teamnote history merge

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<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;
+}