Problem p01410 (C++) — buggy submission, verdict: Time Limit Exceeded

#include <bits/stdc++.h>

#define FOR(i, a, b) for (int i = (a); i < ((int)b); ++i)
#define RFOR(i, a) for (int i = (a); i >= 0; --i)
#define FOE(i, a) for (auto i : a)
#define ALL(c) (c).begin(), (c).end()
#define RALL(c) (c).rbegin(), (c).rend()
#define DUMP(x) cerr << #x << " = " << (x) << endl;
#define SUM(x) std::accumulate(ALL(x), 0LL)
#define MIN(v) *std::min_element(v.begin(), v.end())
#define MAX(v) *std::max_element(v.begin(), v.end())
#define EXIST(v, x) (std::find(v.begin(), v.end(), x) != v.end())
#define BIT(n) (1LL << (n))
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end());

typedef long long LL;
template <typename T> using V = std::vector<T>;
template <typename T> using VV = std::vector<std::vector<T>>;
template <typename T> using VVV = std::vector<std::vector<std::vector<T>>>;
template <class T> inline T ceil(T a, T b) { return (a + b - 1) / b; }
template <class T> inline void print(T x) { std::cout << x << std::endl; }
template <class T> inline bool inside(T y, T x, T H, T W) {
  return 0 <= y and y < H and 0 <= x and x < W;
}
inline double distance(double y1, double x1, double y2, double x2) {
  return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}

const int INF = 1L << 30;
const double EPS = 1e-9;
const std::string YES = "YES", Yes = "Yes", NO = "NO", No = "No";
const std::vector<int> dy = {0, 1, 0, -1},
                       dx = {1, 0, -1, 0}; // 4近傍（右, 下, 左, 上）

using namespace std;

// 最小費用流
class PrimalDual {
  struct Edge {
    const int to;      // 行き先のノードid
    int flow;          // 流量
    const int cap;     // 容量
    const int cost;    // コスト
    const int rev;     // 逆辺のノードid
    const bool is_rev; // 逆辺かどうか
    Edge(int to, int flow, int cap, int cost, int rev, bool is_rev)
        : to(to), flow(flow), cost(cost), cap(cap), rev(rev), is_rev(is_rev) {
      assert(this->cap >= 0);
    }
  };

  // s-tまでの最短経路
  struct Route {
    vector<int> dist;  // 最短距離
    vector<int> prevv; // 前の頂点
    vector<int> preve; // 直前の辺
    vector<int> h;     // ポテンシャル
    Route(vector<int> &dist, vector<int> &prevv, vector<int> &preve,
          vector<int> &h)
        : dist(dist), prevv(prevv), preve(preve), h(h) {}
  };

  const unsigned long V;      // 頂点数
  vector<vector<Edge>> graph; // グラフの隣接リスト表現
  vector<int> h;              // ポテンシャル
  vector<int> dist;           // 最短距離
  vector<int> prevv, preve;   // 直前の頂点と辺

public:
  PrimalDual(unsigned long num_of_node) : V(num_of_node) {
    graph.resize(V);
    h.resize(V, 0);
    dist.resize(V);
    prevv.resize(V);
    preve.resize(V);
  }

  // sからtへの流量fの最小費用流を求める
  // 流せない場合は-1を返す
  int min_cost_flow2(int s, int t, int f) {
    int res = 0;

    while (f > 0) {

      // ダイクストラ法を用いてhを更新する
      priority_queue<pair<int, int>, vector<pair<int, int>>,
                     greater<pair<int, int>>>
          que;
      fill(dist.begin(), dist.end(), INT_MAX);
      dist[s] = 0;
      que.push(make_pair(0, s));
      while (not que.empty()) {
        pair<int, int> p = que.top(); // firstは最短距離, secondは頂点の番号
        que.pop();
        int v = p.second;
        if (dist[v] < p.first) {
          continue;
        }
        for (int i = 0; i < graph[v].size(); ++i) {
          Edge &e = graph[v][i];
          if (e.cap - e.flow > 0 &&
              dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {
            dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
            prevv[e.to] = v;

