模板 - 可持久化无旋Treap
Posted yinku
tags:
篇首语：本文由小常识网(cha138.com)小编为大家整理，主要介绍了模板 - 可持久化无旋Treap相关的知识，希望对你有一定的参考价值。
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;
以上是关于模板 - 可持久化无旋Treap的主要内容，如果未能解决你的问题，请参考以下文章
[您有新的未分配科技点]无旋treap：从好奇到入门（例题：bzoj3224 普通平衡树）
luoguP5055 模板可持久化文艺平衡树 可持久化非旋转treap