update ucpc2026

.clangd

@@ -0,0 +1,2 @@
+CompileFlags:
+  Add: [-include, /home/remote/teamnote/lib/default.cpp, --std=c++23]

.vscode/settings.json

@@ -13,5 +13,10 @@
             "%DOC%"
         ],
         "env": {}
-    }],
+    }
+],
+    // "latex-workshop.viewer.pdf.internal.host": "0.0.0.0",
+    "latex-workshop.view.outline.sync.viewer": true,
+    "latex-workshop.view.pdf.internal.urlPrefix": "https://code.spweber.com/latex-workshop-pdf",
+    // "latex-workshop.latex.clean.subfolder.enabled": false,
 }

lib/default.cpp

@@ -0,0 +1,24 @@
+#include <bits/stdc++.h>
+
+#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<int,int>;   using pll = pair<ll,ll>;
+using vi = vector<int>;      using vl = vector<ll>;
+using vii = vector<pii>;     using vll = vector<pll>;
+
+const int N = 2e5+7, inf=1e9+7;

main.tex

@@ -11,6 +11,10 @@
 \usepackage{subfiles}
 \usepackage{amsmath}
 
+\usepackage{tkz-euclide}
+\usetikzlibrary{calc}
+
+
 \usepackage{etoolbox}
 \AtBeginEnvironment{align*}{%
 
@@ -38,7 +42,7 @@
 \usepackage{multicol}
 \setlength\columnseprule{0.5pt}
 
-\teamnote{POSTECH}{ConSpirito}{}{ICPC Seoul Regional}
+\teamnote{UCPC 2025 Final}{아팀명모하지}{아팀명모하지}{}
 
 \ShowUsage
 \ShowComplexity
@@ -72,6 +76,7 @@
     \item calculating error bound on a real number usage?
 \end{itemize}
 
+
 \subsection{checked...}
 
 \begin{itemize}
@@ -378,11 +383,16 @@ When you don't have any ideas, please bruteforce it.
 \end{tcolorbox}
 
 
-\Algorithm{POROGOD}{}{}{bash}{source/poro.cpp}
+\Algorithm{POROGOD}{}{}{bash}{source/poro.sh}
 
-\pagebreak
+% \pagebreak
 
 % \Algorithm{astilate}{}{}{cpp}{source/Fundemental.cpp}
+\Algorithm{cy4n1de}{}{}{cpp}{source/cy4n1de.cpp}
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\section{Math}
 
 \subsection{Tips for Inequality with Rational Number}
 Let $A$, $B$, $x$, $n$ be integer, and operator `/' means floor division(quotient).
@@ -393,9 +403,7 @@ Let $A$, $B$, $x$, $n$ be integer, and operator `/' means floor division(quotien
     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}
 
@@ -485,7 +493,7 @@ $$\sum_{x=0}^{N-1} \left\lfloor  \frac{Ax+B}{C} \right\rfloor $$}
 
 
 \Algorithm{NTT - Number Theoretic Transform}
-{helloworld}
+{}
 {}
 {cpp}
 {source/Math/NTT.cpp}
@@ -760,8 +768,8 @@ D_{min}(p) &= \min_i|A_i-B_{p_i}| && \text{ maximize } D_{min} &&& \Rightarrow p
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{DP}
 
-\Algorithm{LIS}
+% \Algorithm{LIS}
-{}{}{cpp}{source/DP/LIS.cpp}
+% {}{}{cpp}{source/DP/LIS.cpp}
 
 \subsection{DP Optimization}
 
@@ -871,6 +879,17 @@ D_{min}(p) &= \min_i|A_i-B_{p_i}| && \text{ maximize } D_{min} &&& \Rightarrow p
 {cpp}
 {source/String/AhoCorasick.cpp}
 