            preve[e.to] = i;
            que.push(make_pair(dist[e.to], e.to));
          }
        }
      }

      if (dist[t] == INT_MAX) {
        // これ以上流せない
        return res;
      }
      for (int v = 0; v < V; v++) {
        h[v] += dist[v];
      }
      // s-t間最短路に沿って目一杯流す
      int d = f;
      for (int v = t; v != s; v = prevv[v]) {
        d = min(d,
                graph[prevv[v]][preve[v]].cap - graph[prevv[v]][preve[v]].flow);
      }
      f -= d;
      res += d * h[t];
      for (int v = t; v != s; v = prevv[v]) {
        Edge &e = graph[prevv[v]][preve[v]];
        e.flow += d;
        graph[v][e.rev].flow -= d;
      }
    }
    return res;
  }

  // fromからtoへ向かう容量cap、コストcostの辺をグラフに追加する
  void add_edge(int from, int to, int cap, int cost) {
    graph[from].emplace_back(Edge(to, 0, cap, cost, graph[to].size(), false));
    graph[to].emplace_back(
        Edge(from, cap, cap, -cost, graph[from].size() - 1, true));
  }

  // sからtへの流量fの最小費用流を求める(流せない場合は-1)
  // O(F|E|log |V|)かO(F|V|^2)
  int min_cost_flow(int s, int t, int f) {
    int res = 0;

    while (f > 0) {
      Route route = dijkstra(s, t);
      vector<int> &dist = route.dist;
      vector<int> &prevv = route.prevv;
      vector<int> &preve = route.preve;
      vector<int> &h = route.h;

      // これ以上流せない
      if (dist[t] == INT_MAX) {
        return res;
        // return -1;
      }

      for (int v = 0; v < V; v++) {
        h[v] += dist[v];
      }

      // s-t間最短路に沿って目一杯流す
      int d = f;
      for (int v = t; v != s; v = prevv[v]) {
        int rest =
            graph[prevv[v]][preve[v]].cap - graph[prevv[v]][preve[v]].flow;
        d = min(d, rest);
      }
      f -= d;
      res += d * h[t];
      for (int v = t; v != s; v = prevv[v]) {
        Edge &e = graph[prevv[v]][preve[v]];
        e.flow += d;
        graph[v][e.rev].flow -= d;
      }
    }
    return res;
  }

  // sからtへの流量fの最小費用流(流せない場合は-1)
  // 負のコストがあってもいい
  // O(F|V||E|)
  int min_cost_flow_bellmanford(int s, int t, int f) {
    int res = 0;
    while (f > 0) {
      Route route = bellmanford(s, t);
      vector<int> &dist = route.dist;
      vector<int> &prevv = route.prevv;
      vector<int> &preve = route.preve;

      // これ以上流せない
      if (dist[t] == INT_MAX) {
        // return -1;
        return res; // 流せた分についての費用がほしいときはこっち
      }

      // s-t間最短路に沿って目一杯流す
      int d = f;
      for (int v = t; v != s; v = prevv[v]) {
        int rest =
            graph[prevv[v]][preve[v]].cap - graph[prevv[v]][preve[v]].flow;
        d = min(d, rest);
      }

      f -= d;
      res += d * dist[t];
      for (int v = t; v != s; v = prevv[v]) {
        Edge &e = graph[prevv[v]][preve[v]];
        e.flow += d;
        graph[v][e.rev].flow -= d;
      }
    }
    return res;
  }

