p >= y->p) + isect(x, erase(y)); + } + ll query(ll x) { + assert(!empty()); + auto l = *lower_bound(x); + return l.k * x + l.m; + } +}; \ No newline at end of file diff --git a/2025spring/source/DP/SlopeTrick.cpp b/2025spring/source/DP/SlopeTrick.cpp new file mode 100644 index 0000000..0358db9 --- /dev/null +++ b/2025spring/source/DP/SlopeTrick.cpp @@ -0,0 +1,52 @@ +const int N = 1e6+7; +int arr[N]; +priority_queue pq; +ll ans = 0; +int main() +{ + getint(n); + forr(i, n) scanf("%d", arr+i); + + pq.push(arr[1]); int t=0; ll val = 0; + fors(i, 2, n) + { + t++; + int r = t + pq.top(); + if(r <= arr[i]) pq.push(arr[i]-t); + else + { + pq.push(arr[i]-t); pq.push(arr[i]-t); pq.pop(); + ans += r-arr[i]; + } + } + + printf("%lld", ans); +} + + +int arr[N]; +priority_queue pq; +int ans2[N]; +int main() +{ + getint(n); + forr(i, n) scanf("%d", arr+i); + + pq.push(arr[1]); ll ans = 0; + ans2[1] = arr[1]; + fors(i, 2, n) + { + int r = (i-1) + pq.top(); + if(r <= arr[i]) pq.push(arr[i]-(i-1)); + else + { + pq.push(arr[i]-(i-1)); pq.push(arr[i]-(i-1)); pq.pop(); + ans += r-arr[i]; + } + + ans2[i] = pq.top() + (i-1); + } + + fore(i, n-1, 1) ans2[i] = min(ans2[i], ans2[i+1]-1); + forr(i, n) printf("%d\n", ans2[i]); +} \ No newline at end of file diff --git a/2025spring/source/DP/SoS.cpp b/2025spring/source/DP/SoS.cpp new file mode 100644 index 0000000..a842eb5 --- /dev/null +++ b/2025spring/source/DP/SoS.cpp @@ -0,0 +1,22 @@ +int n = 20; +vector a(1 << n); + +// keeps track of the sum over subsets +// with a certain amount of matching bits in the prefix +vector> dp(1 << n, vector(n)); + +vector sos(1 << n); +for (int mask = 0; mask < (1 << n); mask++) { + dp[mask][-1] = a[mask]; + for (int x = 0; x < n; x++) { + dp[mask][x] = dp[mask][x - 1]; + if (mask & (1 << x)) { dp[mask][x] += dp[mask - (1 << x)][x - 1]; } + } + sos[mask] = dp[mask][n - 1]; +} + +//////////////////////////////////////////// +D[i]에 미리 i에 해당하는 값을 넣어둔다 +fors(d, 0, 19) fors(i,0,(1<<20)-1) + if(i & (1< D[i] : sum of subset of mask i \ No newline at end of file diff --git a/2025spring/source/DS/Fenwick.cpp b/2025spring/source/DS/Fenwick.cpp new file mode 100644 index 0000000..42bd6ef --- /dev/null +++ b/2025spring/source/DS/Fenwick.cpp @@ -0,0 +1,9 @@ +ll tree[N]; +void update(int i,ll x) { + while(i < N) tree[i] += x, i += i&-i; +} +int query(int i) { + ll s = 0; + while(i) s += tree[i], i -= i&-i; + return s; +} \ No newline at end of file diff --git a/2025spring/source/DS/LiChaoTree.cpp b/2025spring/source/DS/LiChaoTree.cpp new file mode 100644 index 0000000..a622fdb --- /dev/null +++ b/2025spring/source/DS/LiChaoTree.cpp @@ -0,0 +1,69 @@ +struct Line +{ + ll a=0, b=(ll)2e18+7; + ll operator()(ll x){return a*x+b;} + Line():a(0),b((ll)2e18+7){} + Line(ll a, ll b):a(a), b(b){} +}; + +ll middle(ll s, ll e){return (s+e+(ll)2e18)/2-(ll)1e18;} +struct Node { + Node *l=0, *r=0; + Line v; + Node():l(0), r(0), v(Line()){} +}; +void insert(Node* node, Line v, ll l, ll r, ll s, ll e) { + ll mid=middle(s, e); + if(e < l or r < s) return; + if(s == e) { + node->v = (node->v(s) < v(s))?node->v:v; + return; + } + if(!node->l) node->l = new Node(); + if(!node->r) node->r = new Node(); + + if(l <= s and e <= r) { + if(node->v(s) >= v(s) and node->v(e) >= v(e)){node->v = v; return;} + if(node->v(s) <= v(s) and node->v(e) <= v(e)) return; + insert(node->l, v, l, r, s, mid); + insert(node->r, v, l, r, mid+1, e); + } + else { + insert(node->l, v, l, r, s, mid); + insert(node->r, v, l, r, mid+1, e); + } +} +ll query(Node* node, ll x, ll s, ll e) +{ + if(!node) return (ll)2e18+7; + if(x < s or e < x) return (ll)2e18+7; + if(s == e) return node->v(x); + + ll mid = middle(s, e); + return min({query(node->l, x, s,mid), query(node->r, x, mid+1, e), node->v(x)}); +} +// 전체 구간을 미리 고정해 놓아야 함. +// (const int L = -1e9, R = 1e9); +// Insert : insert(root, Line 객체, l, r, L, R); +// Query : query(root, x, L, R); +int main() { + Node *root = new Node(); + getint(n); getint(Q); + forr(i, n) { + getll(l); getll(r); getll(a); getll(b); + insert(root, Line(a,b), l,r-1,(ll)-1e9-7, (ll)1e9+7); + } + while(Q--) { + getint(q); + if(q == 0) { + getll(l); getll(r); getll(a); getll(b); + insert(root, Line(a,b), l,r-1,(ll)-1e9-7, (ll)1e9+7); + } + if(q == 1) { + getll(x); + ll ans = query(root, x,(ll)-1e9-7, (ll)1e9+7); + if(ans == (ll)2e18+7) printf("INFINITY\n"); + else printf("%lld\n", ans); + } + } +} \ No newline at end of file diff --git a/2025spring/source/DS/PBDS.cpp b/2025spring/source/DS/PBDS.cpp new file mode 100644 index 0000000..f869d81 --- /dev/null +++ b/2025spring/source/DS/PBDS.cpp @@ -0,0 +1,37 @@ +#include +#include +#include +#include +using namespace __gnu_pbds; +using namespace __gnu_cxx; + +template +using indexed_set = tree, rb_tree_tag, tree_order_statistics_node_update>; + +indexed_set s; +s.insert(3); s.insert(2); s.insert(3); s.insert(9); s.insert(7); //2 3 7 9 +s.insert(5); //2 3 5 7 9 +s.erase(5); //2 3 7 9 + +auto x = s.find_by_order(2); // *x : 7 + +s.order_of_key(6) // 2 +s.order_of_key(7) // 2 +s.order_of_key(8) // 3 + +///////////////////////////////////////////////////////////// +// greater_equal <- ordered_multiset / greater <- ordered_multiset +#define oset_greater tree, rb_tree_tag, tree_order_statistics_node_update> +#define oset_less tree, rb_tree_tag, tree_order_statistics_node_update> + +void oset_m_erase(ordered_set_greater &OS, ll val){ + int index = OS.order_of_key(val); + oset_greater::iterator it = OS.find_by_order(index); + if(it != OS.end() && *it == val) OS.erase(it); +} + + +///////////////////////////////////////////////////////////// +rope r; +r.insert(r.size() - t, i); //r.size()-t번째 자리에 i를 삽입 +r.substr(a, b - a + 1) // a부터 (b-a+1)개 만큼을 잘라낸다. 즉, [a, b] 선택 diff --git a/2025spring/source/DS/SegmentTree.cpp b/2025spring/source/DS/SegmentTree.cpp new file mode 100644 index 0000000..c91d9c7 --- /dev/null +++ b/2025spring/source/DS/SegmentTree.cpp @@ -0,0 +1,160 @@ +namespace GMS +{ + template + class Segtree { + class Node { + Node *l, *r; + int s,e; D v; + public: + Node(int s, int e) :l(0), r(0), s(s), e(e), v(_e){}; + ~Node(){delete l; delete r;} + + template + friend void init(Node* node, Dini arr[] = NULL) { + int s = node->s, e=node->e, mid=(s+e)/2; + if(s == e) { + node->v = D(arr?arr[s]:_e); + return; + } + + node->l = new Node(s, mid); + init(node->l, arr); + node->r = new Node(mid+1, e); + init(node->r, arr); + + node->v = join(node->l->v, node->r->v); + } + friend D _query(Node* node, int a, int b) { + int s=node->s, e=node->e; + if(a <= s and e <= b) return node->v; + if(b < s or e < a) return _e; + + return join(_query(node->l, a, b), _query(node->r, a, b)); + } + friend void _update + (Node* node, int i, function upd) { + int s=node->s, e=node->e; + if(i < s or e < i) return; + if(s == e) + { + node->v = upd(node->v); + return; + } + + _update(node->l, i, upd); + _update(node->r, i, upd); + + node->v = join(node->l->v, node->r->v); + } + }; + + Node *root; + public: + template + Segtree(int s,int e, Dini arr[] = NULL) { + root = new Node(s, e); + init(root, arr); + } + ~Segtree(){delete root;} + D query(int s, int e) + {return _query(root, s, e);} + void update(int i, function upd) + {_update(root, i, upd);} + }; + + + template + class LZSegtree { + class Node { + Node *l, *r; + int s,e; + D v; L lz; + + void prop() { + v = apply(v, lz, e-s+1); + if(l) l->lz = give(l->lz, lz); + if(r) r->lz = give(r->lz, lz); + + lz = _l; + } + + public: + Node(int s, int e) + :l(0), r(0), s(s), e(e), v(_e), lz(_l){}; + ~Node(){delete l; delete r;} + + template + friend void init(Node* node, Dini arr[] = NULL) { + int s = node->s, e=node->e, mid=(s+e)/2; + if(s == e) + { + node->v = D(arr?arr[s]:_e); + return; + } + + node->l = new Node(s, mid); + init(node->l, arr); + node->r = new Node(mid+1, e); + init(node->r, arr); + + node->v = join(node->l->v, node->r->v); + } + friend D _query(Node* node, int a, int b) { + node->prop(); + int s=node->s, e=node->e; + if(a <= s and e <= b) return node->v; + if(b < s or e < a) return _e; + + return join(_query(node->l, a, b), _query(node->r, a, b)); + } + friend void _update + (Node* node, int a, int b, function upd){ + node->prop(); + int s=node->s, e=node->e; + if(b < s or e < a) return; + if(a <= s and e <= b) + { + node->lz = upd(node->lz); + node->prop(); + return; + } + + _update(node->l, a, b, upd); + _update(node->r, a, b, upd); + + node->v = join(node->l->v, node->r->v); + } + }; + + Node *root; + public: + template + LZSegtree(int s,int e, Dini arr[] = NULL) + { + root = new Node(s, e); + init(root, arr); + } + ~LZSegtree(){delete root;} + D query(int s, int e){return _query(root, s, e);} + void update(int s, int e, function upd){_update(root, s, e, upd);} + }; +} // namespace GMS + +////////////////////////////////////////////////////// +#define data _data + +struct data { + int m, m_cnt; + constexpr data(int m):m(m), m_cnt(1){} + constexpr data(int m, int m_cnt):m(m), m_cnt(m_cnt){} +}; +data join(data A, data B) { + if(A.m == B.m) return data(A.m, A.m_cnt+B.m_cnt); + if(A.m < B.m) return A; + else return B; +} +data apply(data A, int lz, int len) + {return {A.m+lz, A.m_cnt};} +int give(int a, int b){return a+b;} + +using Seg = GMS::LZSegtree; diff --git a/2025spring/source/DS/SplayTree.cpp b/2025spring/source/DS/SplayTree.cpp new file mode 100644 index 0000000..7e682a1 --- /dev/null +++ b/2025spring/source/DS/SplayTree.cpp @@ -0,0 +1,174 @@ +struct Node +{ + Node *p, *l, *r; + int cnt; + ll val; ll m, M, sum; ll lazy; + bool flip; bool dum; + + Node(ll val, bool dum = false):p(0),l(0), r(0), cnt(1), val(val), m(val), M(val), sum(val), lazy(0), flip(0), dum(dum){} + + void fix(){ + cnt = 1+(l?l->cnt:0)+(r?r->cnt:0); + sum = val+(l?l->sum:0)+(r?r->sum:0); + m = min({val, (l?l->m:inf), (r?r->m:inf)}); + M = max({val, (l?l->M:-1), (r?r->M:-1)}); + } + void prop(){ + if(flip){ + swap(l, r); + if(l) l->flip = !l->flip; + if(r) r->flip = !r->flip; + + flip = false; + } + if(lazy){ + val += lazy; sum += cnt * lazy; + if(l) l->lazy += lazy; + if(r) r->lazy += lazy; + + lazy = 0; + } + } + +} *root; + +// 자기보다 더 높은 노드를 루트로 하는 SplayTree를 조작하는 경우, 하위 SplayTree는 unvalid된다. +struct SplayTree{ + Node *root = NULL, *rp = NULL; + + SplayTree(){} + SplayTree(Node *rt){ + if(!rt) return; + + root = rt; + rp = rt->p; + } + + void mop(Node *node){ + if(node == root) node->prop(); + else mop(node->p); + + if(node->l) node->l->prop(); + if(node->r) node->r->prop(); + } + + void rotate(Node *node){ + if(!root) return; + + if(node->p == rp) return; + if(node->p->l == node){ + Node *p = node->p, *g = p->p; + Node *a = node->l, *b = node->r, *c = p->r; + + p->l = b; if(b) b->p = p; + p->r = c; if(c) c->p = p; + + node->l = a; if(a) a->p = node; + node->r = p; p->p = node; + + node->p = g; if(g) (g->l == p?g->l:g->r) = node; + + p->fix(); node->fix(); + + if(p == root) root = node; + } + else{ + Node *p = node->p, *g = p->p; + Node *a = p->l, *b = node->l, *c = node->r; + + p->l = a; if(a) a->p = p; + p->r = b; if(b) b->p = p; + + node->l = p; p->p = node; + node->r = c; if(c) c->p = node; + + node->p = g; if(g) (g->l == p?g->l:g->r) = node; + + p->fix(); node->fix(); + + if(p == root) root = node; + } + + } + + void splay(Node* node){ + if(!root) return; + assert(node); mop(node); + + while(node->p != rp){ + Node *p, *g; + p = node->p; g = p->p; + + if(g == rp) rotate(node); + else if((p->l == node) == (g->l == p)) rotate(p), rotate(node); + else rotate(node), rotate(node); + } + + root = node; + } + + Node* insert(ll val, bool dum = false){ + if(!root){ + root = new Node(val, dum); + return root; + } + else{ + Node *now = root; + while(now->r) now = now->r; + Node* ret = now->r = new Node(val, dum); + now->r->p = now; + + splay(ret); return ret; + } + } + + Node* find_kth(int k) { // 0-indexed + assert(root); + assert(root->cnt > k); + Node *now = root; now->prop(); + while(true){ + while(now->l and now->l->cnt > k) now = now->l, now->prop(); + k -= now->l?now->l->cnt:0; + + if(k == 0) break; + k--; now = now->r; + now->prop(); + } + + splay(now); + return now; + } + // s-1, e+1번째 노드가 항상 존재해야 한다. + Node* gather(int s, int e){ + find_kth(e+1); + SplayTree(root->l).find_kth(s-1); + + assert(root->l->r); + return root->l->r; + } + void update(int i, int j, ll val){ + Node *node = gather(i, j); + + node->lazy += val; node->prop(); + node->p->fix(); node->p->p->fix(); + } + void reverse(int i, int j){ + Node *node = gather(i, j); + node->flip = !node->flip; + } + + void p_vals(){p_vals(root, 0, false);} + void p_vals(Node* node, ll lz, bool flip){ + lz += node->lazy; flip ^= node->flip; + if(!flip){ + if(node->l) p_vals(node->l, lz, flip); + if(!node->dum) printf("%lld ", node->val+lz); + if(node->r) p_vals(node->r, lz, flip); + } + else{ + if(node->r) p_vals(node->r, lz, flip); + if(!node->dum) printf("%lld ", node->val+lz); + if(node->l) p_vals(node->l, lz, flip); + } + } +}; \ No newline at end of file diff --git a/2025spring/source/DS/UF_QUndo.cpp b/2025spring/source/DS/UF_QUndo.cpp new file mode 100644 index 0000000..29462d5 --- /dev/null +++ b/2025spring/source/DS/UF_QUndo.cpp @@ -0,0 +1,60 @@ +struct dsu_pb { + const int N; + vi par; stack > s; + + dsu_pb(int N):N(N), par(N) { + fors(i, 0, N-1) par[i] = -1; + } + int root(int i) { + if(par[i] < 0) return i; + return root(par[i]); + } + bool join(int i, int j) { + i = root(i); j = root(j); + s.push({{i, par[i]}, {j, par[j]}}); + if(i == j) return false; + if(-par[i] < -par[j]) swap(i, j); + par[i] += par[j]; par[j] = i; + return true; + } + +protected: + void unjoin() { + assert(!s.empty()); + auto [i, j] = s.top(); s.pop(); + par[i.fi] = i.se; par[j.fi] = j.se; + } +}; + +struct dsu_pf : public dsu_pb { + vector > st; // fi==0 -> B type, fi==1 -> A type + vector > tmp[2]; + int A=0, B=0; + dsu_pf(int N):dsu_pb(N){} + + bool join(int i, int j) { + st.pb({0, {i, j}}); B++; + return dsu_pb::join(i, j); + } + void pop_front() { + assert(!st.empty()); + if(A == 0) { + forr(i, B) unjoin(); + A = B; B = 0; reverse(all(st)); + for(auto &[b, p]:st) b = 1, dsu_pb::join(p.fi, p.se); + } + else if(st.back().fi == false) { + tmp[st.back().fi].pb(st.back()); st.pop_back(); unjoin(); + while(tmp[0].size() != tmp[1].size() and (unsigned) A != tmp[1].size()) { + tmp[st.back().fi].pb(st.back()); + st.pop_back(); + unjoin(); + } + for(auto i:{0, 1}) reverse(all(tmp[i])); + for(auto i:{0, 1}) for(auto v:tmp[i]) + st.pb(v), dsu_pb::join(v.se.fi, v.se.se); + tmp[0].clear(); tmp[1].clear(); + } + A--; st.pop_back(); unjoin(); + } +}; \ No newline at end of file diff --git a/2025spring/source/Fundemental.cpp b/2025spring/source/Fundemental.cpp new file mode 100644 index 0000000..1c61be6 --- /dev/null +++ b/2025spring/source/Fundemental.cpp @@ -0,0 +1,22 @@ +#include + +#define getint(n) int n; scanf("%d%*c", &n) +#define getll(n) long long n; scanf("%lld%*c", &n) +#define getchar(n) char n; scanf("%c%*c", &n); +#define intab getint(a); getint(b) + +#define forr(i, n) for(int i=1;i<=(n);i++) +#define fors(i, s, e) for(int i=(s); i<=(e); i++) +#define fore(i, e, s) for(int i=(e); i>=(s); i--) + +#define fi first +#define se second +#define all(v) (v).begin(), (v).end() +#define rall(v) (v).rbegin(), (v).rend() +#define pb push_back + +using namespace std; +using ll = long long; using lll = __int128_t; +using pii = pair; using pll = pair; +using vi = vector; using vl = vector; +using