算法笔记--可撤销并查集 && 可持久化并查集

可撤销并查集模板：

struct UFS {
    stack<pair<int*, int>> stk;
    int fa[N], rnk[N];
    inline void init(int n) {
        for (int i = 0; i <= n; ++i) fa[i] = i, rnk[i] = 0;
    }
    inline int Find(int x) {
        while(x^fa[x]) x = fa[x];
        return x;
    }
    inline void Merge(int x, int y) {
        x = Find(x), y = Find(y);
        if(x == y) return ;
        if(rnk[x] <= rnk[y]) {
            stk.push({fa+x, fa[x]});
            fa[x] = y;
            if(rnk[x] == rnk[y]) {
                stk.push({rnk+y, rnk[y]});
                rnk[y]++;
            }
        }
        else {
            stk.push({fa+y, fa[y]});
            fa[y] = x;
        }
    }
    inline void Undo() {
        *stk.top().fi = stk.top().se;
        stk.pop();
    }
}ufs;

可持久化并查集模板：

struct Sustainable_DSU {
    static const int N = 1e5 + 5, M = 2e6 + 5;
    int root[N], lson[M], rson[M], fa[M], rnk[M], tot, n;

    inline void build(int &rt, int l, int r) {
        rt = ++tot;
        if(l == r) {fa[rt] = l; return ;}
        int m = l+r >> 1;
        build(lson[rt], l, m);
        build(rson[rt], m+1, r);
    }
    inline void init(int _n) {
        n = _n;
        tot = 0;
        build(root[0], 1, n);
    }
    inline void Update(int old, int &rt, int p, int v, int l, int r) {
        rt = ++tot;
        lson[rt] = lson[old], rson[rt] = rson[old];
        if(l == r) {
            fa[rt] = v;
            rnk[rt] = rnk[old];
            return ;
        }
        int m = l+r >> 1;
        if(p <= m) Update(lson[rt], lson[rt], p, v, l, m);
        else Update(rson[rt], rson[rt], p, v, m+1, r);
    }
    inline void update(int rt, int p, int l, int r) {
        if(l == r) { rnk[rt]++; return ;}
        int m = l+r >> 1;
        if(p <= m) update(lson[rt], p, l, m);
        else update(rson[rt], p, m+1, r);
    }
    ///返回rt版本p位置fa数组下标
    inline int query(int rt, int p, int l, int r) {
        if(l == r) return rt;
        int m = l+r >> 1;
        if(p <= m) return query(lson[rt], p, l, m);
        else return query(rson[rt], p, m+1, r);
    }
    ///返回rt版本p所在并查集fa数组下标
    inline int Find(int rt, int p) {
        int now = query(rt, p, 1, n);
        if(fa[now] == p) return now;
        else return Find(rt, fa[now]);
    }
    ///在i时刻合并x和y所在并查集
    inline void Merge(int i, int x, int y) {
        root[i] = root[i-1];
        int px = Find(root[i], x), py = Find(root[i], y);
        if(fa[px] != fa[py]) {
            if(rnk[px] > rnk[py]) swap(px, py);
            Update(root[i-1], root[i], fa[px], fa[py], 1, n);
            if(rnk[px] == rnk[py]) update(root[i], fa[py], 1, n);
        }
    }
};

P3402 【模板】可持久化并查集

代码：

#pragma GCC optimize(2)
#pragma GCC optimize(3)
#pragma GCC optimize(4)
#include<bits/stdc++.h>
using namespace std;
#define y1 y11
#define fi first
#define se second
#define pi acos(-1.0)
#define LL long long
//#define mp make_pair
#define pb push_back
#define ls rt<<1, l, m
#define rs rt<<1|1, m+1, r
#define ULL unsigned LL
#define pll pair<LL, LL>
#define pli pair<LL, int>
#define pii pair<int, int>
#define piii pair<pii, int>
#define pdd pair<double, double>
#define mem(a, b) memset(a, b, sizeof(a))
#define debug(x) cerr << #x << " = " << x << "\n";
#define fio ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
//head

struct Sustainable_DSU {
    static const int N = 2e5 + 5, M = 4e6 + 5;
    int root[N], lson[M], rson[M], fa[M], rnk[M], tot, n;

    inline void build(int &rt, int l, int r) {
        rt = ++tot;
        if(l == r) {fa[rt] = l; return ;}
        int m = l+r >> 1;
        build(lson[rt], l, m);
        build(rson[rt], m+1, r);
    }
    inline void init(int _n) {
        n = _n;
        tot = 0;
        build(root[0], 1, n);
    }
    inline void Update(int old, int &rt, int p, int v, int l, int r) {
        rt = ++tot;
        lson[rt] = lson[old], rson[rt] = rson[old];
        if(l == r) {
            fa[rt] = v;
            rnk[rt] = rnk[old];
            return ;
        }
        int m = l+r >> 1;
        if(p <= m) Update(lson[rt], lson[rt], p, v, l, m);
        else Update(rson[rt], rson[rt], p, v, m+1, r);
    }
    inline void update(int rt, int p, int l, int r) {
        if(l == r) { rnk[rt]++; return ;}
        int m = l+r >> 1;
        if(p <= m) update(lson[rt], p, l, m);
        else update(rson[rt], p, m+1, r);
    }
    ///返回rt版本p位置fa数组下标
    inline int query(int rt, int p, int l, int r) {
        if(l == r) return rt;
        int m = l+r >> 1;
        if(p <= m) return query(lson[rt], p, l, m);
        else return query(rson[rt], p, m+1, r);
    }
    ///返回rt版本p所在并查集fa数组下标
    inline int Find(int rt, int p) {
        int now = query(rt, p, 1, n);
        if(fa[now] == p) return now;
        else return Find(rt, fa[now]);
    }
    ///在i时刻合并x和y所在并查集
    inline void Merge(int i, int x, int y) {
        root[i] = root[i-1];
        int px = Find(root[i], x), py = Find(root[i], y);
        if(fa[px] != fa[py]) {
            if(rnk[px] > rnk[py]) swap(px, py);
            Update(root[i-1], root[i], fa[px], fa[py], 1, n);
            if(rnk[px] == rnk[py]) update(root[i], fa[py], 1, n);
        }
    }
}s;
int n, m, op, a, b;
int main() {
    scanf("%d %d", &n, &m);
    s.init(n);
    for (int i = 1; i <= m; ++i) {
        scanf("%d", &op);
        if(op == 1) scanf("%d %d", &a, &b), s.Merge(i, a, b);
        else if(op == 2) scanf("%d", &a), s.root[i] = s.root[a];
        else {
            scanf("%d %d", &a, &b);
            s.root[i] = s.root[i-1];
            a = s.Find(s.root[i], a);
            b = s.Find(s.root[i], b);
            if(s.fa[a] == s.fa[b]) printf("1\n");
            else printf("0\n");
        }
    }
    return 0;
}