P3369-[模板]普通平衡树【Splay】

版权声明：原创，未经作者允许禁止转载 https://blog.csdn.net/Mr_wuyongcong/article/details/85846307

正题

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题目大意

要求支持查询一个数字的排名，查询该排名的数字，插入数字，删除数字，求前驱后继。

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解题思路

Splay不解释。

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$code$

#include<cstdio>
#include<algorithm>
#define INF 2100000000
#define N 100010
using namespace std;
struct splay{
	int v[N],father[N];
	int l[N],r[N];
	int sum[N],recy[N];
	int n,points;
	#define root r[0]
	void Updata(int x){
		sum[x]=sum[l[x]]+sum[r[x]]+recy[x];
	}
	int Identify(int x){
		return l[father[x]]==x?0:1;
	}
	void Connect(int x,int f,int son){
		father[x]=f;
		if(son) r[f]=x;
		else l[f]=x;
	}
	void Rotate(int x){
		int y=father[x];
		int mroot=father[y];
		int mrootson=Identify(y);
		int yson=Identify(x);
		int B=(yson?l[x]:r[x]);
		Connect(B,y,yson);Connect(y,x,(yson^1));
		Connect(x,mroot,mrootson);
		Updata(y);Updata(x);
	}
	void Splay(int at,int to){
		to=father[to];
		while(father[at]!=to){
			int up=father[at];
			if(father[up]==to) Rotate(at);
			else if(Identify(up)==Identify(at)){
				Rotate(up);
				Rotate(at);
			}
			else{
				Rotate(at);
				Rotate(at);
			}
		}
	}
	int CrePoint(int vs,int fathers){
		n++;
		v[n]=vs;
		father[n]=fathers;
		sum[n]=recy[n]=1;
		return n;
	}
	void Destory(int x){
		v[x]=l[x]=r[x]=sum[x]=father[x]=recy[x]=0;
		if(x==n)n--;
	}
	int getroot(){return root;}
	int FindVal(int vs){
		int now=root;
		if(!now) return 0;
		while(true){
			if(v[now]==vs){
				Splay(now,root);
				return root;
			}
			int next=vs<v[now]?0:1;
			if(!(next?r[now]:l[now])) return 0;
			now=(next?r[now]:l[now]);
		}
	}
	int Build(int vs){
		points++;
		if(!n){
			root=1;
			CrePoint(vs,0);
		}
		else{
			int now=root;
			while(1){
				sum[now]++;
				if(vs==v[now]){
					recy[now]++;
					return now;
				}
				int next=vs<v[now]?0:1;
				if(!(next?r[now]:l[now])){
					CrePoint(vs,now);
					if(next) r[now]=n;
					else l[now]=n;
					return n;
				}
				now=next?r[now]:l[now];
			}
		}
		return 0;
	}
	void Insert(int vs){
		int add=Build(vs);
		Splay(add,root);
	}
	void Remove(int vs){
		int deal=FindVal(vs);
		if(!deal) return;
		points--;
		if(recy[deal]>1){
			recy[deal]--;
			sum[deal]--;
			return;
		}
		if(!l[deal]){
			root=r[deal];
			father[root]=0;
		}
		else{
			int lef=l[deal];
			while(r[lef]) lef=r[lef];
			Splay(lef,l[deal]);
			int rig=r[deal];
			Connect(rig,lef,1);Connect(lef,0,1);
			Updata(lef);
		}
		Destory(deal);
	}
	int GetRankByVal(int vs){
		int now=root;
		if(!now) return 0;
		while((vs>v[now]?r[now]:l[now])&&vs!=v[now])
		    now=(vs>v[now]?r[now]:l[now]);
		Splay(now,root);
		return sum[l[root]];
	}
	int GetValByRank(int x){
		if(x>points) return -INF;
		int now=root;
		while(1){
			int minused=sum[now]-sum[r[now]];
			if(x>sum[l[now]]&&x<=minused) break;
			if(x<minused)now=l[now];
			else{
			  x-=minused;
			  now=r[now];
			}
		}
		Splay(now,root);
		return v[now];
	}
	int Upper(int vs){
		int now=root;
		int result=INF;
		while(now){
			if(v[now]>vs&&v[now]<result) result=v[now];
			if(vs<v[now]) now=l[now];
			else now=r[now];
		}
		return result;
	}
	int Lower(int vs){
		int now=root;
		int result=-INF;
		while(now){
			if(v[now]<vs&&v[now]>result) result=v[now];
			if(vs>v[now]) now=r[now];
			else now=l[now];
		}
		return result;
	}
	#undef root
}a;
int main(){
	freopen("testdata.in","r",stdin);
	freopen("data.out","w",stdout);
	a.Insert(-INF);
    a.Insert(INF);
	int m;
	scanf("%d",&m);
	while(m--){
		int opt,x;
		scanf("%d%d",&opt,&x);
		if(opt==1) a.Insert(x);
		if(opt==2) a.Remove(x);
		if(opt==3) printf("%d\n",a.GetRankByVal(x));
		if(opt==4) printf("%d\n",a.GetValByRank(x+1));
		if(opt==5) printf("%d\n",a.Lower(x));
		if(opt==6) printf("%d\n",a.Upper(x));
	}
}