Description:

A Binary Search Tree (BST) is recursively defined as a binary tree which has the following properties:

• The left subtree of a node contains only nodes with keys less than or equal to the node's key.
• The right subtree of a node contains only nodes with keys greater than the node's key.
• Both the left and right subtrees must also be binary search trees.

Insert a sequence of numbers into an initially empty binary search tree. Then you are supposed to count the total number of nodes in the lowest 2 levels of the resulting tree.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (≤) which is the size of the input sequence. Then given in the next line are the N integers in [which are supposed to be inserted into an initially empty binary search tree.

Output Specification:

For each case, print in one line the numbers of nodes in the lowest 2 levels of the resulting tree in the format:

n1 + n2 = n

where n1 is the number of nodes in the lowest level, n2 is that of the level above, and n is the sum.

Sample Input:

9

25 30 42 16 20 20 35 -5 28

Sample Output:

2 + 4 = 6

• 二叉查找树（Binary Search Tree）

Attention:

• BST定义有时候会不一样，等号跟左子树还是右子树要看清楚，注意审题

Code:

 /*

 Data: 2019-06-26 15:55:13

 Problem: PAT_A1115#Counting Nodes in a BST

 AC: 17:15

 题目大意：

 BST定义：lchild <= root < rchild

 根据插入序列建立BST树，统计最底层和次底层的结点数量

 基本思路：

 建树，记录结点层次，全局变量记录树的最大深度

 更新最大深度的同时，统计底层和次底层的结点个数

 */

 #include<cstdio>

 int deep=,n1=,n2=;

 struct node

 {

     int data;

     node *lchild,*rchild;

 };

 void Insert(node *&root, int x, int height)

 {

     if(root == NULL)

     {

         if(deep == height)

             n1++;

         else if(deep == height+)

             n2++;

         else if(deep == height-)

         {

             deep++;

             n2 = n1;

             n1 = ;

         }

         root = new node;

         root->data = x;

         root->lchild = root->rchild = NULL;

     }

     else if(x <= root->data)

         Insert(root->lchild, x, height+);

     else

         Insert(root->rchild, x, height+);

 }

 int main()

 {

 #ifdef ONLINE_JUDGE

 #else

     freopen("Test.txt", "r", stdin);

 #endif // ONLINE_JUDGE

     int n,x;

     scanf("%d", &n);

     node *root = NULL;

     for(int i=; i<n; i++)

     {

         scanf("%d", &x);

         Insert(root,x,);

     }

     printf("%d + %d = %d", n1,n2,n1+n2);

     return ;

 }