+% % gemini flash : lyndon word, lyndon decomp를 설명해
+% \Algorithm{Duval's}
+% {A string is called simple (or a Lyndon word), if it is strictly smaller than any of its own nontrivial suffixes. Examples of simple strings are a,b,ab,aab,abb,abcd,abaca, b, ab, aab, abb, abcd, abac.
+% It can be shown that a string is simple, if and only if it is strictly smaller than all its nontrivial cyclic shifts. As a corollary, it can be observed that simple words are never periodic (it is not a repetition of some words for 22 or more times).
+% The Lyndon decomposition of string ss is a factorization $s = w_1w_2 \ldots w_k$, where all strings $w_i$ are simple, and are in non-increasing order $w_1 \geq w_2 \geq \ldots \geq w_k$.
+% Alternatively, the Lyndon decomposition of string s can be represented as $s = w_1^{p_1} w_2^{p_2} \ldots w_k^{p_k}$. Here, $p_i$ are positive integers, and $w^p_i$ denotes the string w repeated for $p_i$ times. All strings $w_i$ are simple, and are in decreasing order $w_1 > w_2 > \ldots > w_k$. The only difference is that the group of identical factors is grouped as a chunk such as $w^p_i$.
+% }
+% {}
+% {cpp}
+% {source/String/Duval.cpp}
+
 \Algorithm{Eertree}
 {}
 {}
@@ -981,15 +1000,16 @@ If we want the result of matching, use:}
 {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}
+\Algorithm{Fenwick Tree}
+{}
+{}
+{cpp}
 {source/DS/Fenwick.cpp}
 
 \Algorithm{Segment Tree}
@@ -1004,11 +1024,11 @@ If we want the result of matching, use:}
 % {cpp}
 % {source/DS/SegmentTree.cpp}
 
-\Algorithm{Segment Tree Beats}
+% \Algorithm{Segment Tree Beats}
-{}
+% {}
-{$\mathcal O(\log N)$ on updating and querying}
+% {$\mathcal O(\log N)$ on updating and querying}
-{cpp}
+% {cpp}
-{source/DS/STBeats.cpp}
+% {source/DS/STBeats.cpp}
 
 \Algorithm{Li-Chao Tree}
 {}
@@ -1023,7 +1043,7 @@ If we want the result of matching, use:}
 {source/DS/SplayTree.cpp}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Numerical Analysis}
+% \section{Numerical Analysis}
 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -1043,8 +1063,6 @@ If we want the result of matching, use:}
 {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);}.}
 {}

source/DS/Fenwick.cpp

@@ -1,9 +1,7 @@
 ll tree[N];
-void update(int i,ll x) {
+void update(int i,ll x){ while(i<N) tree[i] += x, i+=i&-i; }
-    while(i < N) tree[i] += x, i += i&-i;
-}
 int query(int i) {
     ll s = 0;
-    while(i) s += tree[i], i -= i&-i;
+    while(i) s += tree[i], i-=i&-i;
     return s;
 }

source/DS/PBDS.cpp

@@ -1,4 +1,4 @@
-#include <bits/stdc++.h>
+// https://codeforces.com/blog/entry/11080
 #include <ext/rope>
 #include <ext/pb_ds/assoc_container.hpp>
 #include <ext/pb_ds/tree_policy.hpp>
@@ -8,30 +8,17 @@ using namespace __gnu_cxx;
 template<typename T>
 using indexed_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
 
-indexed_set<int> s;
+// indexed_set<int> s;
-s.insert(3); s.insert(2); s.insert(3); s.insert(9); s.insert(7); //2 3 7 9
+// 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.insert(5); //2 3 5 7 9
-s.erase(5); //2 3 7 9
+// s.erase(5); //2 3 7 9
 
-auto x = s.find_by_order(2); // *x : 7
+// 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
+// indexed_multiset: use {key, unique} as key
 
-s.order_of_key(6) // 2
+// rope<ll> r;
-s.order_of_key(7) // 2
+// r.insert(r.size() - t, i); //r.size()-t번째 자리에 i를 삽입
-s.order_of_key(8) // 3
+// r.substr(a, b - a + 1) // a부터 (b-a+1)개 만큼을 잘라낸다. 즉, [a, b] 선택
-
-/////////////////////////////////////////////////////////////
-// greater_equal <- ordered_multiset / greater <- ordered_multiset
-#define oset_greater tree<ll, null_type, greater_equal<ll>, rb_tree_tag, tree_order_statistics_node_update> 
-#define oset_less tree<ll, null_type, less_equal<ll>, 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<ll> 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

source/DS/SplayTree.cpp

@@ -20,7 +20,7 @@ val += lazy; sum += cnt * lazy; if(l) l->lazy += lazy; if(r) r->lazy += lazy; la
     