vii = vector; using vll = vector; \ No newline at end of file diff --git a/2025spring/source/Geometry/Mindset.cpp b/2025spring/source/Geometry/Mindset.cpp new file mode 100644 index 0000000..77af704 --- /dev/null +++ b/2025spring/source/Geometry/Mindset.cpp @@ -0,0 +1,47 @@ +using pii=pair; +pii operator+(pii A, pii B){return {A.fi+B.fi, A.se+B.se};} +pii operator-(pii A, pii B){return {A.fi-B.fi, A.se-B.se};} +ll operator*(pii A, pii B){return (ll)A.fi*B.fi+(ll)A.se*B.se;} // inner product +ll operator/(pii A, pii B){return (ll)A.fi*B.se-(ll)A.se*B.fi;} // outer product + +// 각도 정렬 (O = pii(0, 0)) +sort(P+1, P+1+n, [](pii A, pii B) { + if(B == O) return false; + if(A == O) return true; + return (AB:A/B<0; +}); + +// 선분 교차 +// Segment : fi에서 시작하는 se 벡터 +// fi + k * se, 0 <= k <= 1 + +using Segment = pair; +int isJoin(const Segment& A, const Segment& B) { + if(B.se/A.se != 0) { + ll p = (A.fi-B.fi)/A.se; + ll q = B.se/A.se; + + if(q<0) q = -q, p = -p; + if(p < 0 or p > q) return false; + + p = (B.fi-A.fi)/B.se; + q = A.se/B.se; + + if(q<0) q = -q, p = -p; + if(p < 0 or p > q) return false; + + return true; + } + else { + if((A.fi-B.fi)/A.se != 0) return false; + + ll p = A.fi*A.se, q = (A.fi+A.se)*A.se; + ll r = B.fi*A.se, s = (B.fi+B.se)*A.se; + + if(p>q) swap(p, q); if(r>s) swap(r, s); + + if(max(p, r) > min(q, s)) return false; + + return true; + } +} diff --git a/2025spring/source/Geometry/PointInConvexPolygon.cpp b/2025spring/source/Geometry/PointInConvexPolygon.cpp new file mode 100644 index 0000000..2a5b574 --- /dev/null +++ b/2025spring/source/Geometry/PointInConvexPolygon.cpp @@ -0,0 +1,16 @@ +auto isunder = [](pii upper[], int u, pii x, bool inv = false){ // inv==true : isover + int r = inv?-1:1; + int idx = lower_bound(upper+1, upper+1+u, x, + [&r](pii a, pii b){return r*a.fi u) return false; + if(idx == 1) { + if(r*x.fi < r*upper[1].fi) return false; + else { + int h = upper[1].se; + if(upper[2].fi == upper[1].fi) h = upper[2].se; + + return r*x.se <= r*h; + } + } + return ccw(upper[idx-1], upper[idx], x) <= 0; +}; \ No newline at end of file diff --git a/2025spring/source/Geometry/geometry_kaere.cpp b/2025spring/source/Geometry/geometry_kaere.cpp new file mode 100644 index 0000000..faa4799 --- /dev/null +++ b/2025spring/source/Geometry/geometry_kaere.cpp @@ -0,0 +1,163 @@ +typedef pair pll; +#define _x first +#define _y second + +pll operator-(const pll &a, const pll &b){ + return {a._x - b._x, a._y - b._y}; +} + +ll cross(const pll &a, const pll &b){ + return a._x * b._y - b._x * a._y; +} + +ll dot(const pll &a, const pll &b){ + return a._x * b._x + a._y * b._y; +} + +int ccw(const pll &p1, const pll &p2, const pll &p3){ + ll res = cross(p2 - p1, p3 - p1); + return (res != 0) * (res < 0 ? -1 : 1); +} + +// dist of point - point +double dist(const pll &p1, const pll &p2){ + return sqrt((p1._x - p2._x) * (p1._x - p2._x) + (p1._y - p2._y) * (p1._y - p2._y)); +} + +// dist of line - point +double dist(const pll &l1, const pll &l2, const pll &p){ + ll area = abs(cross(l2 - l1, p - l1)); + return area / dist(l1, l2); +} + +// dist of seg - point +double segDist(P& s, P& e, P& p) { + if (s==e) return (p-s).dist(); + auto d = (e-s).dist2(), t = min(d,max(.0,(p-s).dot(e-s))); + return ((p-s)*d-(e-s)*t).dist()/d; +} + +P perp() const { return P(-y, x); } // rotates +90 degrees +int sgn(T x) { return (x > 0) - (x < 0); } // sign of x + +// Returns where p is as seen from s towards e. 1/0/-1 <-> left/on line/right. +int sideOf(P s, P e, P p) { return sgn(s.cross(e, p)); } + +// Returns a vector of either 0, 1, or 2 intersection points. +template +vector

circleLine(P c, double r, P a, P b) { + P ab = b - a, p = a + ab * (c-a).dot(ab) / ab.dist2(); + double s = a.cross(b, c), h2 = r*r - s*s / ab.dist2(); + if (h2 < 0) return {}; + if (h2 == 0) return {p}; + P h = ab.unit() * sqrt(h2); + return {p - h, p + h}; +} + +// Computes the pair of points at which two circles intersect. +typedef Point P; +bool circleInter(P a,P b,double r1,double r2,pair* out) { + if (a == b) { assert(r1 != r2); return false; } + P vec = b - a; + double d2 = vec.dist2(), sum = r1+r2, dif = r1-r2, + p = (d2 + r1*r1 - r2*r2)/(d2*2), h2 = r1*r1 - p*p*d2; + if (sum*sum < d2 || dif*dif > d2) return false; + P mid = a + vec*p, per = vec.perp() * sqrt(fmax(0, h2) / d2); + *out = {mid + per, mid - per}; + return true; +} + +// Returns true iff p lies on the line segment from s to e. +template bool onSegment(P s, P e, P p) { + return p.cross(s, e) == 0 && (s - p).dot(e - p) <= 0; +} + +// Circumcircle +typedef Point P; +double ccRadius(const P& A, const P& B, const P& C) { + return (B-A).dist()*(C-B).dist()*(A-C).dist()/ + abs((B-A).cross(C-A))/2; +} +P ccCenter(const P& A, const P& B, const P& C) { + P b = C-A, c = B-A; + return A + (b*c.dist2()-c*b.dist2()).perp()/b.cross(c)/2; +} + +// Minimum enclosing circle +pair mec(vector

ps) { + shuffle(all(ps), mt19937(time(0))); + P o = ps[0]; + double r = 0, EPS = 1 + 1e-8; + rep(i,0,sz(ps)) if ((o - ps[i]).dist() > r * EPS) { + o = ps[i], r = 0; + rep(j,0,i) if ((o - ps[j]).dist() > r * EPS) { + o = (ps[i] + ps[j]) / 2; + r = (o - ps[i]).dist(); + rep(k,0,j) if ((o - ps[k]).dist() > r * EPS) { + o = ccCenter(ps[i], ps[j], ps[k]); + r = (o - ps[i]).dist(); + } + } + } + return {o, r}; +} + +// point inside convex hull in logN +bool inHull(const vector

& l, P p, bool strict = true) { + int a = 1, b = sz(l) - 1, r = !strict; + if (sz(l) < 3) return r && onSegment(l[0], l.back(), p); + if (sideOf(l[0], l[a], l[b]) > 0) swap(a, b); + if (sideOf(l[0], l[a], p) >= r || sideOf(l[0], l[b], p)<= -r) + return false; + while (abs(a - b) > 1) { + int c = (a + b) / 2; + (sideOf(l[0], l[c], p) > 0 ? b : a) = c; + } + return sgn(l[a].cross(l[b], p)) < r; +} + +// convex hull +vector convex_hull(vector &arr){ + vector up, down; + for(auto p : arr){ + while(up.size() >= 2 && ccw(up[up.size() - 2], up[up.size() - 1], p) >= 0) up.pop_back(); + while(down.size() >= 2 && ccw(down[down.size() - 2], down[down.size() - 1], p) <= 0) down.pop_back(); + up.push_back(p); + down.push_back(p); + } + up.insert(up.end(), down.rbegin() + 1, down.rend()); + return up; +} + +// rotating callipers +typedef Point P; +array hullDiameter(vector

S) { + int n = sz(S), j = n < 2 ? 0 : 1; + pair> res({0, {S[0], S[0]}}); + rep(i,0,j) + for (;; j = (j + 1) % n) { + res = max(res, {(S[i] - S[j]).dist2(), {S[i], S[j]}}); + if ((S[(j + 1) % n] - S[j]).cross(S[i + 1] - S[i]) >= 0) + break; + } + return res.second; +} + +// Closest pair +typedef Point P; +pair closest(vector

v) { + assert(sz(v) > 1); + set

