SPOJ 3273 - Order statistic set , Treap

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题意:

集合S支持一下四种操作:

  INSERT(S,x) :   假设S中没有x,则插入x

DELETE(S,x):  假设S中有x,则删除x

K-TH(S):            输出S中第K小的数

COUNT(S,x):    统计S中小于x的数有多少个

一共同拥有Q(1 ≤ Q ≤ 200000)次操作。

Treap模板。。

#include<cstdio>
#include<cstring>
#include<cstdlib>
const int inf=0x3f3f3f3f; struct Node {
Node *ch[2];
int r, v, s;
Node(int v):v(v) { ch[0] = ch[1] = NULL; r = rand(); s = 1; } int cmp(int x) const {
if (x == v) return -1;
return (x < v) ? 0 : 1;
} void maintain() {
s = 1;
if(ch[0] != NULL) s += ch[0]->s;
if(ch[1] != NULL) s += ch[1]->s;
}
}; void rotate(Node* &o, int d) {
Node* k = o->ch[d^1]; o->ch[d^1] = k->ch[d]; k->ch[d] = o;
o->maintain(); k->maintain(); o = k;
} void insert(Node* &o, int x) {
if(o == NULL) o = new Node(x);
else{
/*int d = (x < o->v ? 0 : 1); // 同意插入同样结点*/
int d =o->cmp(x); if(d==-1) return ; //不同意插入同样结点*/
insert(o->ch[d], x);
if(o->ch[d]->r > o->r) rotate(o, d^1);
else o->maintain();
}
} void remove(Node* &o, int x) {
int d = o->cmp(x);
if(d == -1) {
Node* u = o;
if(o->ch[0] != NULL && o->ch[1] != NULL) {
int d2 = (o->ch[0]->r > o->ch[1]->r) ? 1 : 0;
rotate(o, d2); remove(o->ch[d2], x);
}else{
if(o->ch[0] == NULL) o = o->ch[1]; else o = o->ch[0];
delete u;
}
}else remove(o->ch[d], x);
if(o != NULL) o->maintain();
} int find(Node* o, int x){
while(o != NULL){
int d = o->cmp(x);
if(d == -1) return 1;
o = o->ch[d];
}
return 0;
} int kth(Node* o,int k){///kth small
while(o != NULL){
int s = (o->ch[0] == NULL) ? 0 : o->ch[0]->s;
if(k==s+1) return o->v;
else if(k<=s) o=o->ch[0];
else{
o=o->ch[1]; k=k-s-1;
}
}
return -inf;
} int rank(Node* o, int x){
int ret = 0;
while(o != NULL){
int s = (o->ch[0] == NULL) ? 0 : o->ch[0]->s;
if(o->v < x){ <span style="color:#ff0000;">//因为是统计比x小的数的个数,所以不能取等号</span>
ret += s + 1;
o = o->ch[1];
}else{
o = o->ch[0];
}
}
return ret;
} int main()
{
int q;
Node* root=NULL;
//freopen("in.txt","r",stdin);
scanf("%d",&q);
while(q--)
{
char cmd[3];int nb;
scanf("%s%d",cmd,&nb);
if(cmd[0]=='I'&&find(root,nb)==0)
{
insert(root,nb);
}
else if(cmd[0]=='D'&&find(root,nb)==1)
{
remove(root,nb);
}
else if(cmd[0]=='K')
{
int temp=kth(root,nb);
if(temp == -inf) puts("invalid");
else printf("%d\n",temp);
}
else if(cmd[0]=='C')
{
printf("%d\n",rank(root,nb));
}
}
return 0;
}
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