Files
teamnote/2025fall/source/Graph/Matching.cpp
2026-06-03 09:36:52 +09:00

74 lines
1.7 KiB
C++

// 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<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;
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<int> (); 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<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 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;
}