結果

問題 No.1301 Strange Graph Shortest Path
ユーザー ChanyuhChanyuh
提出日時 2020-12-31 17:43:15
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 215 ms / 3,000 ms
コード長 6,759 bytes
コンパイル時間 1,956 ms
コンパイル使用メモリ 148,684 KB
実行使用メモリ 36,432 KB
最終ジャッジ日時 2024-10-09 16:48:09
合計ジャッジ時間 10,822 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
このコードへのチャレンジ
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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
6,820 KB
testcase_01 AC 2 ms
6,816 KB
testcase_02 AC 162 ms
36,392 KB
testcase_03 AC 132 ms
32,628 KB
testcase_04 AC 195 ms
34,968 KB
testcase_05 AC 138 ms
35,464 KB
testcase_06 AC 178 ms
32,360 KB
testcase_07 AC 164 ms
34,336 KB
testcase_08 AC 132 ms
32,464 KB
testcase_09 AC 143 ms
31,444 KB
testcase_10 AC 129 ms
32,056 KB
testcase_11 AC 165 ms
33,244 KB
testcase_12 AC 168 ms
33,336 KB
testcase_13 AC 147 ms
35,580 KB
testcase_14 AC 173 ms
31,988 KB
testcase_15 AC 142 ms
32,680 KB
testcase_16 AC 188 ms
34,732 KB
testcase_17 AC 170 ms
36,432 KB
testcase_18 AC 155 ms
33,092 KB
testcase_19 AC 151 ms
32,440 KB
testcase_20 AC 173 ms
31,476 KB
testcase_21 AC 161 ms
34,936 KB
testcase_22 AC 187 ms
32,320 KB
testcase_23 AC 146 ms
36,216 KB
testcase_24 AC 182 ms
32,436 KB
testcase_25 AC 177 ms
35,136 KB
testcase_26 AC 161 ms
33,412 KB
testcase_27 AC 150 ms
33,584 KB
testcase_28 AC 134 ms
35,192 KB
testcase_29 AC 215 ms
34,076 KB
testcase_30 AC 162 ms
35,320 KB
testcase_31 AC 175 ms
34,360 KB
testcase_32 AC 2 ms
6,816 KB
testcase_33 AC 97 ms
29,656 KB
testcase_34 AC 160 ms
36,316 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include<iostream>
#include<array>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<complex>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<tuple>
#include<cassert>
using namespace std;
typedef long long ll;
typedef unsigned int ui;
const ll mod = 1000000007;
const ll INF = (ll)1000000007 * 1000000007;
typedef pair<int, int> P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define Per(i,sta,n) for(int i=n-1;i>=sta;i--)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
typedef long double ld;
const ld eps = 1e-8;
const ld pi = acos(-1.0);
typedef pair<ll, ll> LP;
int dx[4]={1,-1,0,0};
int dy[4]={0,0,1,-1};
template<class T>bool chmax(T &a, const T &b) {if(a<b){a=b;return 1;}return 0;}
template<class T>bool chmin(T &a, const T &b) {if(b<a){a=b;return 1;}return 0;}

template <class Cap, class Cost> struct MinCostFlow{
  public:
    MinCostFlow() {}
    MinCostFlow(int n) : _n(n), g(n) {}

    int add_edge(int from, int to, Cap cap, Cost cost) {//cost>=0!!!
        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;
};

using edge = MinCostFlow<int,ll>::edge;//cap,costの型を入れる

int n,m;

void solve(){
  cin >> n >> m;
  MinCostFlow<int,ll> mcf(n+2);
  rep(i,m){
    int a,b,c,d;cin >> a >> b >> c >> d;a--;b--;
    mcf.add_edge(a,b,1,c);mcf.add_edge(a,b,1,d);
    mcf.add_edge(b,a,1,c);mcf.add_edge(b,a,1,d);
  }
  mcf.add_edge(n,0,2,0);
  mcf.add_edge(n-1,n+1,2,0);
  //cout << m << endl;
  cout << mcf.flow(n,n+1,2).second << endl;
}

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout << fixed << setprecision(50);
    solve();
}
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