PAT_A1115#Counting Nodes in a BST

Source:

PAT A1115 Counting Nodes in a BST (30 分)

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

Keys:

• 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 ;
 }