graph/shortest-path/bellman-ford.hpp

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• Last update: 2024-10-04 14:05:18+02:00
• Include: #include "graph/shortest-path/bellman-ford.hpp"

Depends on

• graph/graph-template.hpp

Verified with

• test/aoj-grl-1-b.test.cpp

Code

#pragma once
#include "../graph-template.hpp"

template <typename T>
vector<T> bellman_ford(const Edges<T> &edges, int n, int s) {
    const auto INF = numeric_limits<T>::max();
    const auto M_INF = numeric_limits<T>::min();

    vector<T> dist(n, INF);

    dist[s] = 0;
    for (int i = 0; i < n; i++) {
        for (auto &e : edges) {
            if (dist[e.from] == INF) continue;
            dist[e.to] = min(dist[e.to], dist[e.from] + e.cost);
        }
    }
    vector<bool> negative(n);
    for (int i = 0; i < n; i++) {
        for (auto &e : edges) {
            if (dist[e.from] == INF) continue;
            if (dist[e.from] + e.cost < dist[e.to]) {
                dist[e.to] = dist[e.from] + e.cost;
                negative[e.to] = true;
            }
            if (negative[e.from]) {
                negative[e.to] = true;
            }
        }
    }
    for (int i = 0; i < n; i++) {
        if (negative[i]) {
            dist[i] = M_INF;
        }
    }
    return dist;
}

#line 2 "graph/graph-template.hpp"
#include <bits/stdc++.h>
using namespace std;

template <typename T = int>
struct Edge {
    int from, to;
    T cost;
    int idx;

    Edge() = default;

    Edge(int from, int to, T cost = 1, int idx = -1)
        : from(from), to(to), cost(cost), idx(idx) {}

    operator int() const { return to; }
};

template <typename T = int>
struct Graph {
    vector<vector<Edge<T> > > g;
    int es;

    Graph() = default;

    explicit Graph(int n) : g(n), es(0) {}

    size_t size() const { return g.size(); }

    virtual void add_directed_edge(int from, int to, T cost = 1) {
        g[from].emplace_back(from, to, cost, es++);
    }

    // virtual 可以被重载，实现多态
    virtual void add_edge(int from, int to, T cost = 1) {
        g[from].emplace_back(from, to, cost, es);
        g[to].emplace_back(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 a, b;
            cin >> a >> b;
            a += padding;
            b += padding;
            T c = T(1);
            if (weighted) cin >> c;
            if (directed)
                add_directed_edge(a, b, c);
            else
                add_edge(a, b, c);
        }
    }

    inline vector<Edge<T> > &operator[](const int &k) { return g[k]; }

    inline const vector<Edge<T> > &operator[](const int &k) const { return g[k]; }
};

template <typename T = int>
using Edges = vector<Edge<T> >;
#line 3 "graph/shortest-path/bellman-ford.hpp"

template <typename T>
vector<T> bellman_ford(const Edges<T> &edges, int n, int s) {
    const auto INF = numeric_limits<T>::max();
    const auto M_INF = numeric_limits<T>::min();

    vector<T> dist(n, INF);

    dist[s] = 0;
    for (int i = 0; i < n; i++) {
        for (auto &e : edges) {
            if (dist[e.from] == INF) continue;
            dist[e.to] = min(dist[e.to], dist[e.from] + e.cost);
        }
    }
    vector<bool> negative(n);
    for (int i = 0; i < n; i++) {
        for (auto &e : edges) {
            if (dist[e.from] == INF) continue;
            if (dist[e.from] + e.cost < dist[e.to]) {
                dist[e.to] = dist[e.from] + e.cost;
                negative[e.to] = true;
            }
            if (negative[e.from]) {
                negative[e.to] = true;
            }
        }
    }
    for (int i = 0; i < n; i++) {
        if (negative[i]) {
            dist[i] = M_INF;
        }
    }
    return dist;
}

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