S; + sort(all(v), [](P a, P b) { return a.y < b.y; }); + pair> ret{LLONG_MAX, {P(), P()}}; + int j = 0; + for (P p : v) { + P d{1 + (ll)sqrt(ret.first), 0}; + while (v[j].y <= p.y - d.x) S.erase(v[j++]); + auto lo = S.lower_bound(p - d), hi = S.upper_bound(p + d); + for (; lo != hi; ++lo) + ret = min(ret, {(*lo - p).dist2(), {*lo, p}}); + S.insert(p); + } + return ret.second; +} \ No newline at end of file diff --git a/2025spring/source/Geometry/namespace_geometry.cpp b/2025spring/source/Geometry/namespace_geometry.cpp new file mode 100644 index 0000000..7cefcba --- /dev/null +++ b/2025spring/source/Geometry/namespace_geometry.cpp @@ -0,0 +1,109 @@ +template +class Point { +public: + T x, y; + Point() : x(0), y(0) {}; + Point(T _x, T _y) : x(_x), y(_y) {}; + + Point operator+(Point p2){ + return Point(x + p2.x, y + p2.y); + } + Point operator-(Point p2){ + return Point(x - p2.x, y - p2.y); + } + T operator*(Point p2){ + return x * p2.x + y * p2.y; + } + T operator/(Point p2) { + return x * p2.y - p2.x * y; + } + T operator==(Point p2) { + return (x == p2.x) && (y == p2.y); + } + T sqdist() { + return x*x + y*y; + } + bool operator<(Point p2) { + if(y == p2.y) + return x < p2.x; + return y < p2.y; + } + +}; + +namespace geometry { + template + ll ccw(Point center, Point p2, Point p3) { + ll res = (p2 - center) / (p3 - center); + return (res > 0) - (res < 0); + } + + template + double theta(Point center, Point p2, Point p3) { + return acos(p2 * p3 / sqrt(p2.sqdist() * p3.sqdist())); + } + + template + function &, Point &, Point)> cmp_point = [](Point &l, Point &r, Point O = {(T)0, (T)0}) -> bool { + return (l < O) != (r < O) ? l < r : l/r > 0; + }; + + template + T sq_dist(Point &p1, Point &p2) { + return (p2.x - p1.x)*(p2.x - p1.x) + (p2.y - p1.y)*(p2.y - p1.y); + } + + template + double dist(Point &p1, Point &p2) { + return sqrt((double)sq_dist(p1, p2)); + } + + template + double line_point_dist(pair, Point> &l, Point p) + { + Point p1 = p - l.first, p2 = l.second - l.first; + return abs(p1 / p2)/(dist(l.first, l.second)); + } + + template + double line_min_dist(pair, Point> &l1, pair, Point> &l2) { + double ans = INFINITY; + ans = min({ans, dist(l1.first, l2.first), dist(l1.first, l2.second), dist(l1.second, l2.first), dist(l1.second, l2.second)}); + + if((l1.second - l1.first)*(l2.first - l1.first) > 0 && (l1.first - l1.second)*(l2.first - l1.second) > 0) + ans = min({ans, line_point_dist(l1, l2.first)}); + if((l1.second - l1.first)*(l2.second - l1.first) > 0 && (l1.first - l1.second)*(l2.second - l1.second) > 0) + ans = min({ans, line_point_dist(l1, l2.second)}); + swap(l1, l2); + if((l1.second - l1.first)*(l2.first - l1.first) > 0 && (l1.first - l1.second)*(l2.first - l1.second) > 0) + ans = min({ans, line_point_dist(l1, l2.first)}); + if((l1.second - l1.first)*(l2.second - l1.first) > 0 && (l1.first - l1.second)*(l2.second - l1.second) > 0) + ans = min({ans, line_point_dist(l1, l2.second)}); + swap(l1, l2); + return ans; + } + + template + vector convex_hull(vector> &pts) { + assert(pts.size() >= 2); + vector> res; + + swap(pts[0], *min_element(pts.begin(), pts.end())); + sort(pts.begin()+1, pts.end(), [&pts](Point &a, Point &b){ + ll cw = ccw(pts[0], a, b); + if(cw) return cw > 0; + return sq_dist(pts[0], a) < sq_dist(pts[0], b); + }); + auto itr = pts.begin(); + res.push_back(*(itr++)); res.push_back(*(itr++)); + + while(itr != pts.end()) + { + while(res.size() >= 2 && ccw(res[res.size()-2], res[res.size()-1], *itr) <= 0) + res.pop_back(); + res.push_back(*(itr++)); + } + return res; + } +} +using namespace geometry; diff --git a/2025spring/source/Graph/BipartiteMatching.cpp b/2025spring/source/Graph/BipartiteMatching.cpp new file mode 100644 index 0000000..7b4c18c --- /dev/null +++ b/2025spring/source/Graph/BipartiteMatching.cpp @@ -0,0 +1,13 @@ +vector sideadj[N]; +int selby[M]; +int chk[M], c; +bool matching(int s) { + for(auto i : sideadj[s]) { + if(chk[i] == c) continue; + chk[i] = c; + if(selby[i] and !matching(selby[i])) continue; + selby[i] = s; + return true; + } + return false; +} \ No newline at end of file diff --git a/2025spring/source/Graph/Dinic.cpp b/2025spring/source/Graph/Dinic.cpp new file mode 100644 index 0000000..b7e5fa1 --- /dev/null +++ b/2025spring/source/Graph/Dinic.cpp @@ -0,0 +1,69 @@ +struct Edge { + int to, cap, now; + Edge* rev; + Edge(int to,int cap):to(to), cap(cap), now(0){} + int left(){return cap - now;} + void flow(int f){now += f; rev->now -= f;} + void reset(){now = 0;} +}; +vector adj[N]; + +int lv[N]; bool chk[N]; +bool bfs(int S, int T) { + queue q; + q.push(S); lv[S] = 0; chk[S] = true; + while(!q.empty()) { + int s = q.front(); q.pop(); + for(auto i : adj[s]) { + if(i->left() and !chk[i->to]) { + lv[i->to] = lv[s]+1; chk[i->to] = true; + q.push(i->to); + } + } + } + return chk[T]; +} + +Edge* hist[N]; int last[N]; +bool dfs(int s, int T) { + if(s == T) return true; + + for(int &j=last[s]; j < adj[s].size(); j++) { + int i = adj[s][j]->to; + if(adj[s][j]->left() == 0 or lv[i] != lv[s]+1) continue; + hist[i] = adj[s][j]; + + if(dfs(i, T)) return true; + } + return false; +} + +ll flow(int S,int T) { + ll ans = 0; + while(bfs(S, T)) { + while(dfs(S, T)) { + int m = 2e9; + int now = T; + while(S != now) { + m = min(m, hist[now]->left()); + now = hist[now]->rev->to; + } + now = T; + while(S != now) + hist[now]->flow(m), now = hist[now]->rev->to; + ans += m; + } + memset(last, 0, sizeof last); + memset(chk, 0, sizeof chk); + } + return ans; +} +// isDir : isDirected => 양방향 간선이면 false +void connect(int from, int to, int cap, bool isDir = true) { + Edge *fw, *bw; + fw = new Edge(to, cap); + bw = new Edge(from, !isDir ? cap : 0); + fw->rev = bw; bw->rev = fw; + adj[from].push_back(fw); + adj[to].push_back(bw); +} \ No newline at end of file diff --git a/2025spring/source/Graph/MCMF.cpp b/2025spring/source/Graph/MCMF.cpp new file mode 100644 index 0000000..ce0dcb6 --- /dev/null +++ b/2025spring/source/Graph/MCMF.cpp @@ -0,0 +1,67 @@ +struct Edge { + int to, cap, now; + ll cost; + Edge* rev; + Edge(int to,int cap, ll cost) + :to(to), cap(cap), now(0), cost(cost){} + int left(){return cap - now;} + ll flow(int f) + {now += f; rev->now -= f; return cost * f;} + void reset(){now = 0;} +}; +vector adj[N]; +Edge* hist[N]; ll dist[N]; bool inQueue[N], chk[N]; +bool spfa(int s, int t) { + memset(dist, 0, sizeof(dist)); + memset(chk, 0, sizeof(chk)); chk[s] = true; + queue q; + memset(inQueue, 0, sizeof(inQueue)); + q.push(s); inQueue[s] = true; + while(!q.empty()) { + int now = q.front(); + q.pop(); inQueue[now] = false; + + for(auto e : adj[now]) { + int next = e->to; + if(e->left() > 0 and + (chk[next] == false + or dist[next] > dist[now] + e->cost)) { + chk[next] = true; + dist[next] = dist[now] + e->cost; + hist[next] = e; + if(!inQueue[next]) + q.push(next), inQueue[next] = true; + } + } + } + return chk[t]; +} +// cost가 들어가면 항상 단방향만 가능하다. (양방향 : 2번 connect) +void connect(int from, int to, int cap, ll cost) { + Edge *fw, *bw; + fw = new Edge(to, cap, cost); + bw = new Edge(from, 0, -cost); + fw->rev = bw; bw->rev = fw; + adj[from].push_back(fw); + adj[to].push_back(bw); +} +//maximum matching & minimum cost +pair flow(int S,int T) { + ll ans = 0; ll cost = 0; + while(spfa(S, T)) { + int m = 2e9; + + int now = T; + while(S != now) { + m = min(m, hist[now]->left()); + now = hist[now]->rev->to; + } + now = T; + while(S != now) { + cost += hist[now]->flow(m); + now = hist[now]->rev->to; + } + ans += m; + } + return {ans, cost}; +} \ No newline at end of file diff --git a/2025spring/source/Graph/TarjanSCC.cpp b/2025spring/source/Graph/TarjanSCC.cpp new file mode 100644 index 0000000..333ae33 --- /dev/null +++ b/2025spring/source/Graph/TarjanSCC.cpp @@ -0,0 +1,28 @@ +vi adj[N]; +int in[N], c = 0; +stack p; +bool fin[N]; int scn[N], nscc = 0; +int dfs(int s) { + in[s] = ++c; + p.push(s); + + int m = c; + for(auto i : adj[s]) { + if(in[i] == 0) m = min(m, dfs(i)); + else if(!fin[i]) m = min(m, in[i]); + } + + if(m == in[s]) { + nscc++; + while(p.top() != s) + { + int i = p.top(); p.pop(); + scn[i] = nscc; fin[i] = true; + } + p.pop(); + scn[s] = nscc; fin[s] = true; + } + return m; +} + +forr(i, n) if(!fin[i]) dfs(i); \ No newline at end of file diff --git a/2025spring/source/Linear Algebra/Matrix.cpp b/2025spring/source/Linear Algebra/Matrix.cpp new file mode 100644 index 0000000..b6a713b --- /dev/null +++ b/2025spring/source/Linear Algebra/Matrix.cpp @@ -0,0 +1,81 @@ +class Matrix { +private: + // c: col 개수, r: row 개수 + ll c, r, mod; + vector> arr; + ll power(ll x, ll y, ll p) { + if (y == 0) return 1; + ll v = power(x, y/2, p) % p; + v = (v * v) % p; + return (y%2 == 0)? v : (x * v) % p; + } + ll modInverse(ll a, ll p) { return power(a, p-2, p); } + +public: + Matrix(int _n, int _m, ll