#1185333 (C++23(gcc16)) No.3699 引き抜き交渉

• 問題: No.3699 引き抜き交渉
• ユーザー: ei1333333
• 提出日時: 2026-09-09 21:29:42
• 言語: C++23(gcc16) (gcc 16.1.0 + boost 1.92.0 + ACL)
• 結果: AC
• 実行時間: 3 ms / 2,000 ms
• コード長: 11,180 bytes
• コンパイル時間: 5,362 ms
• コンパイル使用メモリ: 407,452 KB
• 実行使用メモリ: 6,528 KB
• 最終ジャッジ日時: 2026-09-09 21:30:11
• 合計ジャッジ時間: 6,746 ms
• ジャッジサーバーID （参考情報）: judge3_0 / judge2_0

ファイルパターン	結果
sample	AC * 2
other	AC * 15

ソースコード

#line 1 "template/template.hpp"
#include <bits/stdc++.h>

#if __has_include(<atcoder/all>)
#include <atcoder/all>

#endif

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream& operator<<(ostream& os, const pair<T1, T2>& p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream& operator>>(istream& is, pair<T1, T2>& p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
  for (size_t i = 0; i < v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream& operator>>(istream& is, vector<T>& v) {
  for (T& in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
bool chmax(T1& a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
bool chmin(T1& a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
enable_if_t<is_class_v<T> == 0> fill_v(T& t, const V& v) {
  t = v;
}

template <typename T, typename V>
enable_if_t<is_class_v<T> != 0> fill_v(T& t, const V& v) {
  for (auto& e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F&& f) : F(std::forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args&&... args) const {
    return F::operator()(*this, std::forward<Args>(args)...);
  }
};

template <typename F>
decltype(auto) MFP(F&& f) {
  return FixPoint<F>{std::forward<F>(f)};
}

#line 2 "graph/flow/burn-bury.hpp"

#include <algorithm>
#include <array>
#include <cassert>
#include <iterator>
#include <map>
#include <optional>
#include <utility>
#include <vector>

#line 2 "structure/union-find/union-find.hpp"

#line 4 "structure/union-find/union-find.hpp"
#include <cstddef>
#line 7 "structure/union-find/union-find.hpp"

struct UnionFind {
  std::vector<int> data;

  UnionFind() = default;

  explicit UnionFind(std::size_t sz) : data(sz, -1) {}

  bool unite(int x, int y) {
    x = find(x), y = find(y);
    if (x == y) return false;
    if (data[x] > data[y]) std::swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return true;
  }

  int find(int k) {
    if (data[k] < 0) return (k);
    return data[k] = find(data[k]);
  }

  int size(int k) { return -data[find(k)]; }

  bool same(int x, int y) { return find(x) == find(y); }

  std::vector<std::vector<int>> groups() {
    int n = (int)data.size();
    std::vector<std::vector<int>> ret(n);
    for (int i = 0; i < n; i++) {
      ret[find(i)].emplace_back(i);
    }
    ret.erase(
        std::remove_if(ret.begin(), ret.end(),
                       [&](const std::vector<int>& v) { return v.empty(); }),
        ret.end());
    return ret;
  }
};
#line 2 "graph/flow/dinic.hpp"

#line 4 "graph/flow/dinic.hpp"
#include <iostream>
#include <limits>
#include <queue>
#line 8 "graph/flow/dinic.hpp"

/**
 * @brief Dinic(最大流)
 *
 */
template <typename flow_t>
struct Dinic {
  const flow_t INF;

  struct edge {
    int to;
    flow_t cap;
    int rev;
    bool isrev;
    int idx;
  };

  std::vector<std::vector<edge> > graph;
  std::vector<int> min_cost, iter;

  explicit Dinic(int V) : INF(std::numeric_limits<flow_t>::max()), graph(V) {}

  void add_edge(int from, int to, flow_t cap, int idx = -1) {
    graph[from].emplace_back(
        (edge){to, cap, (int)graph[to].size(), false, idx});
    graph[to].emplace_back(
        (edge){from, 0, (int)graph[from].size() - 1, true, idx});
  }

