Bellman-Ford algorithm (ベルマンフォード法)
(graph/bellman_ford.hpp)

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• Last update: 2024-01-25 10:46:02+09:00
• Include: #include "graph/bellman_ford.hpp"

• 到達できない場合は INF
• 負閉路を使って小さくできる場合は -INF
• 多始点スタートに対応
• s に始点となる頂点を入れて、auto [dist, par, root] = bellman_ford(G, s, INF); で距離、親、始点が各頂点について得られる

Depends on

• graph/graph_template.hpp

Verified with

• verify/aoj_grl/aoj_grl_1_b.test.cpp

Code

#pragma once

#include "graph/graph_template.hpp"

template <class T>
std::tuple<std::vector<T>, std::vector<int>, std::vector<int>>  //
bellman_ford(Graph<T> &G, std::vector<int> &s, const T INF) {
    int N = (int)G.size();
    std::vector<T> dist(N, INF);
    std::vector<int> par(N, -1), root(N, -1);

    for (auto &v : s) {
        dist[v] = 0;
        root[v] = v;
    }
    int loop_count = 0;

    while (true) {
        loop_count++;
        bool update = false;
        for (int cur = 0; cur < N; cur++) {
            if (dist[cur] == INF) continue;
            for (auto &e : G[cur]) {
                T nd = std::max(-INF, dist[cur] + e.cost);
                if (dist[e.to] > nd) {
                    par[e.to] = cur;
                    root[e.to] = root[cur];
                    update = true;
                    if (loop_count >= N) nd = -INF;
                    dist[e.to] = nd;
                }
            }
        }
        if (!update) break;
    }
    return {dist, par, root};
}

#line 2 "graph/bellman_ford.hpp"

#line 2 "graph/graph_template.hpp"

#include <vector>
template <class T> struct Edge {
    int from, to;
    T cost;
    int id;

    Edge() = default;
    Edge(int from, int to, T cost = 1, int id = -1) : from(from), to(to), cost(cost), id(id) {}

    friend std::ostream &operator<<(std::ostream &os, const Edge<T> &e) {
        // output format: "{ id : from -> to, cost }"
        return os << "{ " << e.id << " : " << e.from << " -> " << e.to << ", " << e.cost << " }";
    }
};

template <class T> using Edges = std::vector<Edge<T>>;
template <class T> using Graph = std::vector<std::vector<Edge<T>>>;
#line 4 "graph/bellman_ford.hpp"

template <class T>
std::tuple<std::vector<T>, std::vector<int>, std::vector<int>>  //
bellman_ford(Graph<T> &G, std::vector<int> &s, const T INF) {
    int N = (int)G.size();
    std::vector<T> dist(N, INF);
    std::vector<int> par(N, -1), root(N, -1);

    for (auto &v : s) {
        dist[v] = 0;
        root[v] = v;
    }
    int loop_count = 0;

    while (true) {
        loop_count++;
        bool update = false;
        for (int cur = 0; cur < N; cur++) {
            if (dist[cur] == INF) continue;
            for (auto &e : G[cur]) {
                T nd = std::max(-INF, dist[cur] + e.cost);
                if (dist[e.to] > nd) {
                    par[e.to] = cur;
                    root[e.to] = root[cur];
                    update = true;
                    if (loop_count >= N) nd = -INF;
                    dist[e.to] = nd;
                }
            }
        }
        if (!update) break;
    }
    return {dist, par, root};
}

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