[Dr.Lib]Note:Data Structures – Bottom-up SPLAY

Let us play！

Let u splay！

BST 平均 O(logn)

Treap 期望 O(logn)

Splay 均摊 O(logn)

AVL 严格 O(logn)

SBT 严格 O(logn)

AVL不大指望能在赛场写出来，SBT在绝大多数时候是个不错的选择，Treap…嗯……但偏偏Splay被人看成是BST中的万金油……为什么呐？

Splay一个最大的特点就是：每一个操作都要splay一下……除此之外没了……

Splay

splay操作的作用就是把某一节点旋转到根，以加快之后的访问速度。它还可以在旋转过程中维持树的基本平衡。

zig: 当目标节点是根节点的左子节点或右子节点时，进行一次zig，将目标节点调整到根节点的位置。
zig-zig:当目标节点是根节点的左（右）子节点的左（右）子节点时，进行一次zig-zig，将目标节点调整到根节点位置。
zig-zag:当目标节点是根节点的左（右）子节点的右（左）子节点时，进行一次zig-zag，将目标节点调整到根节点位置。

重复这几种操作直到目标节点为根。

一次zig、zig-zig、zig-zag又可以分解为几次单旋。

Search/Insert/Rank/Select

与BST相同，只不过记得把插入的节点Splay到根。

Join

作用是把两棵子树S1,S2连成一个Splay，其中S1中所有元素小于S2。

先找到S1中的最大节点x，Splay到S1的根，再把x的右子树链接到S2。

Delete

先找到目标节点，Splay到根，执行Join操作即可。

代码

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<vector>
#include<cmath>
#include<queue>

#define C(x) ((int)(T[T[(x)].f].s[1]==(x)))
#define S(x) T[(x)].s
#define L(x) T[(x)].s[0]
#define Ln(x) T[T[(x)].s[0]]
#define R(x) T[(x)].s[1]
#define Rn(x) T[T[(x)].s[1]]
#define F(x) T[(x)].f
#define W(x) T[(x)].w
#define Z(x) T[(x)].size
using namespace std;
typedef long long LL;
const int MAXN=300;
const int INF=2147483647;
const int NINF=-1<<30;
const int ERR=-1;

struct Node{
	int size,w,f;int s[2];//0-L,1-R;
	Node():size(0),w(0),f(0){s[0]=s[1]=0;}
};

Node T[MAXN*3];
int root,sz;
void link(int s,int f,int t){F(s)=f;S(f)[t]=s;}
void Up(int x);void Down(int x);void Join(int f,int s);
int Max(int x);int Min(int x);
void Rot(int x,int c){
	int f=F(x);
	link(x,F(f),C(f));
	link(S(x)[1^c],f,c);
	link(f,x,1^c);
	Up(f);
}
void Splay(int x,int g){
	for(Down(x);F(x)!=g;){
		int f=F(x);
		if(F(f)==g)			Rot(x,C(x));else{
			if(C(x)==C(f))	Rot(f,C(f));  
              else 			Rot(x,C(x));  
							Rot(x,C(x));  
		}
	}
	Up(x);
	if(!g)root=x;
}
void Up(int x){Z(x)=Z(L(x))+Z(R(x))+1;}
void Down(int x){/*Do YOLO*/}
void Insert(int &s,int f,int v) {
	if(s==0) {
		s=++sz;W(s)=v;Z(s)=1;F(s)=f;int x=s;Splay(x,0);
		return;
	}
	Z(s)++;
	if(W(s)>v) 	Insert(L(s),s,v);
	else		Insert(R(s),s,v);	
}
int Search(int s,int v) {
	if(s==0)return ERR;
	if(W(s)==v)return	Splay(s,0),s;
	if(W(s)>v)return 	Search(L(s),v);
	return				Search(R(s),v);
}
void Join(int l,int r){
	int lm=l;if (!l){root=r;F(r)=0; return; }
	while(R(lm))lm=R(lm);
	Splay(lm,F(l));
	R(lm)=r;
	F(r)=lm;
	F(lm)=0;
	Up(lm);
	root=lm;
}
int Delete(int s,int v){
	int x=Search(s,v);
	if(x==ERR)return ERR;
	//Splay(x,0);
	Join(L(x),R(x));
	return 0;
}
int Select(int s,int k) {
	int Lt=Z(L(s));
	if(k==Lt)return Splay(s,0),W(s);
	if(Lt>k)return	Select(L(s),k);
	return			Select(R(s),k-Lt-1);
}
int Rank(int s,int v) {
	int Lt=Z(L(s));
	if(W(s)==v)return	Splay(s,0),Lt;
	if(W(s)>v) return	Rank(L(s),v);
	return				Rank(R(s),v)+Lt+1;
}