  bool build_augment_path(int s, int t) {
    min_cost.assign(graph.size(), -1);
    std::queue<int> que;
    min_cost[s] = 0;
    que.push(s);
    while (!que.empty() && min_cost[t] == -1) {
      int p = que.front();
      que.pop();
      for (auto& e : graph[p]) {
        if (e.cap > 0 && min_cost[e.to] == -1) {
          min_cost[e.to] = min_cost[p] + 1;
          que.push(e.to);
        }
      }
    }
    return min_cost[t] != -1;
  }

  flow_t find_min_dist_augment_path(int idx, const int t, flow_t flow) {
    if (idx == t) return flow;
    for (int& i = iter[idx]; i < (int)graph[idx].size(); i++) {
      edge& e = graph[idx][i];
      if (e.cap > 0 && min_cost[idx] < min_cost[e.to]) {
        flow_t d = find_min_dist_augment_path(e.to, t, std::min(flow, e.cap));
        if (d > 0) {
          e.cap -= d;
          graph[e.to][e.rev].cap += d;
          return d;
        }
      }
    }
    return 0;
  }

  flow_t max_flow(int s, int t) {
    flow_t flow = 0;
    while (build_augment_path(s, t)) {
      iter.assign(graph.size(), 0);
      flow_t f;
      while ((f = find_min_dist_augment_path(s, t, INF)) > 0) flow += f;
    }
    return flow;
  }

  void output() {
    for (int i = 0; i < graph.size(); i++) {
      for (auto& e : graph[i]) {
        if (e.isrev) continue;
        auto& rev_e = graph[e.to][e.rev];
        std::cout << i << "->" << e.to << " (flow: " << rev_e.cap << "/"
                  << e.cap + rev_e.cap << ")" << std::endl;
      }
    }
  }

  std::vector<bool> min_cut(int s) {
    std::vector<bool> used(graph.size());
    std::queue<int> que;
    que.emplace(s);
    used[s] = true;
    while (not que.empty()) {
      int p = que.front();
      que.pop();
      for (auto& e : graph[p]) {
        if (e.cap > 0 and not used[e.to]) {
          used[e.to] = true;
          que.emplace(e.to);
        }
      }
    }
    return used;
  }
};
#line 14 "graph/flow/burn-bury.hpp"

/**
 * @brief Burn Bury(燃やす埋める)
 */
template <typename T, bool minimize = true>
struct BurnBury {
 private:
  using MaxFlow = Dinic<T>;
  using UF = UnionFind;
  using arr2 = std::array<T, 2>;
  using arr4 = std::array<T, 4>;

  int n;
  T alpha;
  std::vector<arr2> theta;
  std::vector<std::map<int, arr4> > phi;
  std::map<std::vector<int>, T> zeta;

 public:
  explicit BurnBury(int n) : n{n}, alpha{}, theta(n), phi(n) {}

  void add_cost(T cost) {
    if (not minimize) cost *= -1;
    alpha += cost;
  }

  void add_cost(int x, T cost) {
    if (not minimize) cost *= -1;
    int a = std::max(~x, x);
    theta[a][x >= 0] += cost;
  }

  void add_cost(int x, int y, T cost) {
    assert(x != y);
    if (not minimize) cost *= -1;
    int a = std::max(~x, x), b = std::max(~y, y);
    if (a < b)
      phi[a][b][((x >= 0) << 1) | (y >= 0)] += cost;
    else
      phi[b][a][((y >= 0) << 1) | (x >= 0)] += cost;
  }

  void add_cost(std::vector<int> xs, T cost) {
    assert(not xs.empty());
    if (xs.size() == 1) {
      add_cost(xs[0], cost);
    } else if (xs.size() == 2) {
      add_cost(xs[0], xs[1], cost);
    } else {
      int m = (int)xs.size();
      std::sort(xs.begin(), xs.end());
      xs.erase(std::unique(xs.begin(), xs.end()), xs.end());
      assert(m == (int)xs.size());
      if (not minimize) cost *= -1;
      zeta[xs] += cost;
    }
  }

