我的第一棵平衡树-SB树

数组实现的SB树(而且竟然没有结构体)

功能就和普通的二茬查找树一样:

insert: 插入元素

erase: 删除元素

pre: 查询一个元素的前驱

suc: 查询一个元素的后继

select: 返回第几小的元素的值

rank: 返回一个值的位置

除了maintain全部非递归实现,并且有assert(似乎并没有什么用)

maintain写得不是很高效,

并且缺储存平衡树中元素个数的变量(size表示总共插入过的元素个数),然而这并不怎么难搞

root: 树的根(并不一定是1)

这其实是洛谷的模板题

#include<stdio.h>
#include<assert.h>
#define N 100005
int root,val[N],lch[N],rch[N],w[N],size;
void rrot(int &t) {
	int x=lch[t]; lch[t]=rch[x]; rch[x]=t;
	w[x]=w[t]; w[t]=w[lch[t]]+w[rch[t]]+1;
	t=x;
}
void lrot(int &t) {
	int x=rch[t]; rch[t]=lch[x]; lch[x]=t;
	w[x]=w[t]; w[t]=w[lch[t]]+w[rch[t]]+1;
	t=x;
}
void mant(int &t) {
	int fl=0,fr=0;
	if(w[lch[lch[t]]]>w[rch[t]]) fr=1, rrot(t);
	else if(w[rch[lch[t]]]>w[rch[t]]) fl=fr=1, lrot(lch[t]), rrot(t);
	else if(w[rch[rch[t]]]>w[lch[t]]) fl=1, lrot(t);
	else if(w[lch[rch[t]]]>w[lch[t]]) fl=fr=1, rrot(rch[t]), lrot(t);
	if(fl) mant(lch[t]); if(fr) mant(rch[t]); if(fl||fr) mant(t);
}
int select(int k) {
	int t=root;
	while(k!=w[lch[t]]+1) {
		assert(t);
		if(k<=w[lch[t]]) t=lch[t];
		else k-=w[lch[t]]+1, t=rch[t];
	}
	return val[t];
}
int rank(int v) {
	int t=root,ret=0,flag=0;
	while(t) {
		if(v==val[t]) return ret+w[lch[t]]+1;
		else {
			if(v<val[t]) t=lch[t];
			else ret+=w[lch[t]]+1, t=rch[t];
		}
	}
	assert(0);
}
int pre(int v) {
	int t=root,ret=0;
	while(1) {
		if(v<=val[t]) {
			if(lch[t]) t=lch[t];
			else break;
		}
		else {
			ret=t;
			if(rch[t]) t=rch[t];
			else break;
		}
	}
	assert(ret);
	return val[ret];
}
int suc(int v) {
	int t=root, ret=0;
	while(1) {
		if(v>=val[t]) {
			if(rch[t]) t=rch[t];
			else break;
		}
		else {
			ret=t;
			if(lch[t]) t=lch[t];
			else break;
		}
	}
	assert(ret);
	return val[ret];
}
void insert(int v) {
	if(!root) {root=++size; val[size]=v; w[size]=1; return; }
	int t=root,*x;
	while(w[t]++) {
		if(v<val[t]) {
			if(lch[t]) t=lch[t];
			else {x=&lch[t]; break; }
		}
		else {
			if(rch[t]) t=rch[t];
			else {x=&rch[t]; break; }
		}
	}
	*x=++size; val[size]=v; w[size]=1;
	mant(root);
}
void erase(int v) {
	int *x=&root;
	while(w[*x]--) {
		if(v<val[*x]) {x=&lch[*x]; continue; }
		if(v>val[*x]) {x=&rch[*x]; continue; }
		break;
	}
	if(!lch[*x]) {*x=rch[*x]; return; }
	if(!rch[*x]) {*x=lch[*x]; return; }
	int *y=&rch[*x];
	while(w[*y]--,lch[*y]) y=&lch[*y];
	val[*x]=val[*y]; *y=rch[*y];
}
int main() {
	int n,x,y;
	scanf("%d",&n);
	while(n--) {
		scanf("%d%d",&x,&y);
		switch(x) {
			case 1: insert(y); break;
			case 2: erase(y); break;
			case 3: printf("%d\n",rank(y)); break;
			case 4: printf("%d\n",select(y)); break;
			case 5: printf("%d\n",pre(y)); break;
			case 6: printf("%d\n",suc(y)); break;
		}
	}
}

