結果

問題 No.1301 Strange Graph Shortest Path
ユーザー tsuyu93tsuyu93
提出日時 2020-11-28 15:43:04
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 188 ms / 3,000 ms
コード長 7,761 bytes
コンパイル時間 3,231 ms
コンパイル使用メモリ 234,116 KB
実行使用メモリ 37,820 KB
最終ジャッジ日時 2024-09-12 23:03:15
合計ジャッジ時間 9,542 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,812 KB
testcase_01 AC 2 ms
6,816 KB
testcase_02 AC 144 ms
36,056 KB
testcase_03 AC 117 ms
32,200 KB
testcase_04 AC 182 ms
34,692 KB
testcase_05 AC 128 ms
35,496 KB
testcase_06 AC 164 ms
32,484 KB
testcase_07 AC 153 ms
34,288 KB
testcase_08 AC 125 ms
32,612 KB
testcase_09 AC 130 ms
30,764 KB
testcase_10 AC 120 ms
31,980 KB
testcase_11 AC 150 ms
33,344 KB
testcase_12 AC 151 ms
33,544 KB
testcase_13 AC 135 ms
35,592 KB
testcase_14 AC 159 ms
30,900 KB
testcase_15 AC 130 ms
31,760 KB
testcase_16 AC 171 ms
34,760 KB
testcase_17 AC 154 ms
36,456 KB
testcase_18 AC 146 ms
33,840 KB
testcase_19 AC 140 ms
32,748 KB
testcase_20 AC 156 ms
31,636 KB
testcase_21 AC 150 ms
35,208 KB
testcase_22 AC 172 ms
32,440 KB
testcase_23 AC 133 ms
35,912 KB
testcase_24 AC 162 ms
32,220 KB
testcase_25 AC 163 ms
34,612 KB
testcase_26 AC 147 ms
33,240 KB
testcase_27 AC 135 ms
33,572 KB
testcase_28 AC 122 ms
35,640 KB
testcase_29 AC 188 ms
34,008 KB
testcase_30 AC 147 ms
34,576 KB
testcase_31 AC 163 ms
34,364 KB
testcase_32 AC 2 ms
6,944 KB
testcase_33 AC 96 ms
29,528 KB
testcase_34 AC 144 ms
37,820 KB
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ソースコード

diff # 

/*
             author:ryo3ihara
            　　　　　　　”継続は力なり、雨だれ石を穿つ”
            　　　　　　　　　　”slow but steady wins the race”


*/

#pragma GCC optimize("Ofast")
#include<bits/stdc++.h>

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())});
    g[from].push_back(_edge{to, int(g[to].size()), cap, cost});
    g[to].push_back(_edge{from, int(g[from].size()) - 1, 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 = -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 == d) {
        result.pop_back();
      }
      result.push_back({flow, cost});
      prev_cost = cost;
    }
    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 atcoder;

/* 
// 多倍長テンプレ
#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/multiprecision/cpp_int.hpp>
namespace mp = boost::multiprecision;
// 任意長整数型
using Bint = mp::cpp_int;
// 仮数部が1024ビットの浮動小数点数型(TLEしたら小さくする)
using Real = mp::number<mp::cpp_dec_float<1024>>;
*/

using namespace std;
using ll = long long;
using ld = long double;
using pll = pair<ll, ll>;
using pli = pair<ll, int>;
using pii = pair<int, int>;
using pld = pair<ll, ld>;
using ppiii =  pair<pii, int>;
using ppiill = pair<pii, ll>;
using ppllll = pair<pll, ll>;
using pplii = pair<pli, int>;
using mii = map<int, int>;
using dll = deque<ll>;
using qll = queue<ll>;
using pqll = priority_queue<ll>;
using pqrll = priority_queue<ll, vector<ll>, greater<ll>>;
using vint = vector<int>;
using vll = vector<ll>;
using vpll = vector<pll>;
using vvll = vector<vector<ll>>;
using vvint = vector<vector<int>>;
using vvpll = vector<vector<pll>>;

//マクロ
//forループ
#define REP(i,n) for(ll i=0;i<ll(n);i++)
#define REPD(i,n) for(ll i=n-1;i>=0;i--)
#define FOR(i,a,b) for(ll i=a;i<=ll(b);i++)
#define FORD(i,a,b) for(ll i=a;i>=ll(b);i--)
#define ALL(x) x.begin(),x.end() 
#define rALL(x) x.rbegin(),x.rend() 
#define SIZE(x) ll(x.size()) 
#define fs first
#define sc second
//定数
const ll MOD = 1000000007;
const int inf = 1e9;
const ll INF = 1e18;
const ll MAXR = 100000; //10^5:配列の最大のrange

inline void Yes(bool b = true) { cout << (b ? "Yes" : "No") << '\n'; }
inline void YES(bool b = true) { cout << (b ? "YES" : "NO") << '\n'; }

//最大化問題最小化問題
template<class T> inline bool chmin(T& a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template<class T> inline bool chmax(T& a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
//高速冪乗化　modの時は一部入れ替える
ll power(ll x, ll y) {
    if(y == 1) {
        return x;
    }
    ll ans;
    if(y % 2 == 1) {
        ll r = power(x,(y-1)/2);
        //ans = r * r % MOD;
        //ans = ans * x % MOD;
        ans = x * r * r;
    }
    else {
        ll r = power(x,y/2);
        //ans = r * r % MOD;
        ans = r * r;
    }
    return ans;
}
/*
Bint powerb(Bint x, Bint y) {
    if(y == 1) {
        return x;
    }
    Bint ans;
    if(y % 2 == 1) {
        Bint r = powerb(x,(y-1)/2);
        //ans = r * r % MOD;
        //ans = ans * x % MOD;
        ans = x * r * r;
    }
    else {
        Bint r = powerb(x,y/2);
        //ans = r * r % MOD;
        ans = r * r;
    }
    return ans;
}
*/

signed main(){
    //入力の高速化用のコード
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    //入力
    int N ,M;
    cin >> N  >> M;

    mcf_graph<int, ll> g(N);
    REP(i, M) {
    int u, v, c, d;
    cin >> u >> v >> c >> d;
    --u, --v;
    g.add_edge(u, v, 1, c);
    g.add_edge(v, u, 1, c);
    g.add_edge(u, v, 1, d);
    g.add_edge(v, u, 1, d);
   }

   cout << g.flow(0, N - 1, 2).second << endl;
    //cout << fixed << setprecision(10) << ans << endl;
  return 0;
}
0