結果

問題 No.1301 Strange Graph Shortest Path
ユーザー 👑 hitonanodehitonanode
提出日時 2020-11-27 21:34:39
言語 C++17
(gcc 13.2.0 + boost 1.83.0)
結果
AC  
実行時間 217 ms / 3,000 ms
コード長 9,287 bytes
コンパイル時間 2,647 ms
コンパイル使用メモリ 222,980 KB
実行使用メモリ 36,448 KB
最終ジャッジ日時 2023-10-10 21:39:10
合計ジャッジ時間 9,600 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge11
このコードへのチャレンジ（β）

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 1 ms
4,348 KB
testcase_01 AC 2 ms
4,352 KB
testcase_02 AC 144 ms
35,876 KB
testcase_03 AC 119 ms
31,888 KB
testcase_04 AC 177 ms
34,676 KB
testcase_05 AC 134 ms
35,928 KB
testcase_06 AC 170 ms
32,352 KB
testcase_07 AC 155 ms
34,344 KB
testcase_08 AC 124 ms
32,080 KB
testcase_09 AC 141 ms
30,592 KB
testcase_10 AC 118 ms
31,960 KB
testcase_11 AC 162 ms
33,500 KB
testcase_12 AC 159 ms
33,288 KB
testcase_13 AC 137 ms
35,668 KB
testcase_14 AC 163 ms
30,676 KB
testcase_15 AC 137 ms
32,540 KB
testcase_16 AC 186 ms
34,576 KB
testcase_17 AC 163 ms
36,448 KB
testcase_18 AC 148 ms
33,072 KB
testcase_19 AC 143 ms
32,276 KB
testcase_20 AC 165 ms
31,648 KB
testcase_21 AC 156 ms
35,092 KB
testcase_22 AC 181 ms
32,344 KB
testcase_23 AC 143 ms
35,700 KB
testcase_24 AC 179 ms
32,216 KB
testcase_25 AC 190 ms
34,628 KB
testcase_26 AC 156 ms
33,344 KB
testcase_27 AC 142 ms
33,748 KB
testcase_28 AC 129 ms
34,972 KB
testcase_29 AC 217 ms
34,516 KB
testcase_30 AC 159 ms
34,376 KB
testcase_31 AC 166 ms
34,004 KB
testcase_32 AC 1 ms
4,348 KB
testcase_33 AC 99 ms
29,436 KB
testcase_34 AC 149 ms
35,964 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 <bits/stdc++.h>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl
#else
#define dbg(x) {}
#endif

// MinCostFlow based on AtCoder Library, no namespace, no private variables, compatible with C++11
// Reference: <https://atcoder.github.io/ac-library/production/document_ja/mincostflow.html>
// **NO NEGATIVE COST EDGES**
template <class Cap, class Cost> struct mcf_graph {
    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);
        assert(0 <= cap);
        assert(0 <= cost);
        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<Cost> dual, dist;
    std::vector<int> pv, pe;
    std::vector<bool> vis;
    struct Q {
        Cost key;
        int to;
        bool operator<(Q r) const { return key > r.key; }
    };
    std::vector<Q> que;
    bool _dual_ref(int s, int t) {
        std::fill(dist.begin(), dist.end(), std::numeric_limits<Cost>::max());
        std::fill(vis.begin(), vis.end(), false);
        que.clear();

        dist[s] = 0;
        que.push_back(Q{0, s});
        std::push_heap(que.begin(), que.end());
        while (!que.empty()) {
            int v = que.front().to;
            std::pop_heap(que.begin(), que.end());
            que.pop_back();
            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_back(Q{dist[e.to], e.to});
                    std::push_heap(que.begin(), que.end());
                }
            }
        }
        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;
    }

    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
        dual.assign(_n, 0), dist.assign(_n, 0);
        pv.assign(_n, 0), pe.assign(_n, 0);
        vis.assign(_n, false);
        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(s, t)) 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;
    }

    struct _edge {
        int to, rev;
        Cap cap;
        Cost cost;
    };

    int _n;
    std::vector<std::pair<int, int>> pos;
    std::vector<std::vector<_edge>> g;
};

int main()
{
    int N, M;
    cin >> N >> M;
    mcf_graph<int, lint> graph(N);
    while (M--) {
        int u, v, c, d;
        cin >> u >> v >> c >> d;
        u--, v--;
        graph.add_edge(u, v, 1, c);
        graph.add_edge(u, v, 1, d);
        graph.add_edge(v, u, 1, c);
        graph.add_edge(v, u, 1, d);
    }

    auto ret = graph.flow(0, N - 1, 2);
    cout << ret.second << '\n';
}
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