  // 水の流れたエッジを取得する
  set<pair<int, int>> get_used_edges() {
    set<pair<int, int>> used_edges;
    for (int from = 0; from < this->graph.size(); ++from) {
      for (Edge edge : graph[from]) {
        int flow = edge.flow;
        bool is_rev = edge.is_rev;

        if (not is_rev and flow > 0) {
          int to = edge.to;
          used_edges.insert(make_pair(from, to));
        }
      }
    }
    return used_edges;
  }

private:
  // dijkstraでsからtへの最短ルートを求める
  Route dijkstra(int s, int t) {
    vector<int> dist(V, INT_MAX), prevv(V, 0), preve(V, 0), h(V, 0);

    priority_queue<pair<int, int>, vector<pair<int, int>>,
                   greater<pair<int, int>>>
        que;
    dist[s] = 0;
    que.push(make_pair(0, s));
    while (not que.empty()) {
      pair<int, int> p = que.top(); // firstは最短距離, secondは頂点の番号
      que.pop();
      int v = p.second;
      if (dist[v] < p.first) {
        continue;
      }
      for (int i = 0; i < graph[v].size(); ++i) {
        Edge &e = graph[v][i];
        if (e.cap - e.flow > 0 and
            dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {
          dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
          prevv[e.to] = v;

          preve[e.to] = i;
          que.push(make_pair(dist[e.to], e.to));
        }
      }
    }

    return Route(dist, prevv, preve, h);
  }

  // bellmanfordでsからtへの最短ルートを求める
  Route bellmanford(int s, int t) {
    vector<int> dist(V, INT_MAX), prevv(V, 0), preve(V, 0), h(V, 0);

    // ベルマンフォード法により、s-t間最短路を求める
    dist[s] = 0;
    bool update = true;
    while (update) {
      update = false;
      for (int v = 0; v < V; v++) {
        if (dist[v] == INT_MAX)
          continue;
        for (int i = 0; i < graph[v].size(); i++) {
          Edge &e = graph[v][i];
          int rest = e.cap - e.flow;
          int new_cost = dist[v] + e.cost;
          if (rest > 0 and dist[e.to] > new_cost) {
            dist[e.to] = new_cost;
            prevv[e.to] = v;
            preve[e.to] = i;
            update = true;
          }
        }
      }
    }

    return Route(dist, prevv, preve, h);
  }
};

int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);

  int N;
  cin >> N;
  V<int> A(N), B(N);
  set<int> value_set;
  FOR(i, 0, N) {
    cin >> A[i] >> B[i];
    value_set.insert(A[i]);
    value_set.insert(B[i]);
  }
  V<int> v(ALL(value_set));

  int s = v.size() + N;
  int t = s + 1;
  int dummy = t + 1;
  PrimalDual pd(v.size() + N + 3);

  FOR(i, 0, v.size()) {
    pd.add_edge(s, i, 1, 0);
    pd.add_edge(i, dummy, INF, 0);
  }

  FOR(i, 0, v.size()) {
    FOR(j, 0, N) {
      int a = A[j], b = B[j];
      if (v[i] == a) {
        pd.add_edge(i, v.size() + j, 1, -b);
      }
      if (v[i] == b) {
        pd.add_edge(i, v.size() + j, 1, -a);
      }
    }
  }

  FOR(j, 0, N) { pd.add_edge(v.size() + j, t, 1, 0); }
  pd.add_edge(dummy, t, INF, 0);

  cout << -1 * pd.min_cost_flow2(s, t, N * 2) << endl;
  return 0;
}


Error: TLE

Fixed submission:

#include <bits/stdc++.h>

#define FOR(i, a, b) for (int i = (a); i < ((int)b); ++i)
#define RFOR(i, a) for (int i = (a); i >= 0; --i)
#define FOE(i, a) for (auto i : a)
#define ALL(c) (c).begin(), (c).end()
#define RALL(c) (c).rbegin(), (c).rend()
#define DUMP(x) cerr << #x << " = " << (x) << endl;
#define SUM(x) std::accumulate(ALL(x), 0LL)
#define MIN(v) *std::min_element(v.begin(), v.end())
#define MAX(v) *std::max_element(v.begin(), v.end())
#define EXIST(v, x) (std::find(v.begin(), v.end(), x) != v.end())
#define BIT(n) (1LL << (n))
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end());

