Library

This documentation is automatically generated by online-judge-tools/verification-helper

View the Project on GitHub ebi-fly13/Library

:heavy_check_mark: dijkstra
(graph/dijkstra.hpp)

説明

辺重みが非負のグラフについて、単一始点最短路を求める。 $O((N+M)\log{M})$

Depends on

Verified with

Code

#pragma once

#include <algorithm>

#include <limits>

#include <queue>

#include <vector>


#include "../graph/base.hpp"


namespace ebi {

template <class T> std::vector<T> dijkstra(int s, const Graph<T> &g) {
    typedef std::pair<T, int> P;
    int n = g.node_number();
    std::vector<T> d(n, std::numeric_limits<T>::max());
    std::priority_queue<P, std::vector<P>, std::greater<P>> que;
    que.push(P(0, s));
    d[s] = 0;
    while (!que.empty()) {
        auto [ret, v] = que.top();
        que.pop();
        if (d[v] < ret) continue;
        for (auto e : g[v]) {
            if (d[e.to] > d[v] + e.cost) {
                d[e.to] = d[v] + e.cost;
                que.push(P(d[e.to], e.to));
            }
        }
    }
    return d;
}

template <class T> struct dijkstra_path {
  public:
    dijkstra_path(int s_, const Graph<T> &g)
        : s(s_),
          dist(g.size(), std::numeric_limits<T>::max()),
          prev(g.size(), -1) {
        dist[s] = 0;
        using P = std::pair<T, int>;
        std::priority_queue<P, std::vector<P>, std::greater<P>> que;
        que.push(P(0, s));
        while (!que.empty()) {
            auto [ret, v] = que.top();
            que.pop();
            if (dist[v] < ret) continue;
            for (auto e : g[v]) {
                if (dist[e.to] > dist[v] + e.cost) {
                    dist[e.to] = dist[v] + e.cost;
                    prev[e.to] = v;
                    que.push(P(dist[e.to], e.to));
                }
            }
        }
    }

    std::pair<T, std::vector<int>> shortest_path(int v) const {
        if (dist[v] == std::numeric_limits<T>::max()) return {dist[v], {}};
        std::vector<int> path;
        int u = v;
        while (u != s) {
            path.emplace_back(u);
            u = prev[u];
        }
        path.emplace_back(u);
        std::reverse(path.begin(), path.end());
        return {dist[v], path};
    }

  private:
    int s;
    std::vector<T> dist;
    std::vector<int> prev;
};

}  // namespace ebi
#line 2 "graph/dijkstra.hpp"

#include <algorithm>

#include <limits>

#include <queue>

#include <vector>


#line 2 "graph/base.hpp"

#include <cassert>
#include <iostream>
#include <ranges>
#line 7 "graph/base.hpp"

#line 2 "data_structure/simple_csr.hpp"

#line 4 "data_structure/simple_csr.hpp"
#include <utility>
#line 6 "data_structure/simple_csr.hpp"

namespace ebi {

template <class E> struct simple_csr {
    simple_csr() = default;

    simple_csr(int n, const std::vector<std::pair<int, E>>& elements)
        : start(n + 1, 0), elist(elements.size()) {
        for (auto e : elements) {
            start[e.first + 1]++;
        }
        for (auto i : std::views::iota(0, n)) {
            start[i + 1] += start[i];
        }
        auto counter = start;
        for (auto [i, e] : elements) {
            elist[counter[i]++] = e;
        }
    }

    simple_csr(const std::vector<std::vector<E>>& es)
        : start(es.size() + 1, 0) {
        int n = es.size();
        for (auto i : std::views::iota(0, n)) {
            start[i + 1] = (int)es[i].size() + start[i];
        }
        elist.resize(start.back());
        for (auto i : std::views::iota(0, n)) {
            std::copy(es[i].begin(), es[i].end(), elist.begin() + start[i]);
        }
    }

    int size() const {
        return (int)start.size() - 1;
    }

    const auto operator[](int i) const {
        return std::ranges::subrange(elist.begin() + start[i],
                                     elist.begin() + start[i + 1]);
    }
    auto operator[](int i) {
        return std::ranges::subrange(elist.begin() + start[i],
                                     elist.begin() + start[i + 1]);
    }

    const auto operator()(int i, int l, int r) const {
        return std::ranges::subrange(elist.begin() + start[i] + l,
                                     elist.begin() + start[i + 1] + r);
    }
    auto operator()(int i, int l, int r) {
        return std::ranges::subrange(elist.begin() + start[i] + l,
                                     elist.begin() + start[i + 1] + r);
    }

  private:
    std::vector<int> start;
    std::vector<E> elist;
};

