题解 P3835 【【模板】可持久化平衡树】

就是可持久化后的普通平衡树嘛（逃

题目描述不写了（懒了

这里是题目

主要思路：FHQ Treap + 可持久化

普通FHQ Treap加上一点可持久化的东西如下：(打上注释的代码是可持久化的特殊操作)

inline int merge(int x, int y) {
    if(!x || !y) return x + y;
    if(z[x].pri < z[y].pri) {
        int rt = newnode(); //
        z[rt] = z[x];       //
        z[rt].ch[1] = merge(z[rt].ch[1], y);
        update(rt);
        return rt;
    } else {
        int rt = newnode(); //
        z[rt] = z[y];       //
        z[rt].ch[0] = merge(x, z[rt].ch[0]);
        update(rt);
        return rt;
    }
}
inline void split(int rt, ll k, int &x, int &y) {
    if(!rt) x = y = 0;
    else {
        if(z[rt].w <= k) {
            x = newnode(); //
            z[x] = z[rt];  //
            split(z[x].ch[1], k, z[x].ch[1], y);
            update(x);
        } else {
            y = newnode(); //
            z[y] = z[rt];  //
            split(z[y].ch[0], k, x, z[y].ch[0]);
            update(y);
        } 
    }
}

然后开个root[]数组，存各个版本的根节点，然后注意下空间就好了。记得开50倍，要不凉凉

code:

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#include<string>
#include<vector>
#include<set>
#include<queue>
#include<stack>
using namespace std;
#define go(i,j,n,k) for(int i=j;i<=n;i+=k)
#define fo(i,j,n,k) for(int i=j;i>=n;i-=k)
#define rep(i,x) for(int i=h[x];i;i=e[i].nxt)
#define mn 500010
#define ld long double
#define fi first
#define se second
#define inf 1<<30
#define ll long long
#define root 1,n,1
#define lson l,m,rt<<1
#define rson m+1,r,rt<<1|1
#define bson l,r,rt
inline ll read(){
    ll x=0,f=1;char ch=getchar();
    while(ch>'9'||ch<'0'){if(ch=='-')f=-f;ch=getchar();}
    while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
    return x*f;
}
struct edge{
    int ch[2], sze, pri;
    ll w;
} z[mn * 50];
int rot[mn], xx, yy, zz, n, cnt;
inline void update(int rt) {
    z[rt].sze = 1;
    if(z[rt].ch[0]) z[rt].sze += z[z[rt].ch[0]].sze;
    if(z[rt].ch[1]) z[rt].sze += z[z[rt].ch[1]].sze;
} 
inline int newnode(ll w = 0) {
    z[++cnt].w = w;
    z[cnt].sze = 1;
    z[cnt].pri = rand();
    return cnt;
}
inline int merge(int x, int y) {
    if(!x || !y) return x + y;
    if(z[x].pri < z[y].pri) {
        int rt = newnode();
        z[rt] = z[x];
        z[rt].ch[1] = merge(z[rt].ch[1], y);
        update(rt);
        return rt;
    } else {
        int rt = newnode();
        z[rt] = z[y];
        z[rt].ch[0] = merge(x, z[rt].ch[0]);
        update(rt);
        return rt;
    }
}
inline void split(int rt, ll k, int &x, int &y) {
    if(!rt) x = y = 0;
    else {
        if(z[rt].w <= k) {
            x = newnode();
            z[x] = z[rt];
            split(z[x].ch[1], k, z[x].ch[1], y);
            update(x);
        } else {
            y = newnode();
            z[y] = z[rt];
            split(z[y].ch[0], k, x, z[y].ch[0]);
            update(y);
        } 
    }
}
inline int findkth(int rt, int k) {
    while(1119) {
        if(k <= z[z[rt].ch[0]].sze)
            rt = z[rt].ch[0];
        else {
            if(z[rt].ch[0]) k -= z[z[rt].ch[0]].sze;
            if(!--k) return rt;
            rt = z[rt].ch[1];
        }
    }
}
int main(){
    n = read();
    go(i, 1, n, 1) {
    	xx = yy = zz = 0;
        int tmp = read(), s = read(); ll a = read();
        rot[i] = rot[tmp];
        if(s == 1) {
            split(rot[i], a, xx, yy);
            rot[i] = merge(merge(xx, newnode(a)), yy);
        } else if(s == 2) {
            split(rot[i], a, xx, zz);
            split(xx, a - 1, xx, yy);
            yy = merge(z[yy].ch[0], z[yy].ch[1]);
            rot[i] = merge(merge(xx, yy), zz);
        } else if(s == 3) {
            split(rot[i], a - 1, xx, yy);
            printf("%lld
", z[xx].sze + 1);
            rot[i] = merge(xx, yy);
        } else if(s == 4) {
            printf("%lld
", z[findkth(rot[i], a)].w);
        } else if(s == 5) {
            split(rot[i], a - 1, xx, yy);
            if(xx == 0) {
            	printf("-2147483647
");
            	continue;
            }
            printf("%lld
", z[findkth(xx, z[xx].sze)].w);
            rot[i] = merge(xx, yy); 
        } else if(s == 6) {
            split(rot[i], a, xx, yy);
            if(yy == 0) {
            	printf("2147483647
");
            	continue;
            }
            printf("%lld
", z[findkth(yy, 1)].w);
            rot[i] = merge(xx, yy);
        }
    }
    return 0;
}

upd on 12.09:

此题有点坑，首先要开long long， 否则就会炸。在split中的参数k也要有long long型。

其次记得边界（好像这道题不卡），就是边界输出(-)2147483647。