匈牙利

#include <cstring> #include <cstdio> #include <algorithm> #include <vector> using namespace std;const int maxn = 1e3 + 7; vector<int>G[maxn]; int match[maxn],vis[maxn]; int n,m,e; void add(int x,int y) {G[x].push_back(y);G[y].push_back(x); } int dfs(int u) {for(int i = 0;i < G[u].size();i++) {int v = G[u][i];if(!vis[v]) {vis[v] = 1;if(!match[v] || dfs(match[v])) {match[v] = u;return 1;}}}return 0; } int query() {int sum = 0;for(int i = 1;i <= n;i++) {memset(vis,0,sizeof(vis));if(dfs(i)) sum++;}return sum; } int main() {scanf("%d%d%d",&n,&m,&e);for(int i = 1;i <= e;i++) {int x,y;scanf("%d%d",&x,&y);add(x,y + n);}n += m;printf("%d\n",query() / 2);return 0; }

最大流

#include<iostream> #include<cstdio> #include<cstring> #include<algorithm> #include<vector> #include<queue> #include <map>using namespace std; typedef long long ll; const int inf = 1 << 29, N = 50010, M = 300010; int head[N], ver[M], edge[M], Next[M], d[N]; int n, m, s, t, tot; ll maxflow; queue<int> q;void add(int x, int y, int z) {ver[++tot] = y, edge[tot] = z, Next[tot] = head[x], head[x] = tot;ver[++tot] = x, edge[tot] = 0, Next[tot] = head[y], head[y] = tot; }bool bfs() { // 在殘量網絡上構造分層圖memset(d, 0, sizeof(d));while (q.size()) q.pop();q.push(s); d[s] = 1;while (q.size()) {int x = q.front(); q.pop();for (int i = head[x]; i; i = Next[i])if (edge[i] && !d[ver[i]]) {q.push(ver[i]);d[ver[i]] = d[x] + 1;if (ver[i] == t) return 1;}}return 0; }int dinic(int x, int flow) { // 在當前分層圖上增廣if (x == t) return flow;int rest = flow, k;for (int i = head[x]; i && rest; i = Next[i])if (edge[i] && d[ver[i]] == d[x] + 1) {k = dinic(ver[i], min(rest, edge[i]));if (!k) d[ver[i]] = 0; // 剪枝，去掉增廣完畢的點edge[i] -= k;edge[i ^ 1] += k;rest -= k;}return flow - rest; }map<pair<int,int>,int>mp;int main() {int e;cin >> n >> m >> e;s = 0,t = n + m + 1; // cin >> s >> t; // 源點、匯點mp.clear();tot = 1;for (int i = 1; i <= e; i++) {int x, y, c;scanf("%d%d", &x, &y);if(x > n || y > m) continue;if(mp[{x,y + n}]) continue;mp[{x,y + n}] = 1;add(x, y + n, 1);}for(int i = 1;i <= n;i++) add(s,i,1);for(int i = n + 1;i <= n + m;i++) add(i,t,1);int flow = 0;while (bfs())while (flow = dinic(s, inf)) maxflow += flow;cout << maxflow << endl; }

總結

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