Minimum Spanning Tree (verify/graph/mst.test.cpp)

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• Last update: 2024-11-21 04:36:37+01:00
• Problem: https://judge.yosupo.jp/problem/minimum_spanning_tree

Depends on

• cp-algo/graph/base.hpp
• cp-algo/graph/edge_types.hpp
• cp-algo/graph/mst.hpp
• cp-algo/structures/dsu.hpp
• cp-algo/structures/stack_union.hpp

Code

// @brief Minimum Spanning Tree
#define PROBLEM "https://judge.yosupo.jp/problem/minimum_spanning_tree"
#pragma GCC optimize("Ofast,unroll-loops")
#include "cp-algo/graph/mst.hpp"
#include <bits/stdc++.h>

using namespace std;
using namespace cp_algo::graph;

void solve() {
    int n, m;
    cin >> n >> m;
    graph<undirected, weighted_edge> g(n);
    g.read_edges(m);
    auto [X, E] = mst(g);
    cout << X << "\n";
    for(int e: E) {cout << e / 2 << " ";}
}

signed main() {
    //freopen("input.txt", "r", stdin);
    ios::sync_with_stdio(0);
    cin.tie(0);
    int t = 1;
    //cin >> t;
    while(t--) {
        solve();
    }
}

#line 1 "verify/graph/mst.test.cpp"
// @brief Minimum Spanning Tree
#define PROBLEM "https://judge.yosupo.jp/problem/minimum_spanning_tree"
#pragma GCC optimize("Ofast,unroll-loops")
#line 1 "cp-algo/graph/mst.hpp"


#line 1 "cp-algo/graph/base.hpp"


#line 1 "cp-algo/graph/edge_types.hpp"


#include <iostream>
#include <cstdint>
namespace cp_algo::graph {
    using node_index = int;
    struct edge_base {
        node_index to;

        edge_base() {}
        edge_base(node_index v): to(v) {}

        static auto read(node_index v0 = 0) {
            node_index u, v;
            std::cin >> u >> v;
            return std::pair{u - v0, edge_base(v - v0)};
        }

        edge_base backedge(int from) const {
            return {from};
        }
    };

    struct weighted_edge: edge_base {
        int64_t w;

        weighted_edge() {}
        weighted_edge(node_index v, int64_t w): edge_base(v), w(w) {}

        static auto read(node_index v0 = 0) {
            node_index u, v;
            int64_t w;
            std::cin >> u >> v >> w;
            return std::pair{u - v0, weighted_edge{v - v0, w}};
        }

        weighted_edge backedge(node_index from) const {
            return {from, w};
        }
    };

    template<typename edge>
    concept edge_type = std::is_base_of_v<edge_base, edge>;
    template<typename edge>
    concept weighted_edge_type = std::is_base_of_v<weighted_edge, edge>;
}

#line 1 "cp-algo/structures/stack_union.hpp"


#include <cstddef>
#include <vector>
namespace cp_algo::structures {
    template<class datatype>
    struct stack_union {
        stack_union(int n = 0): head(n), next(1), data(1) {}

        void push(int v, datatype const& vdata) {
            next.push_back(head[v]);
            head[v] = (int)std::size(next) - 1;
            data.push_back(vdata);
        }
        template<typename... Args>
        void emplace(int v, Args&&... vdata) {
            next.push_back(head[v]);
            head[v] = size(next) - 1;
            data.emplace_back(std::forward<Args...>(vdata...));
        }

        void reserve(int m) {
            data.reserve(m);
            next.reserve(m);
        }

        size_t size() const {return std::size(head);}
        size_t nodes() const {return std::size(data);}

        std::vector<int> head, next;
        std::vector<datatype> data;
    };
}

#line 5 "cp-algo/graph/base.hpp"
#include <ranges>
#line 7 "cp-algo/graph/base.hpp"
namespace cp_algo::graph {
    using edge_index = int;
    enum type {directed = 0, undirected = 1};
    template<type _undirected, edge_type edge_t = edge_base>
    struct graph {
        static constexpr bool undirected = _undirected;
        graph(int n, int v0 = 0): v0(v0), adj(n) {}

