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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