typedef long long LL;
template <typename T> using V = std::vector<T>;
template <typename T> using VV = std::vector<std::vector<T>>;
template <typename T> using VVV = std::vector<std::vector<std::vector<T>>>;
template <class T> inline T ceil(T a, T b) { return (a + b - 1) / b; }
template <class T> inline void print(T x) { std::cout << x << std::endl; }
template <class T> inline bool inside(T y, T x, T H, T W) {
  return 0 <= y and y < H and 0 <= x and x < W;
}
inline double distance(double y1, double x1, double y2, double x2) {
  return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}

const int INF = 1L << 30;
const double EPS = 1e-9;
const std::string YES = "YES", Yes = "Yes", NO = "NO", No = "No";
const std::vector<int> dy = {0, 1, 0, -1},
                       dx = {1, 0, -1, 0}; // 4近傍（右, 下, 左, 上）

using namespace std;

// 最小費用流
class PrimalDual {
  struct Edge {
    const int to;      // 行き先のノードid
    int flow;          // 流量
    const int cap;     // 容量
    const int cost;    // コスト
    const int rev;     // 逆辺のノードid
    const bool is_rev; // 逆辺かどうか
    Edge(int to, int flow, int cap, int cost, int rev, bool is_rev)
        : to(to), flow(flow), cost(cost), cap(cap), rev(rev), is_rev(is_rev) {
      assert(this->cap >= 0);
    }
  };

  // s-tまでの最短経路
  struct Route {
    vector<int> dist;  // 最短距離
    vector<int> prevv; // 前の頂点
    vector<int> preve; // 直前の辺
    vector<int> h;     // ポテンシャル
    Route(vector<int> &dist, vector<int> &prevv, vector<int> &preve,
          vector<int> &h)
        : dist(dist), prevv(prevv), preve(preve), h(h) {}
  };

  const unsigned long V;      // 頂点数
  vector<vector<Edge>> graph; // グラフの隣接リスト表現

public:
  PrimalDual(unsigned long num_of_node) : V(num_of_node) { graph.resize(V); }

  // fromからtoへ向かう容量cap、コストcostの辺をグラフに追加する
  void add_edge(int from, int to, int cap, int cost) {
    graph[from].emplace_back(Edge(to, 0, cap, cost, graph[to].size(), false));
    graph[to].emplace_back(
        Edge(from, cap, cap, -cost, graph[from].size() - 1, true));
  }

  // sからtへの流量fの最小費用流を求める(流せない場合は-1)
  // O(F|E|log |V|)かO(F|V|^2)
  int min_cost_flow(int s, int t, int f) {
    int res = 0;

    while (f > 0) {
      Route route = dijkstra(s, t);
      vector<int> dist = route.dist;
      vector<int> prevv = route.prevv;
      vector<int> preve = route.preve;
      vector<int> h = route.h;

      // これ以上流せない
      if (dist[t] == INT_MAX) {
        return res;
        // return -1;
      }

      for (int v = 0; v < V; v++) {
        h[v] += dist[v];
      }

      // s-t間最短路に沿って目一杯流す
      int d = f;
      for (int v = t; v != s; v = prevv[v]) {
        int rest =
            graph[prevv[v]][preve[v]].cap - graph[prevv[v]][preve[v]].flow;
        d = min(d, rest);
      }
      f -= d;
      res += d * h[t];
      for (int v = t; v != s; v = prevv[v]) {
        Edge &e = graph[prevv[v]][preve[v]];
        e.flow += d;
        graph[v][e.rev].flow -= d;
      }
    }
    return res;
  }

  // sからtへの流量fの最小費用流(流せない場合は-1)
  // 負のコストがあってもいい
  // O(F|V||E|)
  int min_cost_flow_bellmanford(int s, int t, int f) {
    int res = 0;
    while (f > 0) {
      Route route = bellmanford(s, t);
      vector<int> dist = route.dist;
      vector<int> prevv = route.prevv;
      vector<int> preve = route.preve;

      // これ以上流せない
      if (dist[t] == INT_MAX) {
        // return -1;
        return res; // 流せた分についての費用がほしいときはこっち
      }

