模板 - 可持久化无旋Treap

空间消耗非常玄学，有多大开多大就完事了。其实是因为单次操作可能会有数次Merge和Split操作，按照下面的版本的话Merge和Split都进行复制，所以一次操作可能复制了4个版本。

四个函数式查询，然后Merge的时候拷贝对应的xy子树，Split的时候拷贝p树。事实上，Merge和Split总是成对出现，只需要在其中喜欢的一个进行可持久化（复制节点）就可以了，比较推荐在Split的时候复制节点。这样单次操作大概复制2个版本。

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define ls(p) ch[p][0]
#define rs(p) ch[p][1]

const int MAXN = 30000000 + 5;
int val[MAXN], ch[MAXN][2], rnd[MAXN], siz[MAXN], tot, root[MAXN];

void Init() {
    tot = 0;
    memset(root,0,sizeof(root));
}

int NewNode(int v) {
    ++tot;
    ch[tot][0] = ch[tot][1] = 0;
    val[tot] = v, rnd[tot] = rand();
    siz[tot] = 1;
    return tot;
}

int CopyNode(int p) {
    ++tot;
    ch[tot][0] = ch[p][0];
    ch[tot][1] = ch[p][1];
    val[tot] = val[p];
    rnd[tot] = rnd[p];
    siz[tot] = siz[p];
    return tot;
}

void PushUp(int p) {
    siz[p] = siz[ls(p)] + siz[rs(p)] + 1;
}

void SplitValue(int p, int v, int &x, int &y) {
    if(!p) {
        x = y = 0;
        return;
    }
    if(v < val[p]) {
        y = CopyNode(p);
        SplitValue(ls(y), v, x, ls(y));
        PushUp(y);
    } else {
        x = CopyNode(p);
        SplitValue(rs(x), v, rs(x), y);
        PushUp(x);
    }
}

/*void SplitRank(int p, int rk, int &x, int &y) {
    if(!p) {
        x = y = 0;
        return;
    }
    if(rk <= siz[ls(p)]) {
        y = p;
        SplitRank(ls(p), rk, x, ls(p));
        PushUp(y);
    } else {
        x = p;
        SplitRank(rs(p), rk - siz[ls(p)] - 1, rs(p), y);
        PushUp(x);
    }
}*/

int Merge(int x, int y) {
    if(!x || !y)
        return x | y;
    if(rnd[x] < rnd[y]) {
        int p = CopyNode(x);
        rs(p) = Merge(rs(p), y);
        PushUp(p);
        return p;
    } else {
        int p = CopyNode(y);
        ls(p) = Merge(x, ls(p));
        PushUp(p);
        return p;
    }
}

void Insert(int &root, int v) {
    int x = 0, y = 0;
    SplitValue(root, v, x, y);
    root = Merge(Merge(x, NewNode(v)), y);
}

void Remove(int &root, int v) {
    int x = 0, y = 0, z = 0;
    SplitValue(root, v, x, z);
    SplitValue(x, v - 1, x, y);
    y = Merge(ls(y), rs(y));
    root = Merge(Merge(x, y), z);
}

int GetRank2(int p, int v) {
    int rk = 1;
    while(p) {
        if(v < val[p])
            p = ls(p);
        else if(v == val[p])
            p = ls(p);
        else {
            rk += siz[ls(p)] + 1;
            p = rs(p);
        }
    }
    return rk;
}

int GetValue2(int p, int rk) {
    while(p) {
        if(rk <= siz[ls(p)])
            p = ls(p);
        else if(rk == siz[ls(p)] + 1)
            return val[p];
        else {
            rk -= siz[ls(p)] + 1;
            p = rs(p);
        }
    }
}

int GetPrev2(int p, int v) {
    int prev;
    while(p) {
        if(v <= val[p])
            p = ls(p);
        else {
            prev = val[p];
            p = rs(p);
        }
    }
    return prev;
}

int GetNext2(int p, int v) {
    int next;
    while(p) {
        if(v < val[p]) {
            next = val[p];
            p = ls(p);
        } else
            p = rs(p);
    }
    return next;
}

int main() {
#ifdef Yinku
    freopen("Yinku.in", "r", stdin);
#endif // Yinku
    int n;
    scanf("%d", &n);
    Init();
    for(int i = 1; i <= n; ++i) {
        int v,op, x;
        scanf("%d%d%d",&v, &op, &x);
        root[i]=root[v];
        switch(op) {
            case 1:
                Insert(root[i], x);
                break;
            case 2:
                Remove(root[i], x);
                break;
            case 3:
                printf("%d\n", GetRank2(root[i], x));
                break;
            case 4:
                printf("%d\n", GetValue2(root[i], x));
                break;
            case 5:
                printf("%d\n", GetPrev2(root[i], x));
                break;
            case 6:
                printf("%d\n", GetNext2(root[i], x));
                break;
        }
    }
    return 0;
}