p) : c(_n), r(_m), mod(p) { + arr.resize(c, vector(r, 0)); + } + + void setI() { + assert(c == r); + for(int i=0; i Inverse() { + assert(c == r); + Matrix victim = *this; + Matrix retm(c, c, mod); + retm.setI(); + + for (int k = 0; k < c; k++) { + int t = k - 1; + while (t + 1 < c && !victim[++t][k]); + if (t == c - 1 && !victim[t][k]) + return {false, Matrix(0, 0, 0)}; + victim.swaprow(k, t), retm.swaprow(k, t); + ll d = victim[k][k]; + + for (int j = 0; j < c; j++) { + victim[k][j] = (victim[k][j] * modInverse(d, mod))%mod; + retm[k][j] = (retm[k][j] * modInverse(d, mod))%mod; + } + + for (int i = 0; i= k) victim[i][j] = (victim[i][j] - victim[k][j] * m + mod*mod)%mod; + retm[i][j] = (retm[i][j] - retm[k][j] * m + mod*mod)%mod; + } + } + } + return {true, retm}; + } + + vector GaussElimination() { + assert(c == r - 1); + vector retv(c, 0.0); + + for(ll i=0; i= 0; p--) { + retv[p] = arr[p][c] / arr[p][p]; + for (q = p - 1; q >= 0; q--) + arr[q][c] = arr[q][c] - arr[q][p] * retv[p]; + } + return retv; + } +}; \ No newline at end of file diff --git a/2025spring/source/Math/CRT.cpp b/2025spring/source/Math/CRT.cpp new file mode 100644 index 0000000..36276b5 --- /dev/null +++ b/2025spring/source/Math/CRT.cpp @@ -0,0 +1,13 @@ +pll crt(pll p, pll q) { + if(p.fi > q.fi) swap(p, q); + auto [a, A] = p; + auto [b, B] = q; + + ll g = gcd(A, B); + if((b-a)%g != 0) return {-1, -1}; + + ll i = A, j = B, k = b-a; + i/=g; j/=g; k/=g; + auto [x, y] = diophantos(i, j); + return {(ll)((a+(lll)A*k*x)%(A*B/g)), A*B/g}; +} \ No newline at end of file diff --git a/2025spring/source/Math/Diophantos.cpp b/2025spring/source/Math/Diophantos.cpp new file mode 100644 index 0000000..ee52470 --- /dev/null +++ b/2025spring/source/Math/Diophantos.cpp @@ -0,0 +1,12 @@ +pll diophantos(ll a, ll b) { + assert(a>0 and b>=0); + if(b == 0) return {1, 0}; + auto [y, x] = diophantos(b, a%b); y = y-(a/b)*x; + if(x < 0 or x >= b) { + ll t = x/b; + if(x%b < 0) t--; + + x -= b*t; y += a*t; + } + return {x, y}; +} \ No newline at end of file diff --git a/2025spring/source/Math/FFTConv.cpp b/2025spring/source/Math/FFTConv.cpp new file mode 100644 index 0000000..5423709 --- /dev/null +++ b/2025spring/source/Math/FFTConv.cpp @@ -0,0 +1,74 @@ +using cpx = complex; +using vcpx = vector; +void fft(vcpx &a, bool inv = false) { + int n = a.size(), j = 0; assert((n&-n) == n); + for(int i=1; i> 1); + while(j >= bit) { + j -= bit; + bit >>= 1; + } + j += bit; + if(i < j) swap(a[i], a[j]); + } + + vcpx roots(n/2); + prec c = 2 * pi * (inv ? -1 : 1); + for(int i=0; i=c or b>=c) return n*(n-1)/2 * (a/c) + n * (b/c) + floor_sum(a%c, b%c, c, n); + ll m = (a*(n-1)+b)/c; + return m*n - floor_sum(c, c-b+a-1, a, m); +} \ No newline at end of file diff --git a/2025spring/source/Math/Harmonic.cpp b/2025spring/source/Math/Harmonic.cpp new file mode 100644 index 0000000..e1d7190 --- /dev/null +++ b/2025spring/source/Math/Harmonic.cpp @@ -0,0 +1,12 @@ +ll harmonic(ll n) { + ll ans = 0; + for(ll i = 1; i <= n; i = n/(n/i)+ 1) { + //for j \in [i, n/(n/i)] : n/j == n/i + + ans += n/i * (n/(n/i) - i + 1); + + // \sum_{i=1}^n {f(n/i)} + // ans += f(n/i) * (n/(n/i) - i + 1) + } + return ans; +} \ No newline at end of file diff --git a/2025spring/source/Math/MillerRabin.cpp b/2025spring/source/Math/MillerRabin.cpp new file mode 100644 index 0000000..4b8dcd4 --- /dev/null +++ b/2025spring/source/Math/MillerRabin.cpp @@ -0,0 +1,26 @@ +ll pow(ll a, ll b, ll mod) { + ll ret = 1; + for(int st=0; (1LL< + ll pow(ll a, ll b) { + static_assert(mod <= (ll)2e9, "mod should be less than 2e9"); + a %= mod; + ll ret = 1; + while(b != 0) { + if(b&1) ret = ret*a%mod; + a = a*a%mod; b>>=1; + } + return ret; + } + template + void ntt(vector &a, bool inv = false) { + static_assert(mod <= (ll)2e9, "mod should be less than 2e9"); + int n = a.size(), j = 0; + + assert((n & -n) == n && (mod-1)%n == 0); + + for(int i=1; i> 1); + while(j >= bit) { + j -= bit; + bit >>= 1; + } + j += bit; + if(i < j) swap(a[i], a[j]); + } + + static vector root[30], iroot[30]; + for(int st=1; (1<(w, (mod-1)/(1<(w, (mod-1)/(1<(t, mod-2); + + iroot[st].pb(1); + for(int i=1; i<(1<<(st-1)); i++) + iroot[st].pb(iroot[st].back()*t%mod); + } + } + + vector* r = (inv?root:iroot); + + for(int st = 1; (1<(n, mod-2); + for(int i=0; i + vl conv(vl A, vl B) { + int n = A.size(), m = B.size(); + int t = 1; while(t < n+m-1) t*=2; + A.resize(t); B.resize(t); + + ntt(A); ntt(B); + + fors(i, 0, t-1) A[i] = A[i]*B[i]%mod; + + ntt(A, true); + A.resize(n+m-1); + + return A; + } +} // namespace GMS \ No newline at end of file diff --git a/2025spring/source/Math/PolladRho.cpp b/2025spring/source/Math/PolladRho.cpp new file mode 100644 index 0000000..3128e35 --- /dev/null +++ b/2025spring/source/Math/PolladRho.cpp @@ -0,0 +1,22 @@ +void fact(ll n, vl& ret) { + if(n == 1) return; + else if(n%2 == 0) ret.pb(2), fact(n/2, ret); + else if(is_p(n)) ret.pb(n); + else { + ll a, b, c, g = n; + auto f = [&c, &n](ll x)->ll{return (c+(lll)x*x)%n;}; + + do { + if(g == n) a=b=rand()%(n-2)+2, c=rand()%20+1; + a=f(a); b=f(f(b)); + g = gcd(a-b, n); + } while(g == 1); + fact(g, ret); fact(n/g, ret); + } +} +vl po_rho(ll n) { + vl ret; + fact(n, ret); + sort(all(ret)); + return ret; +} \ No newline at end of file diff --git a/2025spring/source/Math/Polynomial.cpp b/2025spring/source/Math/Polynomial.cpp new file mode 100644 index 0000000..920b3e9 --- /dev/null +++ b/2025spring/source/Math/Polynomial.cpp @@ -0,0 +1,180 @@ +namespace GMS { + template + struct Qring : public vl { + using poly = Qring; + Qring() : vl(1, 0) {} + Qring(ll c) : vl(1, c%mod) {} + Qring(ll c, int n) : vl(n, c%mod) {} + Qring(const vl& cp) : vl(cp) {for(auto &i:*this) i%=mod;} + + ll& operator[](ll idx) { + if((unsigned)idx < size()) return vl::operator[](idx); + this->resize(idx+1); return vl::operator[](idx); + } + ll operator[](ll idx) const { + if((unsigned)idx < size()) return vl::operator[](idx); + return 0LL; + } + + void adjust() { + while(size() > 1 and back() == 0) pop_back(); + } + void adjust(int n){resize(n, 0);} + + ll operator()(ll x) { + x %= mod; ll ret = 0; + for(auto it=rbegin(); it!=rend(); it++) + ret = (ret*x+*it)%mod; + + return ret; + } + + friend poly operator%(const poly& A, int B){ // remainder by x^B + poly ret(A); ret.resize(B, 0); + return ret; + } + + friend poly operator+(const poly& A, const poly& B) { + int n = max(A.size(), B.size()); poly ret(0, n); + fors(i, 0, n-1) ret[i] = A[i]+B[i]; + for(auto&i:ret) if(i >= mod) i -= mod; + return ret.adjust(), ret; + } + + friend poly operator-(const poly& A) { + int n = A.size(); poly ret(0, n); + fors(i, 0, n-1) ret[i] = A[i]?mod-A[i]:0; + return ret; + } + + friend poly operator-(const poly& A, const poly& B) { + int n = max(A.size(), B.size()); + poly ret(0, n); + fors(i, 0, n-1) ret[i] = (mod+A[i]-B[i])%mod; + ret.adjust(); + return ret; + } + + friend poly operator*(ll x, const poly& B) { + poly ret(B); x %= mod; + for(auto &i : ret) i = (i*x)%mod; + ret.adjust(); + return ret; + } + + friend poly operator*(const poly& A, const poly& B) { + poly ret = conv(A, B); + // ACL : poly ret = atcoder::convolution(A, B); + ret.adjust(); + return ret; + } + + friend poly inv(const poly& A, int t) { assert(A[0] != 0); + poly g = pow(A[0], mod-2); + + int st=1; + while(st < t){st*=2; g = (-A%st*g%st+2)*g%st;} + + g.adjust(t); + return g; + } + + friend poly diff(const poly& A) { + int n = A.size(); poly ret(0, n-1); + fors(i, 0, n-2) ret[i] = (i+1)*A[i+1]%mod; + return ret; + } + friend poly inte(const poly& A) { + static vector inv(1, 1); + int n = A.size(); poly ret(0, n+1); + inv.resize(max((int)inv.size(), n+1)); + + fors(i, 1, n) if(inv[i] == 0) inv[i] = pow(i, mod-2); + fors(i, 