Rollback DSU
(datastructure/rollback_dsu.hpp)

• View this file on GitHub
• Last update: 2026-10-26 01:30:50+09:00
• Include: #include "datastructure/rollback_dsu.hpp"

概要

• 結合を取り消せる Union-Find。

使い方

• rollback_dsu(n): $n$ 頂点 $0$ 辺の無向グラフを作る。
• merge(a, b): 辺 $(a, b)$ を追加し、代表元を返す。
• undo(): 直前の merge を取り消す。
• time(): これまでの merge の回数から undo で取り消した分を引いた数を返す。
• rollback(t): time() が t になるまで undo する。
• same(a, b): 頂点 a, b が連結かを返す。
• leader(a): 頂点 a の属する連結成分の代表元を返す。
• size(a): 頂点 a の属する連結成分のサイズを返す。
• groups(): 連結成分ごとの頂点のリストを返す。

制約

• $0 \le a, b < n$
• undo: $1 \le$ time()
• rollback: $0 \le t \le$ time()

計算量

• merge, same, leader, size: $\mathcal{O}(\log n)$
• undo: $\mathcal{O}(1)$
• rollback(t): $\mathcal{O}(\text{time}() - t)$
• groups: $\mathcal{O}(n \log n)$

Verified with

• test/library-checker/persistent_unionfind.test.cpp
• test/unit/rollback_dsu.test.cpp

Code

#pragma once
#include <algorithm>
#include <cassert>
#include <utility>
#include <vector>
struct rollback_dsu {
public:
    rollback_dsu() : rollback_dsu(0) {
    }
    explicit rollback_dsu(int n) : _n(n), parent_or_size(n, -1) {
    }
    int merge(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        int x = leader(a), y = leader(b);
        if (x == y) {
            history.emplace_back(-1, -1);
            return x;
        }
        if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);
        history.emplace_back(y, parent_or_size[y]);
        parent_or_size[x] += parent_or_size[y];
        parent_or_size[y] = x;
        return x;
    }
    void undo() {
        assert(!history.empty());
        auto [y, s] = history.back();
        history.pop_back();
        if (y == -1) return;
        parent_or_size[parent_or_size[y]] -= s;
        parent_or_size[y] = s;
    }
    int time() const {
        return int(history.size());
    }
    void rollback(int t) {
        assert(0 <= t && t <= time());
        while (time() > t) undo();
    }
    bool same(int a, int b) const {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        return leader(a) == leader(b);
    }
    int leader(int a) const {
        assert(0 <= a && a < _n);
        while (parent_or_size[a] >= 0) a = parent_or_size[a];
        return a;
    }
    int size(int a) const {
        assert(0 <= a && a < _n);
        return -parent_or_size[leader(a)];
    }
    std::vector<std::vector<int>> groups() const {
        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;
    }

private:
    int _n;
    std::vector<int> parent_or_size;
    std::vector<std::pair<int, int>> history;  // (attached leader, its old parent_or_size)
};

#line 2 "datastructure/rollback_dsu.hpp"
#include <algorithm>
#include <cassert>
#include <utility>
#include <vector>
struct rollback_dsu {
public:
    rollback_dsu() : rollback_dsu(0) {
    }
    explicit rollback_dsu(int n) : _n(n), parent_or_size(n, -1) {
    }
    int merge(int a, int b) {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        int x = leader(a), y = leader(b);
        if (x == y) {
            history.emplace_back(-1, -1);
            return x;
        }
        if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y);
        history.emplace_back(y, parent_or_size[y]);
        parent_or_size[x] += parent_or_size[y];
        parent_or_size[y] = x;
        return x;
    }
    void undo() {
        assert(!history.empty());
        auto [y, s] = history.back();
        history.pop_back();
        if (y == -1) return;
        parent_or_size[parent_or_size[y]] -= s;
        parent_or_size[y] = s;
    }
    int time() const {
        return int(history.size());
    }
    void rollback(int t) {
        assert(0 <= t && t <= time());
        while (time() > t) undo();
    }
    bool same(int a, int b) const {
        assert(0 <= a && a < _n);
        assert(0 <= b && b < _n);
        return leader(a) == leader(b);
    }
    int leader(int a) const {
        assert(0 <= a && a < _n);
        while (parent_or_size[a] >= 0) a = parent_or_size[a];
        return a;
    }
    int size(int a) const {
        assert(0 <= a && a < _n);
        return -parent_or_size[leader(a)];
    }
    std::vector<std::vector<int>> groups() const {
        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;
    }

private:
    int _n;
    std::vector<int> parent_or_size;
    std::vector<std::pair<int, int>> history;  // (attached leader, its old parent_or_size)
};

Back to top page