edmonds-karp

const int MAXN = 1e4+5;
const int INF = 1e9;

struct edge {
    int a, b, cap, flow;
};

int n, s, t, f[MAXN], p[MAXN];
vector<edge> e;
vi g[MAXN];

void add_edge (int a, int b, int cap) {
    edge e1 = { a, b, cap, 0 };
    edge e2 = { b, a, 0, 0 };
    g[a].push_back ((int) e.size());
    e.push_back (e1);
    g[b].push_back ((int) e.size());
    e.push_back (e2);
}

int bfs () {
    memset(f, 0, n*sizeof(f[0]));
    queue<int> q;
    q.push(s), f[s] = INF;
    while(!f[t]) {
        if(q.empty()) return 0;
        int u = q.front(); q.pop();
        for(auto id: g[u]) {
            int to = e[id].b;
            if(!f[to] && e[id].cap > e[id].flow)
                q.push(to), p[to] = id, f[to] = min(f[u], e[id].cap - e[id].flow);
        }
    }

    for(int u = t; u != s; u=e[p[u]].a) {
        e[p[u]].flow += f[t];
        e[p[u]^1].flow -= f[t];
    }

    return f[t];
}

int edmonds_karp() {
    int flow = 0, pushed;
    do {
        flow += pushed = bfs();
    } while(pushed);
    return flow;
}