1, n) ret[i] = inv[i]*A[i-1]%mod; + return ret; + } + + friend poly log(const poly& A, int t) { assert(A[0] == 1); + return inte(diff(A) * inv(A, t)%t)%t; + } + + friend poly exp(const poly& A, int t) { assert(A[0] == 0); + poly g = 1; int st = 1; + while(st < t) {st*=2; g = (A%st-log(g, st)+1)*g%st;} + return g.adjust(), g; + } + + friend poly pow(const poly& A, ll b, ll t) { + poly ret(A); ret.adjust(); + if(ret.size() == 1) { + ret[0] = pow(ret[0], b); + ret.adjust(t); + return ret; + } + + ll idx = 0; while(ret[idx] == 0) idx++; + if((__int128_t) idx * b >= t) return poly(0, t); + + ll c = ret[idx]; ll ic = pow(ret[idx], mod-2); poly g; + int n = ret.size(); + fors(i, idx, n-1) g[i-idx] = ret[i]*ic%mod; + g.resize(t-idx*b); + + g = exp(b * log(g, t-idx*b), t-idx*b); + c = pow(c, b); + + ret = poly(0, t); fors(i, idx*b, t-1) ret[i] = g[i-idx*b] * c % mod; + + return ret; + } + + //Only just Polynomial, not Qring + void rev() { + int n=size(); poly& F = *this; + for(int i=0; i(fac, mod-2)*n%mod; + fore(i, n-1, 0) C[i] = C[i]*fac%mod, fac = fac*i%mod; + + poly B = C*A; B.resize(n); B.rev(); + fore(i, n-1, 0) B[i] = B[i]*facc%mod, facc = facc*i%mod; + return B; + } + friend void calcG(vector& G, int i, int l, int r, const vl& p) { + if(l == r){ll g = p[l]?mod-p[l]:0; G[i] = vl({g, 1}); return;} + int mid = (l+r)/2; + calcG(G, i*2, l, mid, p); calcG(G, i*2+1, mid+1, r, p); + G[i] = G[i*2]*G[i*2+1]; + } + friend void eval(const vector& G, int i, int l, int r, poly&& F, vl& ret) { + if(l == r){ret[l] = F[0];return;} + int mid=(l+r)/2; + eval(G, i*2, l, mid, div_rem(F, G[i*2]), ret); + eval(G, i*2+1, mid+1, r, div_rem(F, G[i*2+1]), ret); + } + friend vl multipoint_eval(const poly& A, const vl& B) { + int m = B.size(); + vector G(4*m); calcG(G, 1, 0, m-1, B); + vl ret(m, 0); eval(G, 1, 0, m-1, div_rem(A, G[1]), ret); + return ret; + } + }; +} // namespace GMS \ No newline at end of file diff --git a/2025spring/source/Math/PrimitiveRoot.cpp b/2025spring/source/Math/PrimitiveRoot.cpp new file mode 100644 index 0000000..09b1621 --- /dev/null +++ b/2025spring/source/Math/PrimitiveRoot.cpp @@ -0,0 +1,23 @@ +ll primary_root(ll p) { + std::random_device rd; + std::mt19937 gen(rd()); + std::uniform_int_distribution distrib(1, p-1); + + //distrib(gen); + vl g = po_rho(p-1); + + while(true) { + ll c = distrib(gen); + + bool ok = true; ll u = p-1; + ll b = 1; + for(auto i:g) { + if(i != b) u = p-1; + ll x = pow(c, u/i, p); + if(x == 1) ok = false; + u /= i; b = i; + } + + if(ok) return c; + } +} \ No newline at end of file diff --git a/2025spring/source/Math/general_lucas.cpp b/2025spring/source/Math/general_lucas.cpp new file mode 100644 index 0000000..daacd68 --- /dev/null +++ b/2025spring/source/Math/general_lucas.cpp @@ -0,0 +1,56 @@ +vector euler(1000003, -1), primes; +//Generate primes and also calculate the euler number +void genprime() { + for(ll i = 2;i<=1000002;i++) { + if(euler[i]==-1) { + primes.push_back(i); + euler[i] = i-1; + for(ll j = 2*i; j<=1000002; j+=i) { + if(euler[j]==-1)euler[j] = j; + euler[j] = (euler[j]/i)*(i-1); + } + } + } +} +//Calculates x raised to the power of p % m +ll powll(ll x, ll p, ll m = 1ll<<62) +// Mod inverse +ll inverse(ll x, ll m) + +//finds (n!)_p +ll ff(ll n, ll p, ll q) +{ + ll x = 1, y = powll(p, q); + for(ll i = 2; i<=n;i++) if(i%p) + x = (x*i)%y; + return x%y; +} + +//Generalized Lucas Theorem calculates nCm mod p^q +ll lucas_pow_comb(ll n, ll m, ll p, ll q) { + ll r = n-m, x = powll(p, q); + ll e0 = 0, eq = 0; + ll mul = (p==2&&q>=3)? 1: -1; + ll cr = r, cm = m, carry = 0, cnt = 0; + while(cr||cm||carry) { + cnt++; + int rr = cr%p, rm = cm%p; + if(rr + rm + carry >= p) { + e0++; + if(cnt>=q)eq++; + } + carry = (carry+rr+rm)/p; + cr/=p; cm/=p; + } + mul = powll(p, e0)*powll(mul, eq); + ll ret = (mul % x + x) % x; + ll temp = 1; + for(ll i = 0;;i++)//This is THE line that calculates the formula { + ret = ((ret*ff((n/temp)%x, p, q)%x)%x*(inverse(ff((m/temp)%x, p, q), x)%x*inverse(ff((r/temp)%x, p, q), x)%x)%x)%x; + + if(temp>n/p && temp>m/p && temp>r/p) + break; + temp = temp*p; + } + return (ret%x+x)%x; +} \ No newline at end of file diff --git a/2025spring/source/Math/math.tex b/2025spring/source/Math/math.tex new file mode 100644 index 0000000..cb1b241 --- /dev/null +++ b/2025spring/source/Math/math.tex @@ -0,0 +1,152 @@ +% Written by Anders Sjoqvist and Ulf Lundstrom, 2009 +% The main sources are: tinyKACTL, Beta and Wikipedia +\subsection{Equations} +\[ax^2+bx+c=0 \Rightarrow x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\] + +The extremum is given by $x = -b/2a$. + +\[\begin{aligned}ax+by=e\\cx+dy=f\end{aligned} +\Rightarrow +\begin{aligned}x=\dfrac{ed-bf}{ad-bc}\\y=\dfrac{af-ec}{ad-bc}\end{aligned}\] + +In general, given an equation $Ax = b$, the solution to a variable $x_i$ is given by +\[x_i = \frac{\det A_i'}{\det A} \] +where $A_i'$ is $A$ with the $i$'th column replaced by $b$. + +% \subsection{Recurrences} +% If $a_n = c_1 a_{n-1} + \dots + c_k a_{n-k}$, and $r_1, \dots, r_k$ are distinct roots of $x^k - c_1 x^{k-1} - \dots - c_k$, there are $d_1, \dots, d_k$ s.t. +% \[a_n = d_1r_1^n + \dots + d_kr_k^n. \] +% Non-distinct roots $r$ become polynomial factors, e.g. $a_n = (d_1n + d_2)r^n$. + +\subsection{Trigonometry} +\begin{align*} +\sin(v+w)&{}=\sin v\cos w+\cos v\sin w\\ +\cos(v+w)&{}=\cos v\cos w-\sin v\sin w\\ +\tan(v+w)&{}=\dfrac{\tan v+\tan w}{1-\tan v\tan w}\\ +\sin v+\sin w&{}=2\sin\dfrac{v+w}{2}\cos\dfrac{v-w}{2}\\ +\cos v+\cos w&{}=2\cos\dfrac{v+w}{2}\cos\dfrac{v-w}{2}\\ +(V+W)\tan(v-w)/2&{}=(V-W)\tan(v+w)/2 +\end{align*} +where $V, W$ are lengths of sides opposite angles $v, w$. +\begin{align*} + a\cos x+b\sin x&=r\cos(x-\phi)\\ + a\sin x+b\cos x&=r\sin(x+\phi) +\end{align*} +where $r=\sqrt{a^2+b^2}, \phi=\operatorname{atan2}(b,a)$. + +\subsection{Geometry} + +\subsubsection{Triangles} +Side lengths: $a,b,c$ + +Semiperimeter: $p=\dfrac{a+b+c}{2}$ + +Area: $A=\sqrt{p(p-a)(p-b)(p-c)}$ + +Circumradius: $R=\dfrac{abc}{4A}$ + +Inradius: $r=\dfrac{A}{p}$ + +Length of the median (divides the triangle into two equal area triangles): $m_a=\tfrac{1}{2}\sqrt{2b^2+2c^2-a^2}$ + +Length of the bisector (divides angles into two): $s_a=\sqrt{bc\left[1-\left(\dfrac{a}{b+c}\right)^2\right]}$ + +Law of sines: $\dfrac{\sin\alpha}{a}=\dfrac{\sin\beta}{b}=\dfrac{\sin\gamma}{c}=\dfrac{1}{2R}$ + +Law of cosines: $a^2=b^2+c^2-2bc\cos\alpha$ + +Law of tangents: $\dfrac{a+b}{a-b}=\dfrac{\tan\dfrac{\alpha+\beta}{2}}{\tan\dfrac{\alpha-\beta}{2}}$ + + +\subsubsection{Quadrilaterals} +With side lengths $a,b,c,d$, diagonals $e, f$, diagonals angle $\theta$, area $A$ and +magic flux $F=b^2+d^2-a^2-c^2$: + +\[ 4A = 2ef \cdot \sin\theta = F\tan\theta = \sqrt{4e^2f^2-F^2} \] + + For cyclic quadrilaterals the sum of opposite angles is $180^\circ$, +$ef = ac + bd$, and $A = \sqrt{(p-a)(p-b)(p-c)(p-d)}$. + +\subsubsection{Spherical coordinates} +\begin{center} +\includegraphics[width=25mm]{source/Math/sphericalCoordinates.pdf} +\end{center} +\[\begin{array}{cc} +x = r\sin\theta\cos\phi & r = \sqrt{x^2+y^2+z^2}\\ +y = r\sin\theta\sin\phi & \theta = \textrm{acos}(z/\sqrt{x^2+y^2+z^2})\\ +z = r\cos\theta & \phi = \textrm{atan2}(y,x) +\end{array}\] + +\subsection{Derivatives/Integrals} +\begin{align*} + \dfrac{d}{dx}\arcsin x = \dfrac{1}{\sqrt{1-x^2}} &&& \dfrac{d}{dx}\arccos x = -\dfrac{1}{\sqrt{1-x^2}} \\ + \dfrac{d}{dx}\tan x = 1+\tan^2 x &&& \dfrac{d}{dx}\arctan x = \dfrac{1}{1+x^2} \\ + \int\tan ax = -\dfrac{\ln|\cos ax|}{a} &&& \int x\sin ax = \dfrac{\sin ax-ax \cos ax}{a^2} \\ + \int e^{-x^2} = \frac{\sqrt \pi}{2} \text{erf}(x) &&& \int xe^{ax}dx = \frac{e^{ax}}{a^2}(ax-1) +\end{align*} + +Integration by parts: +\[\int_a^bf(x)g(x)dx = [F(x)g(x)]_a^b-\int_a^bF(x)g'(x)dx\] + +\subsection{Sums} +\[ c^a + c^{a+1} + \dots + c^{b} = \frac{c^{b+1} - c^a}{c-1}, c \neq 1 \] +\begin{align*} + 1 + 2 + 3 + \dots + n &= \frac{n(n+1)}{2} \\ + 1^2 + 2^2 + 3^2 + \dots + n^2 &= \frac{n(2n+1)(n+1)}{6} \\ + 1^3 + 2^3 + 3^3 + \dots + n^3 &= \frac{n^2(n+1)^2}{4} \\ + 1^4 + 2^4 + 3^4 + \dots + n^4 &= \frac{n(n+1)(2n+1)(3n^2 + 3n - 1)}{30} \\ +\end{align*} + +\subsection{Series} +$$e^x = 1+x+\frac{x^2}{2!