Description

在残余网络上bfs标号建立层次图，然后在层次图上多次dfs不断寻找增广路径增广，增广路径上的结点要按层次图上标号递增的顺序。如果找不到增广路径就重新标记层次图，直到元源点与汇点不再相连。

Code

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <queue>
using namespace std;
typedef long long ll;
const int INF = 0x3f3f3f3f;
const int N = 1e3 + 10;
const int M = 2e3 + 10;struct Edge
{int to, c, next;Edge() {}Edge(int to, int c, int next) : to(to), c(c), next(next) {}
} edge[M];
int adj[N], tot;void init()
{memset(adj, -1, sizeof(adj));tot = 0;
}void add(int u, int v, int c)
{edge[tot] = Edge(v, c, adj[u]);adj[u] = tot++;edge[tot] = Edge(u, 0, adj[v]);adj[v] = tot++;
}int level[N];
queue<int> q;
bool bfs(int s, int t)
{while (!q.empty()) q.pop();memset(level, -1, sizeof(level));level[s] = 0; q.push(s);while (!q.empty()){int u = q.front(); q.pop();for (int i = adj[u]; i != -1; i = edge[i].next){Edge &e = edge[i];if (e.c && level[e.to] == -1){level[e.to] = level[u] + 1;if (e.to == t) return true;q.push(e.to);}}}return false;
}int cur[N];
int dfs(int u, int t, int flow)
{if (u == t) return flow;for (int &i = cur[u]; i != -1; i = edge[i].next){Edge &e = edge[i];if (e.c && level[e.to] > level[u]){int f = dfs(e.to, t, min(flow, e.c));if (f){e.c -= f;edge[i ^ 1].c += f;return f;}}}return 0;
}int dinic(int s, int t)
{int flow = 0;while (bfs(s, t)){memcpy(cur, adj, sizeof(adj));int f; int c = 0;while (f = dfs(s, t, INF)) flow += f;}return flow;
}int main()
{int n, m;scanf("%d%d", &n, &m);init();while (m--){int u, v, c;scanf("%d%d%d", &u, &v, &c);add(u, v, c);}int s, t;scanf("%d%d", &s, &t);int ans = dinic(s, t);printf("%d\n", ans);return 0;
}

Input

第一行给出结点数\(n\)和边数\(m\)，接下来的\(m\)行，每行给出两个三个整数\(u\)，\(v\)和\(c\)，表示从\(u\)到\(v\)有一条容量为\(c\)的边。最后一行给出源点\(s\)和汇点\(t\)。

Output

输出一个整数，表示最大流。

Sample Input

6 9
0 1 10
0 2 10
1 2 2
1 3 4
1 4 8
2 4 9
3 5 10
4 3 6
4 5 10
0 5

Sample Output

19