简化代码后的SBT

没有assert了,不过明显短了很多

#include<stdio.h>
#define N 100005
int root,val[N],lch[N],rch[N],w[N],size,cnt;
void rrot(int &t) {
    int x=lch[t]; lch[t]=rch[x]; rch[x]=t;
    w[x]=w[t]; w[t]=w[lch[t]]+w[rch[t]]+1;
    t=x;
}
void lrot(int &t) {
    int x=rch[t]; rch[t]=lch[x]; lch[x]=t;
    w[x]=w[t]; w[t]=w[lch[t]]+w[rch[t]]+1;
    t=x;
}
void mant(int &t) {
    int fl=0,fr=0;
    if(w[lch[lch[t]]]>w[rch[t]]) fr=1, rrot(t);
    else if(w[rch[lch[t]]]>w[rch[t]]) fl=fr=1, lrot(lch[t]), rrot(t);
    else if(w[rch[rch[t]]]>w[lch[t]]) fl=1, lrot(t);
    else if(w[lch[rch[t]]]>w[lch[t]]) fl=fr=1, rrot(rch[t]), lrot(t);
    if(fl) mant(lch[t]); if(fr) mant(rch[t]); if(fl||fr) mant(t);
}
void insert(int v) {
    size++; int *x=&root;
    while(w[*x]++) {
        if(v<val[*x]) x=&lch[*x];
        else x=&rch[*x];
    }
    *x=++cnt; val[cnt]=v; w[cnt]=1;
    w[0]=0; mant(root);
}
void erase(int v) {
	size--; int *x=&root;
    while(w[*x]--) {
        if(v<val[*x]) {x=&lch[*x]; continue; }
        if(v>val[*x]) {x=&rch[*x]; continue; }
        break;
    }
    if(!lch[*x]) {*x=rch[*x]; return; }
    if(!rch[*x]) {*x=lch[*x]; return; }
    int *y=&rch[*x];
    while(w[*y]--,lch[*y]) y=&lch[*y];
    val[*x]=val[*y]; *y=rch[*y];
}
int select(int k) {
    int t=root;
    while(k!=w[lch[t]]+1) {
        if(k<=w[lch[t]]) t=lch[t];
        else k-=w[lch[t]]+1, t=rch[t];
    }
    return val[t];
}
int rank(int v) {
	int t=root,ret=0;
	while(t) {
		if(v<=val[t]) t=lch[t];
		else ret+=w[lch[t]]+1, t=rch[t];
	}
	return ret+1;
}
int pre(int v) {
    int t=root,ret=0;
    while(t) {
        if(v<=val[t]) t=lch[t];
        else ret=t, t=rch[t];
    }
    return val[ret];
}
int suc(int v) {
    int t=root,ret=0;
    while(t) {
        if(v>=val[t]) t=rch[t];
        else ret=t, t=lch[t];
    }
    return val[ret];
}
int main() {
    int n,x,y;
    scanf("%d",&n);
    while(n--) {
        scanf("%d%d",&x,&y);
        switch(x) {
            case 1: insert(y); break;
            case 2: erase(y); break;
            case 3: printf("%d\n",rank(y)); break;
            case 4: printf("%d\n",select(y)); break;
            case 5: printf("%d\n",pre(y)); break;
            case 6: printf("%d\n",suc(y)); break;
        }
    }
}

然而 展开之后...

