mincostmaxflow.cc

// https://open.kattis.com/problems/mincostmaxflow
#include <bits/stdc++.h>

// code in the atcode namespace is taken from
// https://github.com/atcoder/ac-library/blob/master/atcoder/mincostflow.hpp
namespace atcoder {

template <class Cap, class Cost> struct mcf_graph {
public:
  mcf_graph() {}
  mcf_graph(int n) : _n(n), g(n) {}

  int add_edge(int from, int to, Cap cap, Cost cost) {
    assert(0 <= from && from < _n);
    assert(0 <= to && to < _n);
    assert(0 <= cap);
    assert(0 <= cost);
    int m = int(pos.size());
    pos.push_back({from, int(g[from].size())});
    int from_id = int(g[from].size());
    int to_id = int(g[to].size());
    if (from == to) to_id++;
    g[from].push_back(_edge{to, to_id, cap, cost});
    g[to].push_back(_edge{from, from_id, 0, -cost});
    return m;
  }

  struct edge {
    int from, to;
    Cap cap, flow;
    Cost cost;
  };

  edge get_edge(int i) {
    int m = int(pos.size());
    assert(0 <= i && i < m);
    auto _e = g[pos[i].first][pos[i].second];
    auto _re = g[_e.to][_e.rev];
    return edge{
        pos[i].first, _e.to, _e.cap + _re.cap, _re.cap, _e.cost,
    };
  }
  std::vector<edge> edges() {
    int m = int(pos.size());
    std::vector<edge> result(m);
    for (int i = 0; i < m; i++) { result[i] = get_edge(i); }
    return result;
  }

  std::pair<Cap, Cost> flow(int s, int t) {
    return flow(s, t, std::numeric_limits<Cap>::max());
  }
  std::pair<Cap, Cost> flow(int s, int t, Cap flow_limit) {
    return slope(s, t, flow_limit).back();
  }
  std::vector<std::pair<Cap, Cost>> slope(int s, int t) {
    return slope(s, t, std::numeric_limits<Cap>::max());
  }
  std::vector<std::pair<Cap, Cost>> slope(int s, int t, Cap flow_limit) {
    assert(0 <= s && s < _n);
    assert(0 <= t && t < _n);
    assert(s != t);
    // variants (C = maxcost):
    // -(n-1)C <= dual[s] <= dual[i] <= dual[t] = 0
    // reduced cost (= e.cost + dual[e.from] - dual[e.to]) >= 0 for all edge
    std::vector<Cost> dual(_n, 0), dist(_n);
    std::vector<int> pv(_n), pe(_n);
    std::vector<bool> vis(_n);
    auto dual_ref = [&]() {
      std::fill(dist.begin(), dist.end(), std::numeric_limits<Cost>::max());
      std::fill(pv.begin(), pv.end(), -1);
      std::fill(pe.begin(), pe.end(), -1);
      std::fill(vis.begin(), vis.end(), false);
      struct Q {
        Cost key;
        int to;
        bool operator<(Q r) const { return key > r.key; }
      };
      std::priority_queue<Q> que;
      dist[s] = 0;
      que.push(Q{0, s});
      while (!que.empty()) {
        int v = que.top().to;
        que.pop();
        if (vis[v]) continue;
        vis[v] = true;
        if (v == t) break;
        // dist[v] = shortest(s, v) + dual[s] - dual[v]
        // dist[v] >= 0 (all reduced cost are positive)
        // dist[v] <= (n-1)C
        for (int i = 0; i < int(g[v].size()); i++) {
          auto e = g[v][i];
          if (vis[e.to] || !e.cap) continue;
          // |-dual[e.to] + dual[v]| <= (n-1)C
          // cost <= C - -(n-1)C + 0 = nC
          Cost cost = e.cost - dual[e.to] + dual[v];
          if (dist[e.to] - dist[v] > cost) {
            dist[e.to] = dist[v] + cost;
            pv[e.to] = v;
            pe[e.to] = i;
            que.push(Q{dist[e.to], e.to});
          }
        }
      }
      if (!vis[t]) { return false; }

      for (int v = 0; v < _n; v++) {
        if (!vis[v]) continue;
        // dual[v] = dual[v] - dist[t] + dist[v]
        //         = dual[v] - (shortest(s, t) + dual[s] - dual[t]) +
        //         (shortest(s, v) + dual[s] - dual[v]) = - shortest(s, t) +
        //         dual[t] + shortest(s, v) = shortest(s, v) - shortest(s, t) >=
        //         0 - (n-1)C
        dual[v] -= dist[t] - dist[v];
      }
      return true;
    };
    Cap flow = 0;
    Cost cost = 0, prev_cost_per_flow = -1;
    std::vector<std::pair<Cap, Cost>> result;
    result.push_back({flow, cost});
    while (flow < flow_limit) {
      if (!dual_ref()) break;
      Cap c = flow_limit - flow;
      for (int v = t; v != s; v = pv[v]) {
        c = std::min(c, g[pv[v]][pe[v]].cap);
      }
      for (int v = t; v != s; v = pv[v]) {
        auto &e = g[pv[v]][pe[v]];
        e.cap -= c;
        g[v][e.rev].cap += c;
      }
      Cost d = -dual[s];
      flow += c;
      cost += c * d;
      if (prev_cost_per_flow == d) { result.pop_back(); }
      result.push_back({flow, cost});
      prev_cost_per_flow = d;
    }
    return result;
  }

private:
  int _n;

  struct _edge {
    int to, rev;
    Cap cap;
    Cost cost;
  };

  std::vector<std::pair<int, int>> pos;
  std::vector<std::vector<_edge>> g;
};

} // namespace atcoder

using namespace std;
using ll = long long;

int main() {
  cin.tie(0), ios::sync_with_stdio(0);
  ll n, m, s, t, u, v, c, w;
  cin >> n >> m >> s >> t;
  atcoder::mcf_graph<ll, ll> g(n);
  for (int i = 0; i < m; i++) cin >> u >> v >> c >> w, g.add_edge(u, v, c, w);
  auto ans = g.flow(s, t);
  cout << ans.first << ' ' << ans.second << '\n';
}