        void add_edge(node_index u, edge_t e) {
            adj.push(u, (edge_index)size(edges));
            edges.push_back(e);
            if constexpr (undirected) {
                adj.push(e.to, (edge_index)size(edges));
            }
            edges.push_back(e.backedge(u));
        }
        void read_edges(node_index m) {
            adj.reserve(m);
            for(edge_index i = 0; i < m; i++) {
                auto [u, e] = edge_t::read(v0);
                add_edge(u, e);
            }
        }
        void call_adjacent(node_index v, auto &&callback, auto &&terminate) const {
            for(int sv = adj.head[v]; sv && !terminate(); sv = adj.next[sv]) {
                callback(adj.data[sv]);
            }
        }
        void call_adjacent(node_index v, auto &&callback) const {
            call_adjacent(v, callback, [](){return false;});
        }
        void call_edges(auto &&callback) const {
            for(edge_index e: edges_view()) {
                callback(e);
            }
        }
        auto nodes_view() const {
            return std::views::iota(0, n());
        }
        auto edges_view() const {
            return std::views::iota(0, 2 * m()) | std::views::filter(
                [](edge_index e) {return !(e % 2);}
            );
        }
        auto const& incidence_lists() const {return adj;}
        edge_t const& edge(edge_index e) const {return edges[e];}
        node_index n() const {return (node_index)adj.size();}
        edge_index m() const {return (edge_index)size(edges) / 2;}
    private:
        node_index v0;
        std::vector<edge_t> edges;
        structures::stack_union<edge_index> adj;
    };
}

#line 1 "cp-algo/structures/dsu.hpp"


#include <numeric>
#line 5 "cp-algo/structures/dsu.hpp"
namespace cp_algo::structures {
    struct disjoint_set_union {
        disjoint_set_union (int n): par(n) {
            std::iota(begin(par), end(par), 0);
        }
        int get(int v) {
            return v == par[v] ? v : par[v] = get(par[v]);
        }
        bool uni(int a, int b) {
            a = get(a);
            b = get(b);
            par[a] = b;
            return a != b;
        }
    private:
        std::vector<int> par;
    };
    using dsu = disjoint_set_union;
}

#line 5 "cp-algo/graph/mst.hpp"
#include <algorithm>
namespace cp_algo::graph {
    template<weighted_edge_type edge_t>
    auto mst(graph<undirected, edge_t> const& g) {
        std::vector<std::pair<int64_t, edge_index>> edges;
        g.call_edges([&](edge_index e) {
            edges.emplace_back(g.edge(e).w, e);
        });
        std::ranges::sort(edges);
        structures::dsu me(g.n());
        int64_t total = 0;
        std::vector<edge_index> mst;
        for(auto [w, e]: edges) {
            if(me.uni(g.edge(e ^ 1).to, g.edge(e).to)) {
                total += w;
                mst.push_back(e);
            }
        }
        return std::pair{total, mst};
    }
}

#line 5 "verify/graph/mst.test.cpp"
#include <bits/stdc++.h>

using namespace std;
using namespace cp_algo::graph;

void solve() {
    int n, m;
    cin >> n >> m;
    graph<undirected, weighted_edge> g(n);
    g.read_edges(m);
    auto [X, E] = mst(g);
    cout << X << "\n";
    for(int e: E) {cout << e / 2 << " ";}
}

signed main() {
    //freopen("input.txt", "r", stdin);
    ios::sync_with_stdio(0);
    cin.tie(0);
    int t = 1;
    //cin >> t;
    while(t--) {
        solve();
    }
}

Test cases

Env	Name	Status	Elapsed	Memory
g++	example_00	AC	5 ms	4 MB
g++	example_01	AC	5 ms	4 MB
g++	example_02	AC	5 ms	4 MB
g++	max_random_00	AC	197 ms	51 MB
g++	max_random_01	AC	200 ms	52 MB
g++	max_random_02	AC	199 ms	51 MB
g++	max_random_03	AC	203 ms	53 MB
g++	max_random_04	AC	205 ms	51 MB
g++	random_00	AC	164 ms	45 MB
g++	random_01	AC	194 ms	49 MB
g++	random_02	AC	130 ms	47 MB
g++	random_03	AC	194 ms	47 MB
g++	random_04	AC	146 ms	40 MB
g++	small_00	AC	114 ms	43 MB
g++	small_01	AC	114 ms	48 MB
g++	small_02	AC	102 ms	41 MB
g++	small_03	AC	13 ms	5 MB
g++	small_04	AC	31 ms	13 MB
g++	small_c01_00	AC	5 ms	4 MB
g++	small_c01_01	AC	5 ms	4 MB
g++	small_c01_02	AC	5 ms	4 MB
g++	small_c01_03	AC	5 ms	4 MB
g++	small_c01_04	AC	5 ms	4 MB
g++	star_00	AC	173 ms	51 MB

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