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#include "graph/kruskal.hpp"
#pragma once #include "data_structure/unionfind.hpp" #include "graph/get_edges.hpp" #include "graph/graph_template.hpp" template <class T> std::pair<T, Edges<T>> kruskal(Graph<T> &G) { auto es = get_edges<T>(G); std::sort(es.begin(), es.end(), [](Edge<T> a, Edge<T> b) { return a.cost < b.cost; }); int N = (int)G.size(); UnionFind uf(N); T ret = 0; Edges<T> es_ret; es_ret.reserve(N - 1); for (auto &&e : es) { if (!uf.same(e.from, e.to)) { ret += e.cost; uf.merge(e.from, e.to); es_ret.push_back(e); } } return {ret, es_ret}; }
#line 2 "graph/kruskal.hpp" #line 2 "data_structure/unionfind.hpp" struct UnionFind { int n; std::vector<int> parents; UnionFind() {} UnionFind(int n) : n(n), parents(n, -1) {} int leader(int x) { return parents[x] < 0 ? x : parents[x] = leader(parents[x]); } bool merge(int x, int y) { x = leader(x), y = leader(y); if (x == y) return false; if (parents[x] > parents[y]) std::swap(x, y); parents[x] += parents[y]; parents[y] = x; return true; } bool same(int x, int y) { return leader(x) == leader(y); } int size(int x) { return -parents[leader(x)]; } std::vector<std::vector<int>> groups() { std::vector<int> leader_buf(n), group_size(n); for (int i = 0; i < n; i++) { leader_buf[i] = leader(i); group_size[leader_buf[i]]++; } std::vector<std::vector<int>> result(n); for (int i = 0; i < n; i++) { result[i].reserve(group_size[i]); } for (int i = 0; i < n; i++) { result[leader_buf[i]].push_back(i); } result.erase(std::remove_if(result.begin(), result.end(), [&](const std::vector<int>& v) { return v.empty(); }), result.end()); return result; } void init(int n) { parents.assign(n, -1); } // reset }; #line 2 "graph/get_edges.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/get_edges.hpp" template <class T> Edges<T> get_edges(Graph<T> &G) { int N = (int)G.size(), M = 0; for (int i = 0; i < N; i++) { for (auto &&e : G[i]) { M = std::max(M, e.id + 1); } } Edges<T> es(M); for (int i = N - 1; i >= 0; i--) { for (auto &&e : G[i]) { es[e.id] = e; } } return es; } #line 6 "graph/kruskal.hpp" template <class T> std::pair<T, Edges<T>> kruskal(Graph<T> &G) { auto es = get_edges<T>(G); std::sort(es.begin(), es.end(), [](Edge<T> a, Edge<T> b) { return a.cost < b.cost; }); int N = (int)G.size(); UnionFind uf(N); T ret = 0; Edges<T> es_ret; es_ret.reserve(N - 1); for (auto &&e : es) { if (!uf.same(e.from, e.to)) { ret += e.cost; uf.merge(e.from, e.to); es_ret.push_back(e); } } return {ret, es_ret}; }