1066. Root of AVL Tree (25)

An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illustrate the rotation rules.

         

Now given a sequence of insertions, you are supposed to tell the root of the resulting AVL tree.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (<=20) which is the total number of keys to be inserted. Then N distinct integer keys are given in the next line. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print ythe root of the resulting AVL tree in one line.

Sample Input 1:

5
88 70 61 96 120

Sample Output 1:

70

Sample Input 2:

7
88 70 61 96 120 90 65

Sample Output 2:

88

在插入结点的过程中维护二叉搜索树的平衡，左子数的height比右子树大2的前提下，如果插入结点在左子树的左子树，直接对根进行左左旋，如果插入结点在左子树的右子树，就对左子树进行右右旋，然后对根进行左左旋。
反过来右子树的height比左子树大2，也一样，如果插入结点在右子树的右子树，直接对根进行右右旋，如果插入结点在右子树的左子树，就对右子树进行左左旋，然后对根进行右右旋。

代码：

#include <stdio.h>
#include <stdlib.h>
typedef struct tree///二叉搜索树结构体
{
    int data;
    struct tree *left,*right;
}tree;
tree *creatnode(int data)///创建新结点
{
    tree *p = (tree *)malloc(sizeof(tree));
    p -> left = p -> right = NULL;
    p -> data = data;
    return p;
}
int max(int a,int b)
{
    return a > b ? a : b;
}
int getheight(tree *t)///返回结点高度 即以当前结点为根的子树的最大层数
{
    if(t == NULL)return 0;
    return max(getheight(t -> left),getheight(t -> right)) + 1;
}
tree *ll_r(tree *t)///左左旋
{
    tree *l = t -> left;
    t -> left = l -> right;
    l -> right = t;
    return l;
}
tree *rr_r(tree *t)///右右旋
{
    tree *r = t -> right;
    t -> right = r -> left;
    r -> left = t;
    return r;
}
tree *lr_r(tree *t)///左右旋
{
    t -> left = rr_r(t -> left);
    return ll_r(t);
}
tree *rl_r(tree *t)///右左旋
{
    t -> right = ll_r(t -> right);
    return rr_r(t);
}
tree *insertavltree(int data,tree *t)///插入并平衡
{
    if(t == NULL)return creatnode(data);
    else if(data < t -> data)
    {
        t -> left = insertavltree(data,t -> left);
    }
    else
    {
        t -> right = insertavltree(data,t -> right);
    }

    if(getheight(t -> left) - getheight(t -> right) == 2)
    {
        if(data < t -> left -> data)t = ll_r(t);
        else t = lr_r(t);
    }
    else if(getheight(t -> left) - getheight(t -> right) == -2)
    {
        if(data < t -> right -> data)t = rl_r(t);
        else t = rr_r(t);
    }
    return t;
}
int main()
{
    int n,d;
    scanf("%d", &n);
    tree *root = NULL;
    for(int i = 0; i < n; i ++)
    {
        scanf("%d",&d);
        root = insertavltree(d,root);
    }
    printf("%d", root->data);
}