rcpl

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:heavy_check_mark: Kruskal's algorithm (クラスカル法)
(graph/kruskal.hpp)

使い方

Graph<T> g;
auto [cost, edges] = kruskal<T>(g);

参考文献

Depends on

Verified with

Code

#pragma once

#include "unionfind/unionfind.hpp"
#include "graph/graph_template.hpp"

#include <algorithm>

template <class T> std::pair<T, std::vector<Edge<T>>> kruskal(Graph<T>& g) {
    auto es = g.edges;
    std::sort(es.begin(), es.end());
    const int n = (int)(g.size());
    Unionfind uf(n);
    T ret = 0;
    std::vector<Edge<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 "unionfind/unionfind.hpp"

#include <algorithm>
#include <cassert>
#include <vector>

// Unionfind
struct Unionfind {
    int n;
    std::vector<int> parent;

    Unionfind() = default;

    explicit Unionfind(int n) : n(n), parent(n, -1) {}

    int leader(int x) {
        assert(0 <= x and x < n);
        if (parent[x] < 0) {
            return x;
        } else {
            return parent[x] = leader(parent[x]);
        }
    }

    int merge(int x, int y) {
        assert(0 <= x and x < n);
        assert(0 <= y and y < n);
        x = leader(x);
        y = leader(y);
        if (x == y) {
            return x;
        }
        if (-parent[x] < -parent[y]) {
            std::swap(x, y);
        }
        parent[x] += parent[y];
        parent[y] = x;
        return x;
    }

    bool same(int x, int y) {
        assert(0 <= x and x < n);
        assert(0 <= y and y < n);
        return leader(x) == leader(y);
    }

    int size(int x) {
        assert(0 <= x and x < n);
        return -parent[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;
    }
};
#line 2 "graph/graph_template.hpp"

#line 5 "graph/graph_template.hpp"

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

    Edge() = default;
    Edge(const int from, const int to, const T cost = T(1), const int id = -1) : from(from), to(to), cost(cost), id(id) {}

    friend bool operator<(const Edge<T>& a, const Edge<T>& b) { return a.cost < b.cost; }

    friend std::ostream& operator<<(std::ostream& os, const Edge<T>& e) {
        // output format: {id: cost(from, to) = cost}
        return os << "{" << e.id << ": cost(" << e.from << ", " << e.to << ") = " << e.cost << "}";
    }
};
template <class T> using Edges = std::vector<Edge<T>>;

template <class T> struct Graph {
    struct EdgeIterators {
       public:
        using Iterator = typename std::vector<Edge<T>>::iterator;
        EdgeIterators() = default;
        EdgeIterators(const Iterator& begit, const Iterator& endit) : begit(begit), endit(endit) {}
        Iterator begin() const { return begit; }
        Iterator end() const { return endit; }
        size_t size() const { return std::distance(begit, endit); }
        Edge<T>& operator[](int i) const { return begit[i]; }

       private:
        Iterator begit, endit;
    };

    int n, m;
    bool is_build, is_directed;
    std::vector<Edge<T>> edges;

    // CSR (Compressed Row Storage) 形式用
    std::vector<int> start;
    std::vector<Edge<T>> csr_edges;

    Graph() = default;
    Graph(const int n, const bool directed = false) : n(n), m(0), is_build(false), is_directed(directed), start(n + 1, 0) {}

    // 辺を追加し, その辺が何番目に追加されたかを返す
    int add_edge(const int from, const int to, const T cost = T(1), int id = -1) {
        assert(!is_build);
        assert(0 <= from and from < n);
        assert(0 <= to and to < n);
        if (id == -1) id = m;
        edges.emplace_back(from, to, cost, id);
        return m++;
    }

    // CSR 形式でグラフを構築
    void build() {
        assert(!is_build);
        for (auto&& e : edges) {
            start[e.from + 1]++;
            if (!is_directed) start[e.to + 1]++;
        }
        for (int v = 0; v < n; v++) start[v + 1] += start[v];
        auto counter = start;
        csr_edges.resize(start.back() + 1);
        for (auto&& e : edges) {
            csr_edges[counter[e.from]++] = e;
            if (!is_directed) csr_edges[counter[e.to]++] = Edge(e.to, e.from, e.cost, e.id);
        }
        is_build = true;
    }

    EdgeIterators operator[](int i) {
        if (!is_build) build();
        return EdgeIterators(csr_edges.begin() + start[i], csr_edges.begin() + start[i + 1]);
    }

    size_t size() const { return (size_t)(n); }

    friend std::ostream& operator<<(std::ostream& os, Graph<T>& g) {
        os << "[";
        for (int i = 0; i < (int)(g.size()); i++) {
            os << "[";
            for (int j = 0; j < (int)(g[i].size()); j++) {
                os << g[i][j];
                if (j + 1 != (int)(g[i].size())) os << ", ";
            }
            os << "]";
            if (i + 1 != (int)(g.size())) os << ", ";
        }
        return os << "]";
    }
};
#line 5 "graph/kruskal.hpp"

#line 7 "graph/kruskal.hpp"

template <class T> std::pair<T, std::vector<Edge<T>>> kruskal(Graph<T>& g) {
    auto es = g.edges;
    std::sort(es.begin(), es.end());
    const int n = (int)(g.size());
    Unionfind uf(n);
    T ret = 0;
    std::vector<Edge<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};
}
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