一些模板

\(1.\) 最大流

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#include <bits/stdc++.h>
#define int long long

using namespace std;

const int inf = 1e9;
const int N = 2e5 + 100;

int n, m, s, t, head[N], tot = 1, dep[N], cur[N];

struct Node {
	int to, nxt, w;
} e[N];

void add(int u, int v, int w) {
	e[++tot] = {v, head[u], w};
	head[u] = tot;
}

bool bfs() {
	queue<int> q;
	q.push(s);
	memset(dep, 0, sizeof(dep));
	dep[s] = 1;
	cur[s] = head[s];
	while (!q.empty()) {
		int u = q.front();
		q.pop();
		for (int i = head[u]; i; i = e[i].nxt) {
			int v = e[i].to;
			if (e[i].w && !dep[v]) {
				dep[v] = dep[u] + 1;
				cur[v] = head[v];
				q.push(v);
				if (v == t) {
					return 1;
				}
			}
		}
	}
	return 0;
}

int dfs(int u, int p) {
	if (u == t) {
		return p;
	}
	int r = p;
	for (int i = cur[u]; i && r; i = e[i].nxt) {
		cur[u] = i;
		int v = e[i].to;
		if (e[i].w && dep[v] == dep[u] + 1) {
			int k = dfs(v, min(r, e[i].w));
			if (!k) {
				dep[v] = 0;
			}
			e[i].w -= k;
			e[i ^ 1].w += k;
			r -= k;
		}
	}
	return p - r;
}

signed main() {
	cin >> n >> m >> s >> t;
	for (int i = 1, u, v, w; i <= m; i++) {
		cin >> u >> v >> w;
		add(u, v, w);
		add(v, u, 0);
	}
	int ans = 0, sum = 0;
	while (bfs()) {
		while (ans = dfs(s, inf)) {
			sum += ans;
		}
	}
	cout << sum << '\n';
	return 0;
}

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