 } *root;
 
-// 자기보다 더 높은 노드를 루트로 하는 SplayTree를 조작하는 경우, 하위 SplayTree는 unvalid된다.
+// 자기보다 더 높은 노드를 루트로 하는 SplayTree를 조작하는 경우, 하위 SplayTree는 invalid.
 struct SplayTree{
     Node *root = NULL, *rp = NULL;
     SplayTree(){}

source/Graph/Matching.cpp

@@ -1,18 +1,15 @@
-// From https://github.com/koosaga/olympiad
+// Originate from https://github.com/koosaga/olympiad
-// matching_short.cpp
+// matching_short.cpp / 1-based Vertex index / const int N = 2020 + 1;
-const int MAXN = 2020 + 1;
+int vis[N], par[N], orig[N], match[N], aux[N], t, n;
-// 1-based Vertex index
+vector<int> conn[N]; queue<int> Q;
-int vis[MAXN], par[MAXN], orig[MAXN], match[MAXN], aux[MAXN], t, N;
+
-vector<int> conn[MAXN];
-queue<int> 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;
+	::n = n; t = 0;
-	for(int i=0; i<=n; ++i) {
+	fors(i, 0, n) conn[i].clear();
-		conn[i].clear();
+	fors(i, 0, n) match[i] = aux[i] = par[i] = 0;
-		match[i] = aux[i] = par[i] = 0;
-	}
 }
+
 void augment(int u, int v) {
 	int pv = v, nv;
 	do {
@@ -35,12 +32,11 @@ 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;
+		orig[v] = orig[w] = a; v = par[w];
-		v = par[w];
 	}
 }
 bool bfs(int u) {
-	fill(vis+1, vis+1+N, -1); iota(orig + 1, orig + N + 1, 1);
+	fill(vis+1, vis+1+n, -1); iota(orig + 1, orig + n + 1, 1);
 	Q = queue<int> (); Q.push(u); vis[u] = 0;
 	while(!Q.empty()) {
 		int v = Q.front(); Q.pop();
@@ -58,17 +54,15 @@ bool bfs(int u) {
 	}
 	return false;
 }
-int Match() {
+int matching() {
 	int ans = 0;
 	// find random matching (not necessary, constant improvement)
-	vector<int> V(N-1); iota(V.begin(), V.end(), 1);
+	vector<int> 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 x: V) if(!match[x]) for(auto y: conn[x]) if(!match[y]) {
-		for(auto y: conn[x]) if(!match[y]) {
+		match[x] = y, match[y] = x;
-			match[x] = y, match[y] = x;
+		++ans; break;
-			++ans; break;
-		}
 	}
-	for(int i=1; i<=N; ++i) if(!match[i] && bfs(i)) ++ans;
+	forr(i, n) if(!match[i] && bfs(i)) ++ans;
 	return ans;
 }

source/Math/NTT.cpp

@@ -1,32 +1,26 @@
 namespace GMS {
 template<ll mod>
 ll pow(ll a, ll b) {
-    a %= mod;
+    ll ret = 1; a %= mod;
-    ll ret = 1;
     while(b != 0) {
         if(b&1) ret = ret*a%mod;
-        a = a*a%mod; b>>=1;
+        a = a*a%mod, b/=2;
     }
     return ret;
 }
 template<ll mod, ll w>
-void ntt(vector<ll> &a, bool inv = false) {
+void ntt(vl& 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<n; i++) {
-        int bit = (n >> 1);
+        int bit = n/2;
-        while(j >= bit) {
+        while(j >= bit) {j -= bit; bit >>= 1;}
-            j -= bit;
+        j += bit; if(i < j) swap(a[i], a[j]);
-            bit >>= 1;
-        }
-        j += bit;
-        if(i < j) swap(a[i], a[j]);
     }
     