}  // namespace ebi
#line 9 "graph/base.hpp"

namespace ebi {

template <class T> struct Edge {
    int from, to;
    T cost;
    int id;
};

template <class E> struct Graph {
    using cost_type = E;
    using edge_type = Edge<cost_type>;

    Graph(int n_) : n(n_) {}

    Graph() = default;

    void add_edge(int u, int v, cost_type c) {
        assert(!prepared && u < n && v < n);
        buff.emplace_back(u, edge_type{u, v, c, m});
        edges.emplace_back(edge_type{u, v, c, m++});
    }

    void add_undirected_edge(int u, int v, cost_type c) {
        assert(!prepared && u < n && v < n);
        buff.emplace_back(u, edge_type{u, v, c, m});
        buff.emplace_back(v, edge_type{v, u, c, m});
        edges.emplace_back(edge_type{u, v, c, m});
        m++;
    }

    void read_tree(int offset = 1, bool is_weighted = false) {
        read_graph(n - 1, offset, false, is_weighted);
    }

    void read_parents(int offset = 1) {
        for (auto i : std::views::iota(1, n)) {
            int p;
            std::cin >> p;
            p -= offset;
            add_undirected_edge(p, i, 1);
        }
        build();
    }

    void read_graph(int e, int offset = 1, bool is_directed = false,
                    bool is_weighted = false) {
        for (int i = 0; i < e; i++) {
            int u, v;
            std::cin >> u >> v;
            u -= offset;
            v -= offset;
            if (is_weighted) {
                cost_type c;
                std::cin >> c;
                if (is_directed) {
                    add_edge(u, v, c);
                } else {
                    add_undirected_edge(u, v, c);
                }
            } else {
                if (is_directed) {
                    add_edge(u, v, 1);
                } else {
                    add_undirected_edge(u, v, 1);
                }
            }
        }
        build();
    }

    void build() {
        assert(!prepared);
        csr = simple_csr<edge_type>(n, buff);
        buff.clear();
        prepared = true;
    }

    int size() const {
        return n;
    }

    int node_number() const {
        return n;
    }

    int edge_number() const {
        return m;
    }

    edge_type get_edge(int i) const {
        assert(prepared);
        return edges[i];
    }

    std::vector<edge_type> get_edges() const {
        assert(prepared);
        return edges;
    }

    const auto operator[](int i) const {
        assert(prepared);
        return csr[i];
    }
    auto operator[](int i) {
        assert(prepared);
        return csr[i];
    }

  private:
    int n, m = 0;

    std::vector<std::pair<int, edge_type>> buff;

    std::vector<edge_type> edges;
    simple_csr<edge_type> csr;
    bool prepared = false;
};

}  // namespace ebi
#line 9 "graph/dijkstra.hpp"

namespace ebi {

template <class T> std::vector<T> dijkstra(int s, const Graph<T> &g) {
    typedef std::pair<T, int> P;
    int n = g.node_number();
    std::vector<T> d(n, std::numeric_limits<T>::max());
    std::priority_queue<P, std::vector<P>, std::greater<P>> que;
    que.push(P(0, s));
    d[s] = 0;
    while (!que.empty()) {
        auto [ret, v] = que.top();
        que.pop();
        if (d[v] < ret) continue;
        for (auto e : g[v]) {
            if (d[e.to] > d[v] + e.cost) {
                d[e.to] = d[v] + e.cost;
                que.push(P(d[e.to], e.to));
            }
        }
    }
    return d;
}

template <class T> struct dijkstra_path {
  public:
    dijkstra_path(int s_, const Graph<T> &g)
        : s(s_),
          dist(g.size(), std::numeric_limits<T>::max()),
          prev(g.size(), -1) {
        dist[s] = 0;
        using P = std::pair<T, int>;
        std::priority_queue<P, std::vector<P>, std::greater<P>> que;
        que.push(P(0, s));
        while (!que.empty()) {
            auto [ret, v] = que.top();
            que.pop();
            if (dist[v] < ret) continue;
            for (auto e : g[v]) {
                if (dist[e.to] > dist[v] + e.cost) {
                    dist[e.to] = dist[v] + e.cost;
                    prev[e.to] = v;
                    que.push(P(dist[e.to], e.to));
                }
            }
        }
    }

    std::pair<T, std::vector<int>> shortest_path(int v) const {
        if (dist[v] == std::numeric_limits<T>::max()) return {dist[v], {}};
        std::vector<int> path;
        int u = v;
        while (u != s) {
            path.emplace_back(u);
            u = prev[u];
        }
        path.emplace_back(u);
        std::reverse(path.begin(), path.end());
        return {dist[v], path};
    }

  private:
    int s;
    std::vector<T> dist;
    std::vector<int> prev;
};

}  // namespace ebi
Back to top page