結果

問題 No.1320 Two Type Min Cost Cycle
コンテスト
ユーザー hitonanode
提出日時 2020-12-17 00:55:01
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 280 ms / 2,000 ms
コード長 5,105 bytes
コンパイル時間 2,782 ms
コンパイル使用メモリ 221,512 KB
最終ジャッジ日時 2025-01-17 02:12:57
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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ファイルパターン 結果
sample AC * 3
other AC * 57
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 <cassert>
#include <limits>
#include <queue>
#include <utility>
#include <vector>

// Shortest cycle detection of UNDIRECTED SIMPLE graphs
// Verified: <https://yukicoder.me/problems/no/1320>
template <typename T> struct ShortestCycleOfUndirectedWeighted {
    int V, E;
    std::vector<std::vector<std::pair<int, T>>> to; // (nxt, weight)
    const T INF;
    ShortestCycleOfUndirectedWeighted() = default;
    ShortestCycleOfUndirectedWeighted(int V) : V(V), E(0), to(V), INF(std::numeric_limits<T>::max() / 2) {}
    void add_edge(int s, int t, T len) {
        assert(0 <= s and s < V);
        assert(0 <= t and t < V);
        assert(len >= 0);
        to[s].emplace_back(t, len);
        to[t].emplace_back(s, len);
        E++;
    }

    std::vector<T> dist;
    std::vector<int> prev;
    // Find minimum length simple cycle which passes vertex `v`
    // - Complexity: O(E log V)
    // - return: (LEN, (a, b))
    //   - LEN: length of the shortest cycles if exists, INF ( = numeric_limits<int>::max() / 2 ) otherwise.
    //   - the cycle consists of vertices [v, ..., prev[prev[a]], prev[a], a, b, prev[b], prev[prev[b]], ..., v]
    std::pair<T, std::pair<int, int>> Solve(int v) {
        assert(0 <= v and v < V);
        dist.assign(V, INF), dist[v] = 0;
        prev.assign(V, -1);

        using P = std::pair<T, std::pair<int, int>>;
        std::priority_queue<P, std::vector<P>, std::greater<P>> pq;
        std::vector<std::pair<std::pair<int, int>, T>> add_edge;

        pq.emplace(0, std::make_pair(v, -1));
        while (!pq.empty()) {
            const int now = pq.top().second.first, prv = pq.top().second.second;
            pq.pop();
            for (const auto &nxt : to[now])
                if (nxt.first != prv) {
                    if (dist[nxt.first] == INF) {
                        dist[nxt.first] = dist[now] + nxt.second;
                        prev[nxt.first] = now;
                        pq.emplace(dist[nxt.first], std::make_pair(nxt.first, now));
                    } else {
                        add_edge.emplace_back(std::make_pair(now, nxt.first), nxt.second);
                    }
                }
        }
        T minimum_cycle = INF;
        int s = -1, t = -1;
        for (auto edge : add_edge) {
            int a = edge.first.first, b = edge.first.second;
            T L = dist[a] + dist[b] + edge.second;
            if (L < minimum_cycle) minimum_cycle = L, s = a, t = b;
        }
        return std::make_pair(minimum_cycle, std::make_pair(s, t));
    }
};

#include <bits/stdc++.h>
using namespace std;
using lint = long long;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define REP(i, n) FOR(i,0,n)
template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }

template <typename T> struct ShortestPath {
    int V, E;
    int INVALID = -1;
    std::vector<std::vector<std::pair<int, T>>> to;
    ShortestPath() = default;
    ShortestPath(int V) : V(V), E(0), to(V) {}
    void add_edge(int s, int t, T len) {
        assert(0 <= s and s < V);
        assert(0 <= t and t < V);
        to[s].emplace_back(t, len);
        E++;
    }

    std::vector<T> dist;
    std::vector<int> prev;
    // Dijkstra algorithm
    // Complexity: O(E log E)
    void Dijkstra(int s) {
        assert(0 <= s and s < V);
        dist.assign(V, std::numeric_limits<T>::max());
        dist[s] = 0;
        prev.assign(V, INVALID);
        using P = std::pair<T, int>;
        std::priority_queue<P, std::vector<P>, std::greater<P>> pq;
        pq.emplace(0, s);
        while (!pq.empty()) {
            T d;
            int v;
            std::tie(d, v) = pq.top();
            pq.pop();
            if (dist[v] < d) continue;
            for (auto nx : to[v]) {
                T dnx = d + nx.second;
                if (dist[nx.first] > dnx) {
                    dist[nx.first] = dnx, prev[nx.first] = v;
                    pq.emplace(dnx, nx.first);
                }
            }
        }
    }
};


int main()
{
    int T, N, M;
    cin >> T >> N >> M;
    lint ret = 1e18;

    if (T == 1) {
        vector<vector<pair<int, int>>> to(N);
        while (M--) {
            int u, v, w;
            cin >> u >> v >> w;
            u--, v--;
            to[u].emplace_back(v, w);
        }
        REP(s, N) {
            ShortestPath<lint> graph(N + 1);
            REP(i, N) for (auto [j, w] : to[i]) {
                graph.add_edge(i, j, w);
                if (j == s) graph.add_edge(i, N, w);
            }
            graph.Dijkstra(s);
            chmin(ret, graph.dist[N]);
        }
    } else {
        ShortestCycleOfUndirectedWeighted<lint> graph(N);
        while (M--) {
            int u, v, w;
            cin >> u >> v >> w;
            u--, v--;
            graph.add_edge(u, v, w);
        }
        REP(i, N) chmin<lint>(ret, graph.Solve(i).first);
    }
    cout << (ret < 1e18 ? ret : -1) << '\n';
}
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