-    static vector<ll> root[30], iroot[30];
+    static vl root[30], iroot[30];
     for(int st=1; (1<<st) <= n; st++) {
         if(root[st].empty()) {
             ll t = pow<mod>(w, (mod-1)/(1<<st));
@@ -46,7 +40,6 @@ void ntt(vector<ll> &a, bool inv = false) {
     }
     
     vector<ll>* r = (inv?root:iroot);
-    
     for(int st = 1; (1<<st) <= n; st++) {
         int i = 1<<st; //int step = n / i;
         for(int j=0; j<n; j+=i) {
@@ -70,12 +63,9 @@ vl conv(vl A, vl B) {
     A.resize(t); B.resize(t);
 
     ntt<mod, w>(A); ntt<mod, w>(B);
-
     fors(i, 0, t-1) A[i] = A[i]*B[i]%mod;
-    
     ntt<mod, w>(A, true);
-    A.resize(n+m-1);
     
-    return A;
+    return A.resize(n+m-1), A;
 }
 } // namespace GMS

source/Math/Polynomial.cpp

@@ -51,7 +51,7 @@ struct Qring : public vl {
     }
     friend poly operator*(const poly& A, const poly& B) {
         poly ret = conv<mod, w>(A, B);
-        // ACL : poly ret = atcoder::convolution<mod>(A, B);
+        // poly ret = atcoder::convolution<mod>(A, B); // ACL
         return ret.adjust(), ret;
     }
     friend poly inv(const poly& A, int t) { assert(A[0] != 0);
@@ -89,16 +89,15 @@ struct Qring : public vl {
         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<mod>(ret[idx], mod-2); poly g;
+        ll c = ret[idx]; ll ic = pow<mod>(ret[idx], mod-2);
-        int n = ret.size();
+        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<mod>(c, b);
         
-        ret = poly(0, t); fors(i, idx*b, t-1) ret[i] = g[i-idx*b] * c % mod;
+        ret = poly(0, t);
-        
+        fors(i, idx*b, t-1) ret[i] = g[i-idx*b] * c % mod;
         return ret;
     }
     

source/Math/PrimitiveRoot.cpp

@@ -1,16 +1,14 @@
+random_device rd; mt19937 rng(rd());
+
 ll primary_root(ll p) {
-    std::random_device rd;
+    uniform_int_distribution<ll> dist(1, p-1);
-    std::mt19937 gen(rd());
+    auto gen = bind(dist, rng);
-    std::uniform_int_distribution<ll> distrib(1, p-1);
 
-    //distrib(gen);
     vl g = po_rho(p-1);
-    
     while(true) {
-        ll c = distrib(gen);
+        ll c = gen(), u = p-1, b = 1;
+        bool ok = true;
 
-        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);

source/Math/math.tex

@@ -33,64 +33,154 @@ If $a_n = c_1 a_{n-1} + \dots + c_k a_{n-k}$, and $r_1, \dots, r_k$ are distinct
 \[a_n = d_1r_1^n + \dots + d_kr_k^n. \]
 Non-distinct roots $r$ become polynomial factors, e.g. $a_n = (d_1n + d_2)r^n$.
 
-% \subsection{Trigonometry}
+\subsection{Trigonometry}
-% \begin{align*}
+\begin{align*}
-% \sin(v+w)&{}=\sin v\cos w+\cos v\sin w\\
+\sin(v+w)&{}=\sin v\cos w+\cos v\sin w\\
-% \cos(v+w)&{}=\cos v\cos w-\sin 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}\\
+\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}\\
+\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}\\
+\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
+(V+W)\tan(v-w)/2&{}=(V-W)\tan(v+w)/2
-% \end{align*}
+\end{align*}
-% where $V, W$ are lengths of sides opposite angles $v, w$.
+where $V, W$ are lengths of sides opposite angles $v, w$.
-% \begin{align*}
+\begin{align*}
-% 	a\cos x+b\sin x&=r\cos(x-\phi)\\
+	a\cos x+b\sin x&=r\cos(x-\phi)\\
-% 	a\sin x+b\cos x&=r\sin(x+\phi)
+	a\sin x+b\cos x&=r\sin(x+\phi)
-% \end{align*}
+\end{align*}
-% where $r=\sqrt{a^2+b^2}, \phi=\operatorname{atan2}(b,a)$.
+where $r=\sqrt{a^2+b^2}, \phi=\operatorname{atan2}(b,a)$.
 