  std::optional<std::pair<T, std::vector<bool> > > solve() {
    std::vector<int> flip(2 * n, -1);
    {
      UF uf(n + n);
      for (int i = 0; i < n; i++) {
        for (auto& [j, cs] : phi[i]) {
          T c = -cs[0] + cs[1] + cs[2] - cs[3];
          if (c < 0) {
            uf.unite(i, j + n);
            uf.unite(i + n, j);
          }
          if (c > 0) {
            uf.unite(i, j);
            uf.unite(i + n, j + n);
          }
        }
      }
      for (auto& [vs, c] : zeta) {
        if (c > 0) return std::nullopt;
        if (c < 0) {
          for (int i = 1; i < (int)vs.size(); i++) {
            int x = vs[i - 1], y = vs[i];
            int a = std::max(x, ~x), b = std::max(y, ~y);
            if ((x >= 0) ^ (y >= 0)) {
              uf.unite(a, b + n);
              uf.unite(a + n, b);
            } else {
              uf.unite(a, b);
              uf.unite(a + n, b + n);
            }
          }
        }
      }
      for (int i = 0; i < n; i++) {
        int x = uf.find(i);
        int y = uf.find(i + n);
        if (x == y) return std::nullopt;
        if (flip[x] < 0) {
          flip[x] = 0;
          flip[y] = 1;
        }
      }
      for (int i = 0; i < n; i++) {
        if (flip[i] < 0) {
          flip[i] = flip[uf.find(i)];
        }
      }
      flip.resize(n);
    }
    {
      for (int i = 0; i < n; i++) {
        for (auto& [j, cs] : phi[i]) {
          if (flip[i]) {
            std::swap(cs[0], cs[2]);
            std::swap(cs[1], cs[3]);
          }
          if (flip[j]) {
            std::swap(cs[0], cs[1]);
            std::swap(cs[2], cs[3]);
          }
          T c = -cs[0] + cs[1] + cs[2] - cs[3];
          alpha += cs[0];
          theta[i][not flip[i]] += cs[2] - cs[0];
          theta[j][not flip[j]] += cs[3] - cs[2];
          cs[1] = c;
          cs[0] = cs[2] = cs[3] = 0;
        }
      }
    }
    {
      for (int i = 0; i < n; i++) {
        auto& cs = theta[i];
        if (flip[i]) {
          std::swap(cs[0], cs[1]);
        }
        if (cs[0] <= cs[1]) {
          alpha += cs[0];
          cs[1] -= cs[0];
          cs[0] = 0;
        } else {
          alpha += cs[1];
          cs[0] -= cs[1];
          cs[1] = 0;
        }
      }
    }

    MaxFlow flow(n + 2 + zeta.size());
    int s = n, t = n + 1;
    {
      for (int i = 0; i < n; i++) {
        auto& cs = theta[i];
        if (cs[1] > 0) {
          flow.add_edge(i, t, cs[1]);
        }
        if (cs[0] > 0) {
          flow.add_edge(s, i, cs[0]);
        }
      }
      for (int i = 0; i < n; i++) {
        for (auto& [j, cs] : phi[i]) {
          if (cs[2] > 0) {
            flow.add_edge(i, j, cs[2]);
          }
          if (cs[1] > 0) {
            flow.add_edge(j, i, cs[1]);
          }
        }
      }
      int u = t + 1;
      for (auto& [vs, c] : zeta) {
        if (c < 0) {
          if ((vs[0] >= 0) ^ flip[std::max(~vs[0], vs[0])]) {
            flow.add_edge(s, u, -c);
            for (auto& p : vs) flow.add_edge(u, std::max(p, ~p), -c);
          } else {
            for (auto& p : vs) flow.add_edge(std::max(p, ~p), u, -c);
            flow.add_edge(u, t, -c);
          }
          alpha += c;
          u++;
        }
      }
    }
    T ans = flow.max_flow(s, t) + alpha;
    std::vector<bool> cut = flow.min_cut(s);
    for (int i = 0; i < n; i++) {
      if (flip[i]) cut[i] = 1 - cut[i];
    }
    cut.resize(n);
    return std::make_pair(minimize ? ans : -ans, cut);
  }
};

int main() {
  int N, M;
  cin >> N >> M;
  BurnBury< int64, false > flow(N);
  for (int i = 0; i < N; i++) {
    int a, b;
    cin >> a >> b;
    flow.add_cost(i, a);
    flow.add_cost(~i, b);
  }
  for (int i = 0; i < M; i++) {
    int u, v, c;
    cin >> u >> v >> c;
    --u, --v;
    flow.add_cost(u, ~v, -c);
    flow.add_cost(~u, v, -c);
  }
  cout << flow.solve()->first << endl;
}