      // s-t間最短路に沿って目一杯流す
      int d = f;
      for (int v = t; v != s; v = prevv[v]) {
        int rest =
            graph[prevv[v]][preve[v]].cap - graph[prevv[v]][preve[v]].flow;
        d = min(d, rest);
      }

      f -= d;
      res += d * dist[t];
      for (int v = t; v != s; v = prevv[v]) {
        Edge &e = graph[prevv[v]][preve[v]];
        e.flow += d;
        graph[v][e.rev].flow -= d;
      }
    }
    return res;
  }

  // 水の流れたエッジを取得する
  set<pair<int, int>> get_used_edges() {
    set<pair<int, int>> used_edges;
    for (int from = 0; from < this->graph.size(); ++from) {
      for (Edge edge : graph[from]) {
        int flow = edge.flow;
        bool is_rev = edge.is_rev;

        if (not is_rev and flow > 0) {
          int to = edge.to;
          used_edges.insert(make_pair(from, to));
        }
      }
    }
    return used_edges;
  }

private:
  // dijkstraでsからtへの最短ルートを求める
  Route dijkstra(int s, int t) {
    vector<int> dist(V, INT_MAX), prevv(V, 0), preve(V, 0), h(V, 0);

    priority_queue<pair<int, int>, vector<pair<int, int>>,
                   greater<pair<int, int>>>
        que;
    dist[s] = 0;
    que.push(make_pair(0, s));
    while (not que.empty()) {
      pair<int, int> p = que.top(); // firstは最短距離, secondは頂点の番号
      que.pop();
      int v = p.second;
      if (dist[v] < p.first) {
        continue;
      }
      for (int i = 0; i < graph[v].size(); ++i) {
        Edge &e = graph[v][i];
        if (e.cap - e.flow > 0 and
            dist[e.to] > dist[v] + e.cost + h[v] - h[e.to]) {
          dist[e.to] = dist[v] + e.cost + h[v] - h[e.to];
          prevv[e.to] = v;

          preve[e.to] = i;
          que.push(make_pair(dist[e.to], e.to));
        }
      }
    }

    return Route(dist, prevv, preve, h);
  }

  // bellmanfordでsからtへの最短ルートを求める
  Route bellmanford(int s, int t) {
    vector<int> dist(V, INT_MAX), prevv(V, 0), preve(V, 0), h(V, 0);

    // ベルマンフォード法により、s-t間最短路を求める
    dist[s] = 0;
    bool update = true;
    while (update) {
      update = false;
      for (int v = 0; v < V; v++) {
        if (dist[v] == INT_MAX)
          continue;
        for (int i = 0; i < graph[v].size(); i++) {
          Edge &e = graph[v][i];
          int rest = e.cap - e.flow;
          int new_cost = dist[v] + e.cost;
          if (rest > 0 and dist[e.to] > new_cost) {
            dist[e.to] = new_cost;
            prevv[e.to] = v;
            preve[e.to] = i;
            update = true;
          }
        }
      }
    }

    return Route(dist, prevv, preve, h);
  }
};

int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);

  int N;
  cin >> N;
  V<int> A(N), B(N);
  set<int> value_set;
  FOR(i, 0, N) {
    cin >> A[i] >> B[i];
    value_set.insert(A[i]);
    value_set.insert(B[i]);
  }
  V<int> v(ALL(value_set));

  int s = v.size() + N;
  int t = s + 1;
  int dummy = t + 1;
  PrimalDual pd(v.size() + N + 3);

  FOR(i, 0, v.size()) {
    pd.add_edge(s, i, 1, 0);
    pd.add_edge(i, dummy, INF, 0);
  }

  FOR(i, 0, v.size()) {
    FOR(j, 0, N) {
      int a = A[j], b = B[j];
      if (v[i] == a) {
        pd.add_edge(i, v.size() + j, 1, -b);
      }
      if (v[i] == b) {
        pd.add_edge(i, v.size() + j, 1, -a);
      }
    }
  }

  FOR(j, 0, N) { pd.add_edge(v.size() + j, t, 1, 0); }
  pd.add_edge(dummy, t, INF, 0);

  cout << -1 * pd.min_cost_flow_bellmanford(s, t, 10000) << endl;
  return 0;
}