連結成分を取得できる Union Find
(library/datastructure/union_find/linked_union_find.hpp)

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• Last update: 2023-07-09 04:04:16+09:00
• Include: #include "library/datastructure/union_find/linked_union_find.hpp"

連結成分を取得できる Union Find

名前が分かりません。素集合の要素の列挙と併合 (単方向循環リスト) これです。

頂点 $v$ が属する連結成分 $C$ を $O(\vert C\vert)$ で取得可能である。

Depends on

• Union Find (library/datastructure/union_find/union_find.hpp)

Required by

• Union Find Lazy (library/datastructure/union_find/union_find_lazy.hpp)

Verified with

• test/src/datastructure/union_find/linked_union_find/past202203_h.test.cpp

Code

#ifndef SUISEN_LINKED_UNION_FIND
#define SUISEN_LINKED_UNION_FIND

#include <numeric>
#include "library/datastructure/union_find/union_find.hpp"

namespace suisen {
    struct LinkedUnionFind : public UnionFind {
        LinkedUnionFind() = default;
        explicit LinkedUnionFind(int n) : UnionFind(n), _link(n) {
            std::iota(_link.begin(), _link.end(), 0);
        }
        // Merge two vertices `x` and `y`.
        bool merge(int x, int y) {
            if (UnionFind::merge(x, y)) {
                std::swap(_link[x], _link[y]);
                return true;
            }
            return false;
        }
        // Get items connected to `x` (including `x`). Let the size of return value be `m`, time complexity is O(m).
        std::vector<int> connected_component(int x) const {
            std::vector<int> comp{ x };
            for (int y = _link[x]; y != x; y = _link[y]) comp.push_back(y);
            return comp;
        }
    protected:
        std::vector<int> _link;
    };
} // namespace suisen

#endif // SUISEN_LINKED_UNION_FIND

#line 1 "library/datastructure/union_find/linked_union_find.hpp"



#include <numeric>
#line 1 "library/datastructure/union_find/union_find.hpp"



#include <algorithm>
#include <vector>

namespace suisen {
    struct UnionFind {
        UnionFind() = default;
        explicit UnionFind(int _n) : _n(_n), _dat(_n, -1) {}
        // Get the root of `x`. equivalent to `operator[](x)`
        int root(int x) {
            static std::vector<int> buf;
            while (_dat[x] >= 0) buf.push_back(x), x = _dat[x];
            while (buf.size()) _dat[buf.back()] = x, buf.pop_back();
            return x;
        }
        // Get the root of `x`. euivalent to `root(x)`
        int operator[](int x) {
            return root(x);
        }
        // Merge two vertices `x` and `y`.
        bool merge(int x, int y) {
            x = root(x), y = root(y);
            if (x == y) return false;
            if (_dat[x] > _dat[y]) std::swap(x, y);
            _dat[x] += _dat[y], _dat[y] = x;
            return true;
        }
        // Check if `x` and `y` belongs to the same connected component.
        bool same(int x, int y) {
            return root(x) == root(y);
        }
        // Get the size of connected componet to which `x` belongs.
        int size(int x) {
            return -_dat[root(x)];
        }
        // Get all of connected components.
        std::vector<std::vector<int>> groups() {
            std::vector<std::vector<int>> res(_n);
            for (int i = 0; i < _n; ++i) res[root(i)].push_back(i);
            res.erase(std::remove_if(res.begin(), res.end(), [](const auto& g) { return g.empty(); }), res.end());
            return res;
        }
    protected:
        int _n;
        std::vector<int> _dat;
    };
} // namespace suisen


#line 6 "library/datastructure/union_find/linked_union_find.hpp"

namespace suisen {
    struct LinkedUnionFind : public UnionFind {
        LinkedUnionFind() = default;
        explicit LinkedUnionFind(int n) : UnionFind(n), _link(n) {
            std::iota(_link.begin(), _link.end(), 0);
        }
        // Merge two vertices `x` and `y`.
        bool merge(int x, int y) {
            if (UnionFind::merge(x, y)) {
                std::swap(_link[x], _link[y]);
                return true;
            }
            return false;
        }
        // Get items connected to `x` (including `x`). Let the size of return value be `m`, time complexity is O(m).
        std::vector<int> connected_component(int x) const {
            std::vector<int> comp{ x };
            for (int y = _link[x]; y != x; y = _link[y]) comp.push_back(y);
            return comp;
        }
    protected:
        std::vector<int> _link;
    };
} // namespace suisen

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