 \subsection{Geometry}
 
+\subsubsection{Spherical coordinates}
+\begin{center}
+\includegraphics[width=25mm]{source/Math/sphericalCoordinates.pdf}
+\end{center}
+\[\begin{array}{cc}
+x = r\sin\theta\cos\phi & r = \sqrt{x^2+y^2+z^2}\\
+y = r\sin\theta\sin\phi & \theta = \textrm{acos}(z/\sqrt{x^2+y^2+z^2})\\
+z = r\cos\theta & \phi = \textrm{atan2}(y,x)
+\end{array}\]
+
 \subsubsection{Triangles}
-Side lengths: $a,b,c$
 
-Semiperimeter: $p=\dfrac{a+b+c}{2}$
+\begin{tikzpicture}[scale=1.1]
 
-Area: $A=\sqrt{p(p-a)(p-b)(p-c)}$
+%------------------------------------------------
+% Triangle
+%------------------------------------------------
+\tkzDefPoint(0,0){B}
+\tkzDefPoint(6,0){C}
+\tkzDefPoint(2,4.5){A}
 
-Circumradius: $R=\dfrac{abc}{4A}$
 
-Inradius: $r=\dfrac{A}{p}$
+\tkzDrawPolygon[thick](A,B,C)
 
-Length of the median (divides the triangle into two equal area triangles): $m_a=\tfrac{1}{2}\sqrt{2b^2+2c^2-a^2}$
+%------------------------------------------------
+% Midpoint & Median
+%------------------------------------------------
+\tkzDefMidPoint(B,C)
+\tkzGetPoint{M}
 
-Length of the bisector (divides angles into two): $s_a=\sqrt{bc\left[1-\left(\dfrac{a}{b+c}\right)^2\right]}$
+\tkzDrawSegment[dashed](A,M)
+\tkzLabelSegment[right](A,M){$m_a$}
+\tkzMarkSegments[mark=||, size=3pt, color=blue](B,M M,C)
 
-Law of sines: $\dfrac{\sin\alpha}{a}=\dfrac{\sin\beta}{b}=\dfrac{\sin\gamma}{c}=\dfrac{1}{2R}$
 
-Law of cosines: $a^2=b^2+c^2-2bc\cos\alpha$
+%------------------------------------------------
+% Angle bisector
+%------------------------------------------------
+\tkzDefLine[bisector](B,A,C)
+\tkzGetPoint{X}
+\tkzInterLL(A,X)(B,C)
+\tkzGetPoint{S}
 