}+\frac{x^3}{3!}+\dots,\,(-\infty0$. +\[f(x) = \left\{ +\begin{array}{cl} +\lambda e^{-\lambda x} & x\geq0\\ +0 & x<0 +\end{array}\right.\] +\[\mu=\frac{1}{\lambda},\,\sigma^2=\frac{1}{\lambda^2}\] + +\subsubsection{Normal distribution} +Most real random values with mean $\mu$ and variance $\sigma^2$ are well described by $\mathcal{N}(\mu,\sigma^2),\,\sigma>0$. +\[ f(x) = \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{(x-\mu)^2}{2\sigma^2}} \] +If $X_1 \sim \mathcal{N}(\mu_1,\sigma_1^2)$ and $X_2 \sim \mathcal{N}(\mu_2,\sigma_2^2)$ then +\[ aX_1 + bX_2 + c \sim \mathcal{N}(\mu_1+\mu_2+c,a^2\sigma_1^2+b^2\sigma_2^2) \] \ No newline at end of file diff --git a/2025spring/source/Math/sphericalCoordinates.pdf b/2025spring/source/Math/sphericalCoordinates.pdf new file mode 100644 index 0000000..0c9a480 --- /dev/null +++ b/2025spring/source/Math/sphericalCoordinates.pdf @@ -0,0 +1,1709 @@ +%PDF-1.4 % +1 0 obj << /Type /Catalog /Pages 2 0 R /Metadata 207 1 R >> endobj 2 0 obj << /Type /Pages /Kids [ 5 0 R ] /Count 1 >> endobj 3 0 obj << /ModDate (D:20090814202111+02'00') /CreationDate (D:20090814175526Z) /Producer (Adobe PDF library 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if(S == T) { + S = buf;T = buf + fread(buf, 1, 100000, stdin); + if(S == T) return EOF; + } + return *S++; +} +void read(int& n) { + n = 0; + char c; bool neg = false; + for(c = get(); c < '0'; c=get()) if(c=='-') neg = true; + for(;c>='0';c=get()) n = n*10+c-'0'; + if(neg) n = -n; +} +void read(ll& n) { + n = 0; + char c; bool neg = false; + for(c = get(); c < '0'; c=get()) if(c=='-') neg = true; + for(;c>='0';c=get()) n = n*10+c-'0'; + if(neg) n = -n; +} +int read(char s[]) { + char c; int p = 0; + while((c = get()) <= ' '); + + s[p++] = c; + while((c = get()) >= ' ') s[p++] = c; + s[p] = '\0'; + + return p; +} \ No newline at end of file diff --git a/2025spring/source/Misc/StressTest.sh b/2025spring/source/Misc/StressTest.sh new file mode 100644 index 0000000..e69de29 diff --git a/2025spring/source/Misc/mt19937.cpp b/2025spring/source/Misc/mt19937.cpp new file mode 100644 index 0000000..0be15b7 --- /dev/null +++ b/2025spring/source/Misc/mt19937.cpp @@ -0,0 +1,7 @@ +const long long rand_L = 1; +const long long rand_R = 10; +mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count()); +uniform_int_distribution dist(rand_L, rand_R); +auto gen = bind(dist, rng); + +gen(); gen(); gen(); \ No newline at end of file diff --git a/2025spring/source/String/F_Z_M_SA_LCP.cpp b/2025spring/source/String/F_Z_M_SA_LCP.cpp new file mode 100644 index 0000000..3c1e4eb --- /dev/null +++ b/2025spring/source/String/F_Z_M_SA_LCP.cpp @@ -0,0 +1,92 @@ +const int N = 1e5+7; +char s[N]; +int F[N], Z[N], M[N]; +int sa[N]; int ord[N], tmp[N], cnt[N]; +int lcp[N]; +int main() { + scanf("%s", s+1); + int n = strlen(s+1); + + // KMP - fail function { + F[1] = 0; int j = 0; + for(int i=2; i<=n;i++) + { + while(j > 0 and s[i] != s[j+1]) j = F[j]; + F[i] = j+=(s[i] == s[j+1]); + } + } + + //Z - Z array { + Z[1] = n; int j = 1, r = 0; + for(int i=2; i<=n; i++) + { + Z[i] = i 0) k--; + } + } + + printf("\nF : "); forr(i, n) printf("%d ", F[i]); + printf("\nZ : "); forr(i, n) printf("%d ", Z[i]); + printf("\nM : "); forr(i, n) printf("%d ", M[i]); + printf("\nSA : "); forr(i, n) printf("%d ", sa[i]); + printf("\nLCP : x "); fors(i, 2, n) printf("%d ", lcp[i]); + + printf("\n"); forr(i, n) printf("%s\n", s+sa[i]); +} \ No newline at end of file diff --git a/2025spring/source/String/KMP.cpp b/2025spring/source/String/KMP.cpp new file mode 100644 index 0000000..dcbd99b --- /dev/null +++ b/2025spring/source/String/KMP.cpp @@ -0,0 +1,17 @@ +int fail[N]; // N : s의 최대 길이 +vi kmp(char obj[], char s[]) { + vi ret; + for(int i = 1, j = 0; s[i]; i++) { + fail[i] = 0; + while(j > 0 and s[i] != s[j]) j = fail[j-1]; + if(s[i] == s[j]) fail[i] = ++j; + } + for(int i = 0, j = 0; obj[i]; i++) { + while(j > 0 and obj[i] != s[j]) j = fail[j-1]; + if(obj[i] == s[j]) { + if(s[j+1]) j++; + else ret.push_back(i-j), j = fail[j]; + } + } + return ret; +} \ No newline at end of file diff --git a/2025spring/source/String/std::string.cpp b/2025spring/source/String/std::string.cpp new file mode 100644 index 0000000..417a0bd --- /dev/null +++ b/2025spring/source/String/std::string.cpp @@ -0,0 +1,132 @@ +///////////////////////////////////////////////////////// +string s; //변수 선언 +///////////////////////////////////////////////////////// + + +///////////////////////////////////////////////////////// +string s = "Hwan"; //output : Hwan +///////////////////////////////////////////////////////// + + +///////////////////////////////////////////////////////// +string s1("Hwan"); //output ㄷ: Hwan +string s2(4, 'A'); //output : AAAA +string s3(s1, 0, s1.length() - 2); //output : HW +string s4(s1, 2, s1.length()); //output : an +string s5(s2); //output : AAAA +string s6("ABCDE", 3); //output : ABC + +char c[] = "TEST Code!!"; +string s7(c); //output : TEST Code!! +/////////////////////////////////////////////////////////​ +string s = "ABCDE123"; + +cout << s.at(2) << endl; //output : C (범위가 맞지 않으면 예외처리를 함) +cout << s[0] << endl; //output : A +cout << s.front() << endl; //output : A +cout << s.back() << endl; //output : 3 + +const char * c = s.c_str(); //배열로써 접근이 가능하며 '\0'에 접근이 가능하다. + +cout << c << endl; //output : ABCDE123 + +cout << (c_arr == s) ? true : false; //output : 1(true) +cout << (&(c_arr[0]) == &(s[0])) ? true : false; //output : 1(true)​ + +///////////////////////////////////////////////////////// +string s = "ABCDE123"; +string::iterator iter = s.begin(); +string r_s, cp; + +for (; iter != s.end(); iter++) { + cout << *iter; + if (*iter == 'E') + break; +} //output : ABCDE + + +copy(s.rbegin(), s.rend(), back_inserter(r_s)); +copy(s.begin(), s.end(), back_inserter(cp)); + +cout << r_s << endl; //output : 321EDCBA +cout << (s == r_s) ? true : false; //output : 0(false) +cout << (s == cp) ? true : false; //output : 1(true) +cout << (&(s[0]) == &(cp[0])) ? true : false; //output : 0(false)​ +///////////////////////////////////////////////////////// +string s = "ABCDE123" + +s.insert(0, "TEST"); //output : TESTABCDE123 +s.insert(s.begin() + s.find_first_of('D') + 1, ':'); // output : TESTABCD:123(문자만 가능) + + +////////// (compare) s = TESTABCD:123 ///////////// +s.compare("TESTABCD:123"); //output : 0 +s.compare("a"); //output : -1 +s.compare("X"); //output : -1 +s.compare("BBBBBBBBBBBBBBB"); //output : 1 +s.compare("100000000000000000000000"); //output : 1 +s.compare("VVVVV"); //output : -1 + + +////////// (erase) s = TESTABCD:123 ///////////// +s.erase(0, 4); //output : ABCD:123 +s.erase(find(s.begin(), s.end(), 'D')); //output : ABC:123('D'만 지움) +s.erase(s.find(':')); //output : ABC(':'부터 뒤 문자까지 모두 지움) + + +////////// (push, pop) s = ABC ///////////// +s.push_back('S'); //output : ABCS +s.pop_back(); //output : ABC + + +////////// (append) s = ABC ///////////// +s.append("TEST"); //output : ABCTEST +s.append(1, '1'); //output : ABCTEST1 +s.append("123456789", 3, 3); //output : ABCTEST1456 + + +////////// (clear) s = ABCTEST1456 ///////////// +const char c[] = "Hwan"; +s.append(c); //output : ABCTEST1456Hwan +s += c; //output : ABCTEST1456HwanHwan(capacity() = 15 -> 31) +s.clear(); //s.size() = 0, s.capacity() = 31 + + +////////// (replace) s = '' ///////////// +s.append("ABCD123"); //output : ABCD123 +s.replace(4, 2, "Hwan"); //output : ABCDHwan3 +s.replace(s.find('H'), s.size() - s.find('H'), "WOW"); //output : ABCDWOW + + +////////// (substr) s = ABCDWOW ///////////// +string temp = s.substr(4); //output : WOW; +temp = s.substr(3, 2); //output : DW; +temp = s.substr(s.size() - 3, 50); //output : WOW; + + +////////// (copy) s = ABCDWOW ///////////// +char arr[5]{}; +s.copy(arr, sizeof arr - 1); //output : ABCD (마지막 '\n' 포함) + + +////////// (resize) s = ABCDWOW ///////////// +s.resize(100); //output : ABCDWOW, s.size() = 100, s.capacity() = 111 +s.resize(4); //output : ABCD, s.size() = 4, s.capacity() = 15 + + +////////// (swap) s = ABCD ///////////// +string sw = "AAA"; +s.swap(sw); //s = "AAA", sw = "ABCD" + + +/////////// c++ 20 /////////////////// +s = "hello Hwan"; +s.starts_with("hello"); //output : true; +s.starts_with('h'); //output : true; +s.starts_with("Hwan"); //output : false; +s.starts_with('x'); //output : false; + +s.ends_with("Hwan"); //output : true; +s.ends_with('n'); //output : true; +s.ends_with("hello"); //output : false; +s.ends_with('q'); //output : false; \ No newline at end of file diff --git a/2025spring/source/Tree/Centroid.cpp b/2025spring/source/Tree/Centroid.cpp new file mode 100644 index 0000000..f5bde31 --- /dev/null +++ b/2025spring/source/Tree/Centroid.cpp @@ -0,0 +1,34 @@ +vi adj[N]; bool cent[N]; +int sz[N], par[N]; + +void getSz(int s){ + sz[s] = 1; + for(auto i:adj[s]){ + if(cent[i]) continue; + if(par[s] == i) continue; + par[i] = s; getSz(i); par[i] = 0; + + sz[s] += sz[i]; + } +} +int getCent(int s, int n){ + for(auto i:adj[s]) + if(!cent[i] and sz[i] < sz[s] and sz[i] > n/2) + return getCent(i, n); + return s; +} + +int cpar[N]; +int getCentTree(int s){ + getSz(s); + int C = getCent(s, sz[s]); + cent[C] = true; + for(auto i:adj[C]){ + if(cent[i]) continue; + int c = getCentTree(i); + cpar[c] = C; + } + return C; +} + +int C = getCentTree(1); cpar[C] = -1; \ No newline at end of file diff --git a/2025spring/source/Tree/HLD.cpp b/2025spring/source/Tree/HLD.cpp new file mode 100644 index 0000000..2e9f38c --- /dev/null +++ b/2025spring/source/Tree/HLD.cpp @@ -0,0 +1,76 @@ +BOJ 트리와 쿼리 1 +1 i c: i번 간선의 비용을 c로 바꾼다. +2 u v: u에서 v로 가는 단순 경로에 존재하는 비용 중에서 가장 큰 것을 출력한다. + +const int N = 1e5+7; + +vi adj[N]; int par[N]; int sz[N]; int d[N]; +void dfs1(int s) { + sz[s] = 1; + for(int i=0;i sz[adj[s][0]]) swap(adj[s][0], i); + } +} +int in[N], c; int top[N]; +void dfs2(int s) { + in[s] = ++c; + for(auto i : adj[s]) { + if(i == adj[s][0]) + top[i] = top[s]; + else top[i] = i; + + dfs2(i); + } +} + +Node *root; // Segment Tree +int query(int a,int b) { + int ans = 0; + while(top[a] != top[b]) { + if(d[top[a]] > d[top[b]]) swap(a, b); + ans = max(ans, query(root, in[top[b]], in[b])); + b = par[top[b]]; + } + + if(d[a] > d[b]) swap(a, b); + ans = max(ans, query(root, in[a]+1, in[b])); + + return ans; +} +map m; +int arr[N]; pii edge[N]; +int main() { + getint(n); + forr(i, n-1) { + intab; adj[a].pb(b); adj[b].pb(a); + getint(c); + m[{a,b}] = m[{b, a}] = c; + edge[i] = {a,b}; + } + + dfs1(1); dfs2(1); + forr(i, n) arr[in[i]] = m[{par[i], i}]; + root = new Node(1, n); init(root, arr); + + getint(Q); + while(Q--) { + getint(q); + if(q == 1) { + getint(i); getint(c); + auto [a, b] = edge[i]; + if(par[b] == a) a = b; + + update(root, in[a], c, true); + } + if(q == 2) { + intab; + printf("%d\n", query(a, b)); + } + } +} diff --git a/2025spring/source/empty.cpp b/2025spring/source/empty.cpp new file mode 100644 index 0000000..e69de29 diff --git a/2025spring/source/qwerty.cpp b/2025spring/source/qwerty.cpp new file mode 100644 index 0000000..814825a --- /dev/null +++ b/2025spring/source/qwerty.cpp @@ -0,0 +1,7 @@ +#pragma GCC optimize("O3") +#pragma GCC optimize("Ofast") +#pragma GCC optimize("unroll-loops") + +#define endl '\n' +#define foreach(i, l, r) for(ll i=(l); i<=(r); i++) +#define forreach(i, l, r) for(ll i=l; i>=(r); i--) \ No newline at end of file diff --git a/2025spring/teamnote.sty b/2025spring/teamnote.sty new file mode 100644 index 0000000..fce7852 --- /dev/null +++ b/2025spring/teamnote.sty @@ -0,0 +1,110 @@ +\ProvidesPackage{teamnote} + +\usepackage[left=1cm,right=1cm,top=2cm,bottom=1cm,a4paper]{geometry} +\usepackage{fancyhdr} +\usepackage{lastpage} +\usepackage{ifthen} +\usepackage{minted} +\usepackage{color} +\usepackage{indentfirst} +\usepackage{amssymb} +\usepackage{amsmath} +\usepackage{import} +\usepackage{caption} +\usepackage[table,xcdraw]{xcolor} +\usepackage[T1]{fontenc} +\usepackage{setspace} + +\setstretch{1} % No line-spacing + +\renewcommand{\@listI}{% No spacing on list +\leftmargin=25pt +\rightmargin=0pt +\labelsep=5pt +\labelwidth=20pt +\itemindent=0pt +\listparindent=0pt +\topsep=0pt plus 2pt minus 4pt +\partopsep=0pt plus 1pt minus 1pt +\parsep=0pt plus 1pt +\itemsep=\parsep} + +\setlength{\columnseprule}{0.4pt} +\pagenumbering{arabic} +\setminted{breaklines=true, tabsize=2, breaksymbolleft=} +\usemintedstyle{perldoc} + +\newcommand{\revised}{Should be \textcolor{red}{\textbf{revised}}.} +\newcommand{\tested}{Should be \textcolor{red}{\textbf{tested}}.} +\newcommand{\added}{Should be \textcolor{red}{\textbf{added}}.} +\newcommand{\WIP}{\textcolor{red}{\textbf{Working in progress.}}} + +\newcommand{\schoolname}{Some University} +\newcommand{\teamname}{Some Teamname} +\newcommand{\authorname}{Some Members} + +\newcommand{\maketitlepage}{\maketitle + +\tableofcontents + +\thispagestyle{fancy} + +} +\DeclareRobustCommand{\teamnote}[3]{ + \renewcommand{\schoolname}{#1} + \renewcommand{\teamname}{#2} + \renewcommand{\authorname}{#3} +} +\pagestyle{fancy} +\lhead{\schoolname{} -- \teamname} +\rhead{Page \thepage{} of +\ifthenelse{\pageref{LastPage} < 26}{\pageref{LastPage}}{\textcolor{red}{\textbf{\pageref{LastPage}}}}} +\fancyfoot{} + +\title{Team Note of \teamname} +\author{\authorname} +\date{Compiled on \today} + + + + +\newboolean{BangShowUsage} +\setboolean{BangShowUsage}{false} +\newcommand{\ShowUsage}{\setboolean{BangShowUsage}{false}} +\newcommand{\HideUsage}{\setboolean{BangShowUsage}{true}} + + +\newboolean{BangShowComplexity} +\setboolean{BangShowComplexity}{false} +\newcommand{\ShowComplexity}{\setboolean{BangShowComplexity}{false}} +\newcommand{\HideComplexity}{\setboolean{BangShowComplexity}{true}} + + +\newboolean{BangShowAuthor} +\setboolean{BangShowAuthor}{false} +\newcommand{\ShowAuthor}{\setboolean{BangShowAuthor}{false}} +\newcommand{\HideAuthor}{\setboolean{BangShowAuthor}{true}} + +\newcommand{\Algorithm}[6]{ + \subsection{#1} + + \ifthenelse{\equal{#2}{} \OR \boolean{BangShowUsage}}{}{\textbf{Usage:} #2} + + \ifthenelse{\equal{#3}{} \OR \boolean{BangShowComplexity}}{}{\textbf{Time Complexity:} #3} + + \ifthenelse{\equal{#6}{} \OR \boolean{BangShowAuthor}}{}{\textbf{Author:} #6} + + \ifthenelse{\equal{#5}{}}{}{\ifthenelse{\equal{#4}{}}{\inputminted[]{cpp}{#5}}{\inputminted[]{#4}{#5}}} +} + +\newcommand{\SubAlgorithm}[6]{ + \subsubsection{#1} + + \ifthenelse{\equal{#2}{} \OR \boolean{BangShowUsage}}{}{\textbf{Usage:} #2} + + \ifthenelse{\equal{#3}{} \OR \boolean{BangShowComplexity}}{}{\textbf{Time Complexity:} #3} + + \ifthenelse{\equal{#6}{} \OR \boolean{BangShowAuthor}}{}{\textbf{Author:} #6} + + \ifthenelse{\equal{#5}{}}{}{\ifthenelse{\equal{#4}{}}{\inputminted[]{cpp}{#5}}{\inputminted[]{#4}{#5}}} +} diff --git a/README.md b/README.md new file mode 100644 index 0000000..fb697e5 --- /dev/null +++ b/README.md @@ -0,0 +1 @@ +# teamnote \ No newline at end of file

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