Dijkstra法
(graph/dijkstra.cpp)

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• Last update: 2020-05-02 12:45:39+09:00

説明

単一始点最短路を求める。負辺があると正しく動作しない。 $O(V \log E)$

Verified with

• test/yosupo_shortest_path.test.cpp

Code

template <typename T>
struct edge {
    int from, to; T cost;
    edge(int to, T cost) : from(-1), to(to), cost(cost) {}
    edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
};

template <typename T>
vector<T> dijkstra(int s,vector<vector<edge<T>>> &G){
    auto n = G.size();
    vector<T> d(n, INF<T>);
    priority_queue<pair<T, int>,vector<pair<T, int>>,greater<>> Q;
    d[s] = 0;
    Q.emplace(0, s);
    while(!Q.empty()){
        T cost; int i;
        tie(cost, i) = Q.top(); Q.pop();
        if(d[i] < cost) continue;
        for (auto &&e : G[i]) {
            auto cost2 = cost + e.cost;
            if(d[e.to] <= cost2) continue;
            d[e.to] = cost2;
            Q.emplace(d[e.to], e.to);
        }
    }
    return d;
}

/**
 * @brief Dijkstra法
 * @docs _md/dijkstra.md
 */

#line 1 "graph/dijkstra.cpp"
template <typename T>
struct edge {
    int from, to; T cost;
    edge(int to, T cost) : from(-1), to(to), cost(cost) {}
    edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
};

template <typename T>
vector<T> dijkstra(int s,vector<vector<edge<T>>> &G){
    auto n = G.size();
    vector<T> d(n, INF<T>);
    priority_queue<pair<T, int>,vector<pair<T, int>>,greater<>> Q;
    d[s] = 0;
    Q.emplace(0, s);
    while(!Q.empty()){
        T cost; int i;
        tie(cost, i) = Q.top(); Q.pop();
        if(d[i] < cost) continue;
        for (auto &&e : G[i]) {
            auto cost2 = cost + e.cost;
            if(d[e.to] <= cost2) continue;
            d[e.to] = cost2;
            Q.emplace(d[e.to], e.to);
        }
    }
    return d;
}

/**
 * @brief Dijkstra法
 * @docs _md/dijkstra.md
 */

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