-Law of tangents: $\dfrac{a+b}{a-b}=\dfrac{\tan\dfrac{\alpha+\beta}{2}}{\tan\dfrac{\alpha-\beta}{2}}$
+\tkzDrawSegment[densely dotted](A,S)
+\tkzLabelSegment[left](A,S){$s_a$}
+
+%------------------------------------------------
+% Incenter & Incircle
+%------------------------------------------------
+\tkzInCenter(A,B,C)
+\tkzGetPoint{I}
+\tkzDrawPoint[fill=black](I)
+
+\tkzDefPointBy[projection=onto B--C](I)
+\tkzGetPoint{H_a}
+
+
+\tkzDrawCircle[thick, red](I, H_a)
+
+\tkzDrawSegment[->](I,H_a)
+\tkzLabelSegment[left](I,H_a){$r$}
+
+%------------------------------------------------
+% Circumcenter & Circumcircle
+%------------------------------------------------
+\tkzCircumCenter(A,B,C)
+\tkzGetPoint{O}
+
+\tkzDrawCircle[thick, blue](O,A)
+
+\tkzDrawSegment(O,C)
+\tkzLabelSegment[above](O,C){$R$}
+
+%------------------------------------------------
+% Labels
+%------------------------------------------------
+\tkzLabelPoints[above](A)
+\tkzLabelPoints[left](B)
+\tkzLabelPoints[right](C)
+\tkzLabelPoints[left](I)
+\tkzLabelPoints[above](O)
+\tkzLabelPoints[below](H_a)
+\tkzLabelPoints[below](M)
+
+\tkzDrawPoint[fill=black](A)
+\tkzDrawPoint[fill=black](B)
+\tkzDrawPoint[fill=black](C)
+\tkzDrawPoint[fill=black](O)
+\tkzDrawPoint[fill=black](H_a)
+\tkzDrawPoint[fill=black](M)
+
+
+\tkzLabelSegment[left=0.7](A,B){$c$}
+\tkzLabelSegment[above right=0.7](A,C){$b$}
+\tkzLabelSegment[below=0.7](B,C){$a$}
+
+\draw[dashed] (A) to[bend right=17] (B);
+\draw[dashed] (B) to[bend right=17] (C);
+\draw[dashed] (C) to[bend right=17] (A);
+
+% \node at (2.7,1.7) {$A$};
+
+\end{tikzpicture}
+
+
+Semiperimeter $s = \dfrac{a+b+c}{2}$; Area $A=\sqrt{s(s-a)(s-b)(s-c)}$
+
+% Circumradius: 
+% Inradius: 
+% Length of the median (divides the triangle into two equal area triangles): 
+$R=\dfrac{abc}{4A}$; $r=\dfrac{A}{s}$; $m_a=\tfrac{1}{2}\sqrt{2b^2+2c^2-a^2}$
+
+
+% Length of the bisector (divides angles into two): 
+$s_a=\sqrt{bc\left[1-\left(\dfrac{a}{b+c}\right)^2\right]}$
+
+$2R=\dfrac{a}{\sin A}=\dfrac{b}{\sin B}=\dfrac{c}{\sin C}$
+
+$a=b\cos C+c\cos B$; $a^2=b^2+c^2-2bc\cos A$; $\dfrac{a+b}{a-b}=\dfrac{\tan\dfrac{\alpha+\beta}{2}}{\tan\dfrac{\alpha-\beta}{2}}$
 
 
 \subsubsection{Quadrilaterals}
 With side lengths $a,b,c,d$, diagonals $e, f$, diagonals angle $\theta$, area $A$ and
 magic flux $F=b^2+d^2-a^2-c^2$:
 
-\[ 4A = 2ef \cdot \sin\theta = F\tan\theta = \sqrt{4e^2f^2-F^2} \]
+\[ 4A = 2ef \sin\theta = F\tan\theta = \sqrt{4e^2f^2-F^2} \]
 
  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*}

source/Misc/NegDiv.cpp

@@ -1,7 +1,5 @@
 #define div _div
-ll div(ll A, ll B)
+ll div(ll A, ll B) {
-{
+    ll q = A/B; if(A<0) q-=(B>0)-(B<0);
-    ll q = A/B;
-    if(A<0) q-=(B>0)-(B<0);
     return q;
 }

source/Misc/mt19937.cpp

@@ -1,7 +1,18 @@
-const long long rand_L = 1;
+const long long L = 1, R = 10;
-const long long rand_R = 10;
+
-mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
+random_device rd; mt19937 rng(rd());
-uniform_int_distribution<int> dist(rand_L, rand_R);
+uniform_int_distribution<int> dist(L, R);
+// discrete_distribution<int> dist({10, 30, 60}); // [0, 2]
+// bernoulli_distribution dist(p); // true(p), false(1-p)
+// binomial_distribution<int> dist(N, p); // # of success
+// geometric_distribution<int> dist(p); // # of failure
+
+// uniform_real_distribution<double> dist(L, R);
+// normal_distribution<double> dist(mean, std);
+// exponential_distribution<double> dist(lambda); // occur time
+// poisson_distribution<int> dist(lambda); // how many?
+// chi_squared_distribution<double> dist(df); // 자유도
+
 auto gen = bind(dist, rng);
 
