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#include "graph/dijkstra.hpp"
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。 $O((N+M)\log{M})$
#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, int n, const Graph<T> &g) { typedef std::pair<T, int> P; 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) { 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) { 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 { return edges[i]; } std::vector<edge_type> get_edges() const { return edges; } const auto operator[](int i) const { return csr[i]; } auto operator[](int i) { 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, int n, const Graph<T> &g) { typedef std::pair<T, int> P; 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