Dijkstra
(library/graph/shortest_path/dijkstra.hpp)

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• Last update: 2026-01-21 11:49:22+09:00
• Include: #include "library/graph/shortest_path/dijkstra.hpp"

Dijkstra

できること

• 最小コストを求める
• 複数始点
  • starts: 始点の配列（デフォルト0）
  • weight: dis[v] := 頂点vまでの最小コスト
  • route: 経路復元用の配列

計算量

$O(ElogV)$

• V: 頂点数
• E: 辺の数

使い方

auto [weight, route] = dijkstra(G, {r});

Depends on

• 辺 (library/graph/base/edge.hpp)
• グラフ (library/graph/base/graph.hpp)

Verified with

• グラフ - 経路復元のテスト (tests/graph.route_restore.test.cpp)
• グラフ - Dijkstraのテスト (tests/graph.shortest_path.dijkstra.test.cpp)

Code

#pragma once
#include "library/graph/base/graph.hpp"
template <typename T> using rev_pq = priority_queue<T, vector<T>, greater<T>>;
pair<vector<long long>, vector<int>> dijkstra(const Graph &G,
                                              const vector<int> &starts = {0}) {
    int N = G.size();
    rev_pq<pair<long long, int>> q; // コスト(小さい順), 頂点
    vector<long long> weight(N, INF);
    vector<int> route(N, -1);
    for (auto &&v : starts) q.emplace(0, v), weight[v] = 0;
    while (!q.empty()) {
        auto [w, v] = q.top();
        q.pop();
        if (weight[v] < w) continue;
        for (auto &&[from, to, cost, idx] : G[v]) {
            long long next_w = w + cost;
            if (weight[to] <= next_w) continue;
            weight[to] = next_w;
            q.emplace(weight[to], to);
            route[to] = v;
        }
    }
    return {weight, route};
}

#line 2 "library/graph/base/edge.hpp"
struct Edge {
    int from, to;
    long long cost;
    int idx;
    Edge(int from, int to, long long cost = 1, int idx = -1)
        : from(from), to(to), cost(cost), idx(idx) {}
};
#line 3 "library/graph/base/graph.hpp"
struct Graph {
    int N;
    vector<vector<Edge>> G;
    int es;
    Graph() = default;
    Graph(int N) : N(N), G(N), es(0) {}
    const vector<Edge> &operator[](int v) const { return G[v]; }
    int size() const { return N; }
    void add(int from, int to, long long cost = 1) {
        G[from].push_back(Edge(from, to, cost, es++));
    }
    void add_both(int from, int to, long long cost = 1) {
        G[from].push_back(Edge(from, to, cost, es));
        G[to].push_back(Edge(to, from, cost, es++));
    }
    void read(int M, int padding = -1, bool weighted = false,
              bool directed = false) {
        for (int i = 0; i < M; i++) {
            int u, v;
            cin >> u >> v;
            u += padding, v += padding;
            long long cost = 1ll;
            if (weighted) cin >> cost;
            if (directed) {
                add(u, v, cost);
            } else {
                add_both(u, v, cost);
            }
        }
    }
};
#line 3 "library/graph/shortest_path/dijkstra.hpp"
template <typename T> using rev_pq = priority_queue<T, vector<T>, greater<T>>;
pair<vector<long long>, vector<int>> dijkstra(const Graph &G,
                                              const vector<int> &starts = {0}) {
    int N = G.size();
    rev_pq<pair<long long, int>> q; // コスト(小さい順), 頂点
    vector<long long> weight(N, INF);
    vector<int> route(N, -1);
    for (auto &&v : starts) q.emplace(0, v), weight[v] = 0;
    while (!q.empty()) {
        auto [w, v] = q.top();
        q.pop();
        if (weight[v] < w) continue;
        for (auto &&[from, to, cost, idx] : G[v]) {
            long long next_w = w + cost;
            if (weight[to] <= next_w) continue;
            weight[to] = next_w;
            q.emplace(weight[to], to);
            route[to] = v;
        }
    }
    return {weight, route};
}

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