#586224 (C++17) No.1301 Strange Graph Shortest Path

• 問題: No.1301 Strange Graph Shortest Path
• ユーザー: stoq
• 提出日時: 2020-11-28 08:04:48
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 188 ms / 3,000 ms
• コード長: 7,764 bytes
• コンパイル時間: 2,641 ms
• コンパイル使用メモリ: 218,516 KB
• 最終ジャッジ日時: 2025-01-16 09:13:01
• ジャッジサーバーID （参考情報）: judge1 / judge5

ファイルパターン	結果
sample	AC * 2
other	AC * 33

ソースコード

#define MOD_TYPE 2

#pragma region Macros

#include <bits/stdc++.h>
using namespace std;

#if 0
#include <boost/multiprecision/cpp_int.hpp>
#include <boost/multiprecision/cpp_dec_float.hpp>
using Int = boost::multiprecision::cpp_int;
using lld = boost::multiprecision::cpp_dec_float_100;
#endif
#if 1
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#endif
using ll = long long int;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pld = pair<ld, ld>;
template <typename Q_type>
using smaller_queue = priority_queue<Q_type, vector<Q_type>, greater<Q_type>>;

constexpr ll MOD = (MOD_TYPE == 1 ? (ll)(1e9 + 7) : 998244353);
constexpr int INF = (int)1e9 + 10;
constexpr ll LINF = (ll)4e18;
constexpr double PI = acos(-1.0);
constexpr double EPS = 1e-7;
constexpr int Dx[] = {0, 0, -1, 1, -1, 1, -1, 1, 0};
constexpr int Dy[] = {1, -1, 0, 0, -1, -1, 1, 1, 0};

#define REP(i, m, n) for (ll i = m; i < (ll)(n); ++i)
#define rep(i, n) REP(i, 0, n)
#define REPI(i, m, n) for (int i = m; i < (int)(n); ++i)
#define repi(i, n) REPI(i, 0, n)
#define MP make_pair
#define MT make_tuple
#define YES(n) cout << ((n) ? "YES" : "NO") << "\n"
#define Yes(n) cout << ((n) ? "Yes" : "No") << "\n"
#define possible(n) cout << ((n) ? "possible" : "impossible") << "\n"
#define Possible(n) cout << ((n) ? "Possible" : "Impossible") << "\n"
#define all(v) v.begin(), v.end()
#define NP(v) next_permutation(all(v))
#define dbg(x) cerr << #x << ":" << x << "\n";

struct io_init
{
  io_init()
  {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << setprecision(30) << setiosflags(ios::fixed);
  };
} io_init;
template <typename T>
inline bool chmin(T &a, T b)
{
  if (a > b)
  {
    a = b;
    return true;
  }
  return false;
}
template <typename T>
inline bool chmax(T &a, T b)
{
  if (a < b)
  {
    a = b;
    return true;
  }
  return false;
}
inline ll CEIL(ll a, ll b)
{
  return (a + b - 1) / b;
}
template <typename A, size_t N, typename T>
inline void Fill(A (&array)[N], const T &val)
{
  fill((T *)array, (T *)(array + N), val);
}
template <typename T, typename U>
constexpr istream &operator>>(istream &is, pair<T, U> &p) noexcept
{
  is >> p.first >> p.second;
  return is;
}
template <typename T, typename U>
constexpr ostream &operator<<(ostream &os, pair<T, U> &p) noexcept
{
  os << p.first << " " << p.second;
  return os;
}
#pragma endregion

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);
      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

void solve()
{
  int n, m;
  cin >> n >> m;
  atcoder::mcf_graph<int, ll> G(n);
  rep(i, m)
  {
    int u, v;
    ll c, d;
    cin >> u >> v >> c >> d;
    u--, v--;
    G.add_edge(u, v, 1, c);
    G.add_edge(u, v, 1, d);
    swap(u, v);
    G.add_edge(u, v, 1, c);
    G.add_edge(u, v, 1, d);
  }
  cout << G.flow(0, n - 1, 2).second << "\n";
}

int main()
{
  solve();
}