网络流EK算法

传送门

EK算法的思想就是不断找到可行流，然后加入最大流中。每次添加反向流，存在一种反悔机制。时间复杂度o(nm²)，n是点数，m是边数。

#include <bits/stdc++.h>
using namespace std;
const int N = 205;
const int inf = 0x3f3f3f3f;
int n, m, st, ed;
int flow[N], pre[N], g[N][N];
int bfs()
{
    memset(pre, 0, sizeof pre);
    memset(flow, 0, sizeof flow);
    queue<int> q;
    q.push(st);
    flow[st] = inf;
    while(!q.empty())
    {
        int u = q.front();
        q.pop();
        for(int i = 1; i <= n; ++i)
        {
            if(i != st && g[u][i] && !pre[i])
            {
                pre[i] = u;
                q.push(i);
                flow[i] = min(flow[u], g[u][i]);
            }
        }
    }
    return pre[ed] ? flow[ed] : -1;
}
int ek_flow()
{
    int ans = 0;
    while(1)
    {
        int okflow = bfs();
        if(okflow == -1) break;
        int now = ed;
        while(now != st)
        {
            int fa = pre[now];
            g[fa][now] -= okflow;
            g[now][fa] += okflow;
            now = fa;
        }
        ans += okflow;
    }
    return ans;
}
signed main()
{
    ios::sync_with_stdio(false), cin.tie(0);
    while(cin >> n >> m)
    {
        memset(g, 0, sizeof g);
        int u, v, w;
        for(int i = 1; i <= n; ++i)
        {
            cin >> u >> v >> w;
            g[u][v] += w;
        }
        st = 1, ed = m;
        cout << ek_flow() << "\n";
    }
    return 0;
}