Size Balance Tree（SBT模板整理）

/*
* tree[x].left   表示以 x 为节点的左儿子
* tree[x].right  表示以 x 为节点的右儿子
* tree[x].size   表示以 x 为根的节点的个数（大小）
*/

struct SBT
{
int key,left,right,size;
} tree[10010];
int root = 0,top = 0;

void left_rot(int &x)         // 左旋
{
int y = tree[x].right;
if (!y)	return;
tree[x].right = tree[y].left;
tree[y].left = x;
tree[y].size = tree[x].size;
tree[x].size = tree[tree[x].left].size + tree[tree[x].right].size + 1;
x = y;
}

void right_rot(int &x)        //右旋
{
int y = tree[x].left;
if (!y)	return;
tree[x].left = tree[y].right;
tree[y].right = x;
tree[y].size = tree[x].size;
tree[x].size = tree[tree[x].left].size + tree[tree[x].right].size + 1;
x = y;
}

void maintain(int &x,bool flag)  //维护SBT状态
{
if (!x)	return;
if (flag == false)           //左边
{
if(tree[tree[tree[x].left].left].size > tree[tree[x].right].size)//左孩子的左孩子大于右孩子
right_rot(x);
else if (tree[tree[tree[x].left].right].size > tree[tree[x].right].size) //左孩子的右孩子大于右孩子
{
left_rot(tree[x].left);
right_rot(x);
}
else
return;
}
else                       //右边
{
if(tree[tree[tree[x].right].right].size > tree[tree[x].left].size)//右孩子的右孩子大于左孩子
left_rot(x);
else if(tree[tree[tree[x].right].left].size > tree[tree[x].left].size) //右孩子的左孩子大于左孩子
{
right_rot(tree[x].right);
left_rot(x);
}
else
return;
}
maintain(tree[x].left,false);
maintain(tree[x].right,true);
maintain(x,true);
maintain(x,false);
}

void insert(int &x,int key)  //插入
{
if (x == 0)
{
x = ++top;
tree[x].left = 0;
tree[x].right = 0;
tree[x].size = 1;
tree[x].key = key;
}
else
{
tree[x].size++;
if(key < tree[x].key)
insert(tree[x].left,key);
else
insert(tree[x].right,key);//相同元素可插右子树
maintain(x,key >= tree[x].key);
}
}

int remove(int &x,int key)  //利用后继删除
{
tree[x].size--;
if(key > tree[x].key)
remove(tree[x].right,key);
else  if(key < tree[x].key)
remove(tree[x].left,key);
else  if(tree[x].left !=0 && !tree[x].right) //有左子树，无右子树
{
int tmp = x;
x = tree[x].left;
return tmp;
}
else if(!tree[x].left && tree[x].right != 0) //有右子树，无左子树
{
int tmp = x;
x = tree[x].right;
return tmp;
}
else if(!tree[x].left && !tree[x].right)    //无左右子树
{
int tmp = x;
x = 0;
return tmp;
}
else                                      //左右子树都有
{
int tmp = tree[x].right;
while(tree[tmp].left)
tmp = tree[tmp].left;
tree[x].key = tree[temp].key;
remove(tree[x].right,tree[tmp].key);
}
}

int getmin(int x)    //求最小值
{
while(tree[x].left)
x = tree[x].left;
return tree[x].key;
}

int getmax(int x)    //求最大值
{
while(tree[x].right)
x = tree[x].right;
return tree[x].key;
}

int pred(int &x,int y,int key)   //前驱，y初始前驱，从0开始, 最终要的是返回值的key值
{
if(x == 0)
return y;
if(key > tree[x].key)
return pred(tree[x].right,x,key);
else
return pred(tree[x].left,y,key);
}

int succ(int &x,int y,int key)   //后继，同上
{
if(x == 0)
return y;
if(key < tree[x].key)
return succ(tree[x].left,x,key);
else
return succ(tree[x].right,y,key);
}

int select(int &x,int k)   //查找第k小的数
{
int r = tree[tree[x].left].size + 1;
if(r == k)
return tree[x].key;
else if(r < k)
return select(tree[x].right,k - r);
else
return select(tree[x].left,k);
}

int rank(int &x,int key)   //key排第几
{
if(key < tree[x].key)
{
return rank(tree[x].left,key);
}
else if(key > tree[x].key)
return rank(tree[x].right,key) + tree[tree[x].left].size + 1;
else
return tree[tree[x].left].size + 1;
}

int main()
{
//insert(root,key);
//delete(root,key)
return 0;
}

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