HDU 2193 AVL Tree

　　An AVL tree is a kind of balanced binary search tree. Named after their inventors, Adelson-Velskii and Landis, they were the first dynamically balanced trees to be proposed. Like red-black trees, they are not perfectly balanced, but pairs of sub-trees differ in height by at most 1, maintaining an O(logn) search time. Addition and deletion operations also take O(logn) time. 
Definition of an AVL tree 
　　An AVL tree is a binary search tree which has the following properties: 
　　1. The sub-trees of every node differ in height by at most one. 
　　2. Every sub-tree is an AVL tree. 

　　Balance requirement for an AVL tree: the left and right sub-trees differ by at most 1 in height.An AVL tree of n nodes can have different height. 
For example, n = 7: 

　　So the maximal height of the AVL Tree with 7 nodes is 3. 
　　Given n,the number of vertices, you are to calculate the maximal hight of the AVL tree with n nodes.

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 1 #include <cstdio>
 2 using namespace std;
 3 const int maxn = 50;
 4 int height[maxn];   
 5 int main(){
 6     height[0] = 1;
 7     height[1] = 2;
 8     for(int i = 2; i < maxn; i++){  //记录1 - 50层最小需要多少节点
 9         height[i] = height[i - 1] + height[i - 2] + 1;
10     }
11     int n;
12     while(scanf("%d", &n) != EOF){  //输入数据
13         if(n == 0)  //如果为0结束程序
14             break;
15         int ans = -1;
16         for(int i = 0; i < maxn; i++){  //从第0层开始比较
17             if(n >= height[i])  //只要输入的数据大于等于该点的最小需求答案高度加一
18                 ans++;
19             else
20                 break;  //否则结束循环
21         }
22         printf("%d\n", ans);    //输出答案
23     }
24     return 0;
25 }