inline bool getint(int &x){
int y,flag;
while(isspace(y=getchar()));
if(y==-1) return false;
if(y=='-') flag=-1,x=0;
else flag=1,x=y-'0';
while(isdigit(y=getchar())) x=x*10+(y-'0');
x*=flag;
return true;
}
int main(){
	int c;
	int x;
	//freopen("SBT.in6","r",stdin);
	//freopen("SBT.outsplay6","w",stdout);
	while(getint(c)) {
		switch(c) {
		case 0:
			getint(x);
			Insert(root,0,x);
			break;
		case 1:
			getint(x);
			Delete(root,x);
			break;
		case 2:
			getint(x);
			printf("%d\n",Search(root,x));
			break;
		case 3:
			getint(x);
			printf("%d\n",Select(root,x));  //x<S(root)
			break;
		case 4:
			getint(x);
			printf("%d\n",Rank(root,x));    //Search(x)>0
			break;
		default:
			printf("\n\n\n");
		}
	}

	return 0;
}

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#include<iostream>

#include<cstdio>

#include<algorithm>

#include<vector>

#include<cmath>

#include<queue>

#define C(x) ((int)(T[T[(x)].f].s[1]==(x)))

#define S(x) T[(x)].s

#define L(x) T[(x)].s[0]

#define Ln(x) T[T[(x)].s[0]]

#define R(x) T[(x)].s[1]

#define Rn(x) T[T[(x)].s[1]]

#define F(x) T[(x)].f

#define W(x) T[(x)].w

#define Z(x) T[(x)].size

using namespace std;

typedef long long LL;

const int MAXN=300;

const int INF=2147483647;

const int NINF=-1<<30;

const int ERR=-1;

struct Node{

int size,w,f;int s[2];//0-L,1-R;

Node():size(0),w(0),f(0){s[0]=s[1]=0;}

};

Node T[MAXN*3];

int root,sz;

void link(int s,int f,int t){F(s)=f;S(f)[t]=s;}

void Up(int x);void Down(int x);void Join(int f,int s);

int Max(int x);int Min(int x);

void Rot(int x,int c){

int f=F(x);

link(x,F(f),C(f));

link(S(x)[1^c],f,c);

link(f,x,1^c);

Up(f);

}

void Splay(int x,int g){

for(Down(x);F(x)!=g;){

int f=F(x);

if(F(f)==g) Rot(x,C(x));else{

if(C(x)==C(f)) Rot(f,C(f));

else Rot(x,C(x));

Rot(x,C(x));

}

Up(x);

if(!g)root=x;

}

void Up(int x){Z(x)=Z(L(x))+Z(R(x))+1;}

void Down(int x){/*Do YOLO*/}

void Insert(int &s,int f,int v) {

if(s==0) {

s=++sz;W(s)=v;Z(s)=1;F(s)=f;int x=s;Splay(x,0);

return;

}

Z(s)++;

if(W(s)>v) Insert(L(s),s,v);

else Insert(R(s),s,v);

}

int Search(int s,int v) {

if(s==0)return ERR;

if(W(s)==v)return Splay(s,0),s;

if(W(s)>v)return Search(L(s),v);

return Search(R(s),v);

}

void Join(int l,int r){

int lm=l;if (!l){root=r;F(r)=0; return; }

while(R(lm))lm=R(lm);

Splay(lm,F(l));

R(lm)=r;

F(r)=lm;

F(lm)=0;

Up(lm);

root=lm;

}

int Delete(int s,int v){

int x=Search(s,v);

if(x==ERR)return ERR;

//Splay(x,0);

Join(L(x),R(x));

return 0;

}

int Select(int s,int k) {

int Lt=Z(L(s));

if(k==Lt)return Splay(s,0),W(s);

if(Lt>k)return Select(L(s),k);

return Select(R(s),k-Lt-1);

}

int Rank(int s,int v) {

int Lt=Z(L(s));

if(W(s)==v)return Splay(s,0),Lt;

if(W(s)>v) return Rank(L(s),v);

return Rank(R(s),v)+Lt+1;

}

inline bool getint(int &x){

int y,flag;

while(isspace(y=getchar()));

if(y==-1) return false;

if(y=='-') flag=-1,x=0;

else flag=1,x=y-'0';

while(isdigit(y=getchar())) x=x*10+(y-'0');

x*=flag;

return true;

}

int main(){

int c;

int x;

//freopen("SBT.in6","r",stdin);

//freopen("SBT.outsplay6","w",stdout);

while(getint(c)) {

switch(c) {

case 0:

getint(x);

Insert(root,0,x);

break;

case 1:

getint(x);

Delete(root,x);

break;

case 2:

getint(x);

printf("%d\n",Search(root,x));

break;

case 3:

getint(x);

printf("%d\n",Select(root,x)); //x<S(root)

break;

case 4:

getint(x);

printf("%d\n",Rank(root,x)); //Search(x)>0

break;

default:

printf("\n\n\n");

}

return 0;

}

[Dr.Lib]Note:Data Structures – Bottom-up SPLAY by Liqueur Librazy is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

[Dr.Lib]Note:Data Structures – Bottom-up SPLAY

Splay

Search/Insert/Rank/Select

Join

Delete

代码

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朋友们

TAG CLOUD

Splay

Search/Insert/Rank/Select

Join

Delete

代码

发表评论 取消回复

朋友们

TAG CLOUD

发表评论取消回复