dinic.cpp

// Dinic's blocking flow algorithm
// Running time:
// * general networks: O(|V|^2 |E|)
// * unit capacity networks: O(E min(V^(2/3), E^(1/2)))
// * bipartite matching networks: O(E sqrt(V))

const int INF = 2000000000;

struct Edge {
  int from, to, cap, flow, index;
  Edge(int from, int to, int cap, int flow, int index) :
    from(from), to(to), cap(cap), flow(flow), index(index) {}
};

struct Dinic {
  int N;
  vector<vector<Edge> > G;
  vector<Edge *> dad;
  vector<int> Q;
  
  // N = number of vertices
  Dinic(int N) : N(N), G(N), dad(N), Q(N) {}
  
  // Add an edge to initially empty network. from, to are 0-based
  void AddEdge(int from, int to, int cap) {
    G[from].push_back(Edge(from, to, cap, 0, G[to].size()));
    if (from == to) G[from].back().index++;
    G[to].push_back(Edge(to, from, 0, 0, G[from].size() - 1));
  }

  long long BlockingFlow(int s, int t) {
    fill(dad.begin(), dad.end(), (Edge *) NULL);
    dad[s] = &G[0][0] - 1;
    
    int head = 0, tail = 0;
    Q[tail++] = s;
    while (head < tail) {
      int x = Q[head++];
      for (int i = 0; i < G[x].size(); i++) {
        Edge &e = G[x][i];
        if (!dad[e.to] && e.cap - e.flow > 0) {
          dad[e.to] = &G[x][i];
          Q[tail++] = e.to;
        }
      }
    }
    if (!dad[t]) return 0;

    long long totflow = 0;
    for (int i = 0; i < G[t].size(); i++) {
      Edge *start = &G[G[t][i].to][G[t][i].index];
      int amt = INF;
      for (Edge *e = start; amt && e != dad[s]; e = dad[e->from]) {
        if (!e) { amt = 0; break; }
        amt = min(amt, e->cap - e->flow);
      }
      if (amt == 0) continue;
      for (Edge *e = start; amt && e != dad[s]; e = dad[e->from]) {
        e->flow += amt;
        G[e->to][e->index].flow -= amt;
      }
      totflow += amt;
    }
    return totflow;
  }

  // Call this to get the max flow. s, t are 0-based.
  // Note, you can only call this once.
  // To obtain the actual flow values, look at all edges with
  // capacity > 0 (zero capacity edges are residual edges).

  long long GetMaxFlow(int s, int t) {
    long long totflow = 0;
    while (long long flow = BlockingFlow(s, t))
      totflow += flow;
    return totflow;
  }
};