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define ls(p) ch[p][0]
#define rs(p) ch[p][1]

const int MAXN = 20000000 + 5;
int val[MAXN], ch[MAXN][2], rnd[MAXN], siz[MAXN], tot, root[MAXN];

void Init() {
    tot = 0;
    memset(root,0,sizeof(root));
}

int NewNode(int v) {
    ++tot;
    ch[tot][0] = ch[tot][1] = 0;
    val[tot] = v, rnd[tot] = rand();
    siz[tot] = 1;
    return tot;
}

int CopyNode(int p) {
    ++tot;
    ch[tot][0] = ch[p][0];
    ch[tot][1] = ch[p][1];
    val[tot] = val[p];
    rnd[tot] = rnd[p];
    siz[tot] = siz[p];
    return tot;
}

void PushUp(int p) {
    siz[p] = siz[ls(p)] + siz[rs(p)] + 1;
}

void SplitValue(int p, int v, int &x, int &y) {
    if(!p) {
        x = y = 0;
        return;
    }
    if(v < val[p]) {
        y = CopyNode(p);
        SplitValue(ls(y), v, x, ls(y));
        PushUp(y);
    } else {
        x = CopyNode(p);
        SplitValue(rs(x), v, rs(x), y);
        PushUp(x);
    }
}

/*void SplitRank(int p, int rk, int &x, int &y) {
    if(!p) {
        x = y = 0;
        return;
    }
    if(rk <= siz[ls(p)]) {
        y = p;
        SplitRank(ls(p), rk, x, ls(p));
        PushUp(y);
    } else {
        x = p;
        SplitRank(rs(p), rk - siz[ls(p)] - 1, rs(p), y);
        PushUp(x);
    }
}*/

int Merge(int x, int y) {
    if(!x || !y)
        return x | y;
    if(rnd[x] < rnd[y]) {
        //int p = CopyNode(x);
        int p=x;
        rs(p) = Merge(rs(p), y);
        PushUp(p);
        return p;
    } else {
        int p=y;
        //int p = CopyNode(y);
        ls(p) = Merge(x, ls(p));
        PushUp(p);
        return p;
    }
}

void Insert(int &root, int v) {
    int x = 0, y = 0;
    SplitValue(root, v, x, y);
    root = Merge(Merge(x, NewNode(v)), y);
}

void Remove(int &root, int v) {
    int x = 0, y = 0, z = 0;
    SplitValue(root, v, x, z);
    SplitValue(x, v - 1, x, y);
    y = Merge(ls(y), rs(y));
    root = Merge(Merge(x, y), z);
}

int GetRank2(int p, int v) {
    int rk = 1;
    while(p) {
        if(v < val[p])
            p = ls(p);
        else if(v == val[p])
            p = ls(p);
        else {
            rk += siz[ls(p)] + 1;
            p = rs(p);
        }
    }
    return rk;
}

int GetValue2(int p, int rk) {
    while(p) {
        if(rk <= siz[ls(p)])
            p = ls(p);
        else if(rk == siz[ls(p)] + 1)
            return val[p];
        else {
            rk -= siz[ls(p)] + 1;
            p = rs(p);
        }
    }
}

int GetPrev2(int p, int v) {
    int prev;
    while(p) {
        if(v <= val[p])
            p = ls(p);
        else {
            prev = val[p];
            p = rs(p);
        }
    }
    return prev;
}

int GetNext2(int p, int v) {
    int next;
    while(p) {
        if(v < val[p]) {
            next = val[p];
            p = ls(p);
        } else
            p = rs(p);
    }
    return next;
}

int main() {
#ifdef Yinku
    freopen("Yinku.in", "r", stdin);
#endif // Yinku
    int n;
    scanf("%d", &n);
    Init();
    for(int i = 1; i <= n; ++i) {
        int v,op, x;
        scanf("%d%d%d",&v, &op, &x);
        root[i]=root[v];
        switch(op) {
            case 1:
                Insert(root[i], x);
                break;
            case 2:
                Remove(root[i], x);
                break;
            case 3:
                printf("%d\n", GetRank2(root[i], x));
                break;
            case 4:
                printf("%d\n", GetValue2(root[i], x));
                break;
            case 5:
                printf("%d\n", GetPrev2(root[i], x));
                break;
            case 6:
                printf("%d\n", GetNext2(root[i], x));
                break;
        }
    }
    return 0;
}