Queue-jumpers - 平衡树

题面

Ponyo and Garfield are waiting outside the box-office for their favorite movie. Because queuing is so boring, that they want to play a game to kill the time. The game is called “Queue-jumpers”. Suppose that there are N people numbered from 1 to N stand in a line initially. Each time you should simulate one of the following operations: 

1.  Top x :Take person x to the front of the queue 

2.  Query x: calculate the current position of person x 

3.  Rank x: calculate the current person at position x 

Where x is in [1, N]. 

Ponyo is so clever that she plays the game very well while Garfield has no idea. Garfield is now turning to you for help.

Input

In the first line there is an integer T, indicates the number of test cases.(T<=50) 

In each case, the first line contains two integers N(1<=N<=10^8), Q(1<=Q<=10^5). Then there are Q lines, each line contain an operation as said above.

Output

For each test case, output “Case d:“ at first line where d is the case number counted from one, then for each “Query x” operation ,output the current position of person x at a line, for each “Rank x” operation, output the current person at position x at a line.

题解

这道题标签是平衡树，所以要用平衡树做。

这道题的N很大，但Q很小，但是又有数字又有序号导致我们不好用离散化。

回想一下线段树，当我们想用离散又不能用的时候，我们就会用动态开点。

这道题也是一个道理，我们一开始用一个大点存1~N，以后每个小点都存一个子区间，

再用另一棵树存出现过的数字，每次找前缀，再通过这个前缀找到包含它的子区间的第一棵树上的节点编号。

CODE

本人代码有点丑，请见谅。

(别复制了，我特地把一个地方改成错的了)

#include<cstdio>
#include<iostream>
#include<cstring>
#include<algorithm>
#define LL long long
#define MAXN 200000 + 5
using namespace std;
inline LL read() {
	LL f = 1,x = 0;char s = getchar();
	while(s < '0' || s > '9') {if(s == '-') f = -1;s = getchar();}
	while(s >= '0' && s <= '9') {x = x * 10 + s - '0';s = getchar();}
	return x * f;
}
LL n,m,i,j,s,o,k,cnt,root,root2;
struct tr{
	int s[2];
	LL key;
	int heap,siz,cntp,nml,nmr;
	tr(){key = 0;s[0] = s[1] = 0;heap = 0;siz = 0;cntp = 0;nml = 0;nmr = 0;}
}tre[MAXN];
int maketre(LL ky,int hp,int numl,int numr) {
	tre[++cnt] = tr();
	tre[cnt].key = ky;
	tre[cnt].heap = hp;
	tre[cnt].s[0] = tre[cnt].s[1] = 0;
	tre[cnt].siz = tre[cnt].cntp = numr - numl + 1;
	tre[cnt].nml = numl;
	tre[cnt].nmr = numr;
	return cnt;
}
void update(int x) {
	tre[x].siz = tre[tre[x].s[0]].siz + tre[tre[x].s[1]].siz + tre[x].cntp;
	return ;
}
int splay(int x,int d) {
	int ad = tre[x].s[d];
	tre[x].s[d] = tre[ad].s[d^1];
	tre[ad].s[d^1] = x;
	update(x);
	update(ad);
	return ad;
}
int ins(int x,LL tk,int numl,int numr) {
	if(x == 0) return maketre(tk,unsigned(rand()) + 1,numl,numr);
	if(tre[x].key == tk) {
		tre[x].cntp ++;
		update(x);
		return x;
	}
	int d = tk > tre[x].key;
	tre[x].s[d] = ins(tre[x].s[d],tk,numl,numr);
	if(tre[tre[x].s[d]].heap < tre[x].heap) return splay(x,d);
	update(x);
	return x;
}
int del(int x,LL ky) {
	if(x == 0) return 0;
	if(tre[x].key == ky) {
		if(tre[x].cntp > 1) {
			tre[x].cntp --;
			update(x);
			return x;
		}
		else {
			if(tre[x].s[0] && tre[x].s[1]) {
				int d = tre[tre[x].s[1]].heap < tre[tre[x].s[0]].heap;
				int rep = splay(x,d);
				tre[rep].s[d^1] = del(x,ky);
				update(rep);
				return rep;
			}
			if(tre[x].s[0]) return tre[x].s[0];
			return tre[x].s[1];
		}
	}
	else {
		int d = ky > tre[x].key;
		tre[x].s[d] = del(tre[x].s[d],ky);
		update(x);
		return x;
	}
}
int idp(int x,LL m) {
	if(x == 0) return 0;
	if(tre[tre[x].s[0]].siz < m && tre[tre[x].s[0]].siz + tre[x].cntp >= m) {
		return x;
	}
	if(tre[tre[x].s[0]].siz >= m) {
		return idp(tre[x].s[0],m);
	}
	return idp(tre[x].s[1],m - tre[tre[x].s[0]].siz - tre[x].cntp);
}
int pa(int x,LL m) {
	int ren;
	if(x == 0) ren = 1;
	else if(tre[x].key == m) {
		ren = tre[tre[x].s[0]].siz + 1;
	}
	else if(tre[x].key > m) {
		ren = pa(tre[x].s[0],m);
	}
	else ren = pa(tre[x].s[1],m) + tre[tre[x].s[0]].siz + tre[x].cntp;
	return ren;
}
int pre(int root,LL m) {
	int rep = pa(root,m);
	return idp(root,rep - 1);
}
int nex(int root,LL m) {
	int rep = pa(root,m);
	int repd = idp(root,rep);
	if(tre[repd].key == m) return idp(root,rep + tre[repd].cntp);
	return idp(root,rep);
}
int main() {
	int T = read(),cn = 0;
	while(T --) {
		printf("Case %d:\n",++cn);
		cnt = root = root2 = 0;
		n = read();m = read();
		root = ins(root,1,1,n);
		root2 = ins(root2,1,cnt,cnt);
		char ss[20];
		for(int i = 1;i <= m;i ++) {
			scanf("%s",ss + 1);s = read();
			if(ss[1] == 'T') {
				int d = pre(root2,s + 1);
				d = tre[d].nml;
				int l = tre[d].nml,r = tre[d].nmr,ky = tre[d].key;
				root = del(root,ky);
				root2 = del(root2,l);
				if(l < s) {
					root = ins(root,ky,l,s - 1);
					root2 = ins(root2,l,cnt,cnt);
				}
				if(r > s) {
					root = ins(root,ky + (s+1 - l),s + 1,r);
					root2 = ins(root2,s + 1,cnt,cnt);
				}
				d = idp(root,1);
				root = ins(root,tre[d].key - 1,s,s);
				root2 = ins(root2,s,cnt,cnt);
			}
			else if(ss[1] == 'Q') {
				int d = pre(root2,s + 1);
				d = tre[d].nml;
				int l = tre[d].nml,r = tre[d].nmr,ky = tre[d].key;
				printf("%d\n",pa(root,ky) + s - l);
			}
			else if(ss[1] == 'R') {
				int d = idp(root,s);
				int p = pa(root,tre[d].key);
				printf("%d\n",tre[d].nml + s - p);
			}
		}
	}
	return 0;
}