Kruskal法
(C++/graph/mst/kruskal.hpp)

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• Last update: 2025-06-14 01:07:36+09:00
• Include: #include "C++/graph/mst/kruskal.hpp"

Depends on

• UnionFind (C++/ds/uf/UnionFind.hpp)
• Edge (C++/graph/edge.hpp)
• 最小全域木 (C++/graph/mst/MST.hpp)

Verified with

• test/manhattan.test.cpp

Code

#pragma once

#include <vector>
#include "C++/graph/mst/MST.hpp"
#include "C++/ds/uf/UnionFind.hpp"
namespace man {
inline MST kruskal(std::vector<edge> edges, const int n) noexcept {
    std::ranges::sort(edges, [&](const edge &e, const edge &f) -> bool { return e.cost < f.cost; });
    UnionFind uf(n);
    std::vector<edge> e;
    long long ret = 0;
    for(const auto &ed: edges) {
        if(uf.unite(ed.src, ed)) {
            e.emplace_back(ed);
            ret += ed.cost;
        }
    }
    return {e, ret};
}
}

/**
 * @brief Kruskal法
 */

#line 2 "C++/graph/mst/kruskal.hpp"

#include <vector>
#line 2 "C++/graph/mst/MST.hpp"

#line 2 "C++/graph/edge.hpp"
#ifndef EDGE
#define EDGE
#endif

namespace man {
struct edge {
    int src, to, id;
    long long cost;
    edge(){}
    edge(const int src_, const int to_, const int id_ = -1, const long long cost_ = 0): src(src_), to(to_), id(id_), cost(cost_){}
    constexpr inline operator int() const noexcept { return to; }
};
}

/**
 * @brief Edge
 */
#line 5 "C++/graph/mst/MST.hpp"
struct MST {
    std::vector<man::edge> tree;
    long long cost;
};

/**
 * @brief 最小全域木
 */
#line 2 "C++/ds/uf/UnionFind.hpp"

#include <cassert>

#line 5 "C++/ds/uf/UnionFind.hpp"
#include <algorithm>

namespace man {
struct UnionFind {
protected:
    std::vector<int> par;
public:
    UnionFind(const int n): par(n, -1){}
    inline int operator[](int i) noexcept {
        while(par[i] >= 0) {
            const int p = par[par[i]];
            if(p < 0) return par[i];
            i = par[i] = p;
        }
        return i;
    }
    inline bool unite(int x, int y) noexcept {
        x = (*this)[x], y = (*this)[y];
        if(x == y) return false;
        if(-par[x] < -par[y]) {
            std::swap(x, y);
        }
        par[x] += par[y], par[y] = x;
        return true;
    }
    inline int size(const int x) noexcept {
        return -par[(*this)[x]];
    }
    inline int size() const noexcept { return par.size(); }
    inline std::vector<std::vector<int>> groups() noexcept {
        const int n = std::ssize(par);
        std::vector<std::vector<int>> res(n);
        for(int i = 0; i < n; ++i) {
            res[(*this)[i]].emplace_back(i);
        }
        const auto it = std::ranges::remove_if(res, [&](const std::vector<int> &v){ return v.empty(); });
        res.erase(it.begin(), it.end());
        return res;
    }
};

inline bool is_bipartite(UnionFind uf) noexcept {
    assert(uf.size() % 2 == 0);
    const int n = uf.size() / 2;
    bool ok = true;
    for(int i = 0; i < n; ++i) {
        ok &= uf[i] != uf[i + n];
    }
    return ok;
}
}
/**
 * @brief UnionFind
 * @see https://github.com/maspypy/library/blob/main/ds/unionfind/unionfind.hpp
 */
#line 6 "C++/graph/mst/kruskal.hpp"
namespace man {
inline MST kruskal(std::vector<edge> edges, const int n) noexcept {
    std::ranges::sort(edges, [&](const edge &e, const edge &f) -> bool { return e.cost < f.cost; });
    UnionFind uf(n);
    std::vector<edge> e;
    long long ret = 0;
    for(const auto &ed: edges) {
        if(uf.unite(ed.src, ed)) {
            e.emplace_back(ed);
            ret += ed.cost;
        }
    }
    return {e, ret};
}
}

/**
 * @brief Kruskal法
 */

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