200行

#include<stdio.h>
#define N 100005
int root,val[N],lch[N],rch[N],w[N],size,cnt;
void rrot(int &t)
{
	int x=lch[t];
	lch[t]=rch[x];
	rch[x]=t;
	w[x]=w[t];
	w[t]=w[lch[t]]+w[rch[t]]+1;
	t=x;
}
void lrot(int &t)
{
	int x=rch[t];
	rch[t]=lch[x];
	lch[x]=t;
	w[x]=w[t];
	w[t]=w[lch[t]]+w[rch[t]]+1;
	t=x;
}
void mant(int &t)
{
	int fl=0,fr=0;
	if(w[lch[lch[t]]]>w[rch[t]])
	{
		fr=1;
		rrot(t);
	}
	else if(w[rch[lch[t]]]>w[rch[t]])
	{
		fl=fr=1;
		lrot(lch[t]);
		rrot(t);
	}
	else if(w[rch[rch[t]]]>w[lch[t]])
	{
		fl=1;
		lrot(t);
	}
	else if(w[lch[rch[t]]]>w[lch[t]])
	{
		fl=fr=1;
		rrot(rch[t]);
		lrot(t);
	}
	if(fl)
	{
		mant(lch[t]);
	}
	if(fr)
	{
		mant(rch[t]);
	}
	if(fl||fr)
	{
		mant(t);
	}
}
void insert(int v)
{
	size++;
	int *x=&root;
	while(w[*x]++)
	{
		if(v<val[*x])
		{
			x=&lch[*x];
		}
		else
		{
			x=&rch[*x];
		}
	}
	*x=++cnt;
	val[cnt]=v;
	w[cnt]=1;
	w[0]=0;
	mant(root);
}
void erase(int v)
{
	size--;
	int *x=&root;
	while(w[*x]--)
	{
		if(v<val[*x])
		{
			x=&lch[*x];
			continue;
		}
		if(v>val[*x])
		{
			x=&rch[*x];
			continue;
		}
		break;
	}
	if(!lch[*x])
	{
		*x=rch[*x];
		return;
	}
	if(!rch[*x])
	{
		*x=lch[*x];
		return;
	}
	int *y=&rch[*x];
	while(w[*y]--,lch[*y])
	{
		y=&lch[*y];
	}
	val[*x]=val[*y];
	*y=rch[*y];
}
int select(int k)
{
	int t=root;
	while(k!=w[lch[t]]+1)
	{
		if(k<=w[lch[t]])
		{
			t=lch[t];
		}
		else
		{
			k-=w[lch[t]]+1;
			t=rch[t];
		}
	}
	return val[t];
}
int rank(int v)
{
	int t=root,ret=0;
	while(t)
	{
		if(v<=val[t])
		{
			t=lch[t];
		}
		else
		{
			ret+=w[lch[t]]+1;
			t=rch[t];
		}
	}
	return ret+1;
}
int pre(int v)
{
	int t=root,ret=0;
	while(t)
	{
		if(v<=val[t])
		{
			t=lch[t];
		}
		else
		{
			ret=t;
			t=rch[t];
		}
	}
	return val[ret];
}
int suc(int v)
{
	int t=root,ret=0;
	while(t)
	{
		if(v>=val[t])
		{
			t=rch[t];
		}
		else
		{
			ret=t;
			t=lch[t];
		}
	}
	return val[ret];
}
int main()
{
	int n,x,y;
	scanf("%d",&n);
	while(n--)
	{
		scanf("%d%d",&x,&y);
		switch(x)
		{
			case 1:
				insert(y);
				break;
			case 2:
				erase(y);
				break;
			case 3:
				printf("%d\n",rank(y));
				break;
			case 4:
				printf("%d\n",select(y));
				break;
			case 5:
				printf("%d\n",pre(y));
				break;
			case 6:
				printf("%d\n",suc(y));
				break;
		}
	}
}