 gen(); gen(); gen();

source/String/Duval.cpp

@@ -0,0 +1,12 @@
+// https://koosaga.com/301
+vi duval(vi &s){
+    int n=s.size(), i=0; vi v;
+    while(i<n) { int j=i+1, k=i;
+        while(j < n && s[k] <= s[j]){
+            if(s[k] == s[j]) j++, k++;
+            else if(s[k] < s[j]) j++, k = i;
+        }
+        while(i <= k) i += j - k, v.pb(i);
+    }
+    return v;
+}

source/Tree/Centroid.cpp

@@ -27,4 +27,4 @@ int getCentTree(int s){
     return C;
 }
 
-int C = getCentTree(1); cpar[C] = -1;
+// int C = getCentTree(1); cpar[C] = -1;

source/Tree/HLD.cpp

@@ -1,14 +1,16 @@
-BOJ 트리와 쿼리 1
+// BOJ 트리와 쿼리 1
-1 i c: i번 간선의 비용을 c로 바꾼다.
+// 1 i c: i번 간선의 비용을 c로 바꾼다.
-2 u v: u에서 v로 가는 단순 경로에 존재하는 비용 중에서 가장 큰 것을 출력한다.
+// 2 u v: u에서 v로 가는 단순 경로에 존재하는 비용 중에서 가장 큰 것을 출력한다.
+int update(vi& seg, int a, int b);
+int query(vi& seg, int l, int r);
+vi seg;
 
 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;
+        adj[i].erase(find(all(adj[i]), s));
         dfs1(i); sz[s] += sz[i];
         if(sz[i] > sz[adj[s][0]]) swap(adj[s][0], i);
     }
@@ -27,14 +29,14 @@ 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]));
+        ans = max(ans, query(seg, 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]));
+    return max(ans, query(seg, in[a]+1, in[b]));
 }
 
 // dfs1(1); dfs2(1);
-// forr(i, n) arr[in[i]] = m[{par[i], i}]; init(root, arr);
+// forr(i, n) arr[in[i]] = m[{par[i], i}]; init(seg, arr);
-// q == 1: update(root, in[a], c); // in[a]를 c로 대체
+// q == 1: update(seg, in[a], c); // in[a]를 c로 대체
 // q == 2: query(a, b);

source/cy4n1de.cpp

@@ -0,0 +1,38 @@
+#include <bits/stdc++.h>
+#ifdef LOCAL
+#define dbg(x) cerr << #x << " = " << (x) << endl
+#else
+#define dbg(x)
+#endif
+
+using ll=long long;
+#define pii pair<int,int>
+#define vi vector<int>
+#define vll vector<ll>
+#define all(v) v.begin(), v.end()
+#define cyan cin.tie(0)->sync_with_stdio(0);
+/*
+auto max_it = max_element(all(v))
+// Find the first element strictly greater than k
+auto it = upper_bound(all(v), k);
+// Find the first element geq than k
+auto it = lower_bound(all(v), 30);
+*/
+//compress- 중복제거해서 정렬
+#define compress(vec) do { \
+    sort((vec).begin(), (vec).end()); \
+    (vec).erase(unique((vec).begin(), (vec).end()), (vec).end()); \
+} while(0)
+
+#define elif else if
+#define endl '\n'
+using namespace std;
+const ll MOD = 1e9+7;
+ll modpow(ll a, ll b, ll m=MOD){ // a^b mod m
+    ll r=1; a%=m;
+    for(; b; b>>=1, a=a*a%m) if(b&1) r=r*a%m;
+    return r;
+}
+int main(){
+    cyan
+}

source/poro.sh

@@ -1,3 +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 solve='g++ main.cpp -o main -g -fsanitize=undefined,address -fno-omit-frame-pointer -Wall -Wextra && echo "Compile Done" && time ./main'
-alias fast='g++ main.cpp -o solve_exefile -O2 -Wall && echo "Compile Done" && time ./solve_exefile'
+alias fast='g++ main.cpp -o main -O2 -Wall && echo "Compile Done" && time ./main'