結果

問題 No.2604 Initial Motion
ユーザー 👑 emthrm
提出日時 2024-01-12 21:41:04
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 675 ms / 3,000 ms
コード長 5,252 bytes
コンパイル時間 3,377 ms
コンパイル使用メモリ 263,024 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-09-27 21:39:49
合計ジャッジ時間 15,393 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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ファイルパターン 結果
sample AC * 3
other AC * 39
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ソースコード

diff #
プレゼンテーションモードにする

#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
using ll = long long;
constexpr int INF = 0x3f3f3f3f;
constexpr long long LINF = 0x3f3f3f3f3f3f3f3fLL;
constexpr double EPS = 1e-8;
constexpr int MOD = 998244353;
// constexpr int MOD = 1000000007;
constexpr int DY4[]{1, 0, -1, 0}, DX4[]{0, -1, 0, 1};
constexpr int DY8[]{1, 1, 0, -1, -1, -1, 0, 1};
constexpr int DX8[]{0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U>
inline bool chmax(T& a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U>
inline bool chmin(T& a, U b) { return a > b ? (a = b, true) : false; }
struct IOSetup {
  IOSetup() {
    std::cin.tie(nullptr);
    std::ios_base::sync_with_stdio(false);
    std::cout << fixed << setprecision(20);
  }
} iosetup;
template <typename T, typename U>
struct MinimumCostSTFlow {
  struct Edge {
    int dst, rev;
    T cap;
    U cost;
    explicit Edge(const int dst, const T cap, const U cost, const int rev)
        : dst(dst), rev(rev), cap(cap), cost(cost) {}
  };
  const U uinf;
  std::vector<std::vector<Edge>> graph;
  explicit MinimumCostSTFlow(const int n,
                             const U uinf = std::numeric_limits<U>::max())
      : uinf(uinf), graph(n), tinf(std::numeric_limits<T>::max()), n(n),
        has_negative_edge(false), prev_v(n, -1), prev_e(n, -1), dist(n),
        potential(n, 0) {}
  void add_edge(const int src, const int dst, const T cap, const U cost) {
    has_negative_edge |= cost < 0;
    graph[src].emplace_back(dst, cap, cost, graph[dst].size());
    graph[dst].emplace_back(src, 0, -cost, graph[src].size() - 1);
  }
  U solve(const int s, const int t, T flow) {
    if (flow == 0) [[unlikely]] return 0;
    U res = 0;
    has_negative_edge ? bellman_ford(s) : dijkstra(s);
    while (true) {
      if (dist[t] == uinf) return uinf;
      res += calc(s, t, &flow);
      if (flow == 0) break;
      dijkstra(s);
    }
    return res;
  }
  U solve(const int s, const int t) {
    U res = 0;
    T flow = tinf;
    bellman_ford(s);
    while (potential[t] < 0 && dist[t] != uinf) {
      res += calc(s, t, &flow);
      dijkstra(s);
    }
    return res;
  }
  std::pair<T, U> minimum_cost_maximum_flow(const int s, const int t,
                                            const T flow) {
    if (flow == 0) [[unlikely]] return {0, 0};
    T f = flow;
    U cost = 0;
    has_negative_edge ? bellman_ford(s) : dijkstra(s);
    while (dist[t] != uinf) {
      cost += calc(s, t, &f);
      if (f == 0) break;
      dijkstra(s);
    }
    return {flow - f, cost};
  }
 private:
  const T tinf;
  const int n;
  bool has_negative_edge;
  std::vector<int> prev_v, prev_e;
  std::vector<U> dist, potential;
  std::priority_queue<std::pair<U, int>, std::vector<std::pair<U, int>>,
                      std::greater<std::pair<U, int>>> que;
  void bellman_ford(const int s) {
    std::fill(dist.begin(), dist.end(), uinf);
    dist[s] = 0;
    bool is_updated = true;
    for (int step = 0; step < n && is_updated; ++step) {
      is_updated = false;
      for (int i = 0; i < n; ++i) {
        if (dist[i] == uinf) continue;
        for (int j = 0; std::cmp_less(j, graph[i].size()); ++j) {
          const Edge& e = graph[i][j];
          if (e.cap > 0 && dist[e.dst] > dist[i] + e.cost) {
            dist[e.dst] = dist[i] + e.cost;
            prev_v[e.dst] = i;
            prev_e[e.dst] = j;
            is_updated = true;
          }
        }
      }
    }
    assert(!is_updated);
    for (int i = 0; i < n; ++i) {
      if (dist[i] != uinf) potential[i] += dist[i];
    }
  }
  void dijkstra(const int s) {
    std::fill(dist.begin(), dist.end(), uinf);
    dist[s] = 0;
    que.emplace(0, s);
    while (!que.empty()) {
      const auto [d, ver] = que.top();
      que.pop();
      if (dist[ver] < d) continue;
      for (int i = 0; std::cmp_less(i, graph[ver].size()); ++i) {
        const Edge& e = graph[ver][i];
        const U nxt = dist[ver] + e.cost + potential[ver] - potential[e.dst];
        if (e.cap > 0 && dist[e.dst] > nxt) {
          dist[e.dst] = nxt;
          prev_v[e.dst] = ver;
          prev_e[e.dst] = i;
          que.emplace(dist[e.dst], e.dst);
        }
      }
    }
    for (int i = 0; i < n; ++i) {
      if (dist[i] != uinf) potential[i] += dist[i];
    }
  }
  U calc(const int s, const int t, T* flow) {
    T f = *flow;
    for (int v = t; v != s; v = prev_v[v]) {
      f = std::min(f, graph[prev_v[v]][prev_e[v]].cap);
    }
    *flow -= f;
    for (int v = t; v != s; v = prev_v[v]) {
      Edge& e = graph[prev_v[v]][prev_e[v]];
      e.cap -= f;
      graph[v][e.rev].cap += f;
    }
    return potential[t] * f;
  }
};
int main() {
  int k, n, m; cin >> k >> n >> m;
  vector<int> players(n);
  REP(_, k) {
    int a; cin >> a; --a;
    ++players[a];
  }
  MinimumCostSTFlow<int, ll> mcf(n + 2);
  REP(i, n) {
    if (players[i] > 0) mcf.add_edge(n, i, players[i], 0);
  }
  REP(i, n) {
    int b; cin >> b;
    mcf.add_edge(i, n + 1, b, 0);
  }
  while (m--) {
    int u, v; ll d; cin >> u >> v >> d; --u; --v;
    mcf.add_edge(u, v, k, d);
    mcf.add_edge(v, u, k, d);
  }
  cout << mcf.solve(n, n + 1, k) << '\n';
  return 0;
}
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