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

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:

 1 /*
 2 Data: 2019-06-26 15:55:13
 3 Problem: PAT_A1115#Counting Nodes in a BST
 4 AC: 17:15
 5 
 6 题目大意：
 7 BST定义：lchild <= root < rchild
 8 根据插入序列建立BST树，统计最底层和次底层的结点数量
 9 
10 基本思路：
11 建树，记录结点层次，全局变量记录树的最大深度
12 更新最大深度的同时，统计底层和次底层的结点个数
13 */
14 #include<cstdio>
15 int deep=0,n1=0,n2=0;
16 struct node
17 {
18     int data;
19     node *lchild,*rchild;
20 };
21 
22 void Insert(node *&root, int x, int height)
23 {
24     if(root == NULL)
25     {
26         if(deep == height)
27             n1++;
28         else if(deep == height+1)
29             n2++;
30         else if(deep == height-1)
31         {
32             deep++;
33             n2 = n1;
34             n1 = 1;
35         }
36         root = new node;
37         root->data = x;
38         root->lchild = root->rchild = NULL;
39     }
40     else if(x <= root->data)
41         Insert(root->lchild, x, height+1);
42     else
43         Insert(root->rchild, x, height+1);
44 }
45 
46 int main()
47 {
48 #ifdef ONLINE_JUDGE
49 #else
50     freopen("Test.txt", "r", stdin);
51 #endif // ONLINE_JUDGE
52 
53     int n,x;
54     scanf("%d", &n);
55     node *root = NULL;
56     for(int i=0; i<n; i++)
57     {
58         scanf("%d", &x);
59         Insert(root,x,1);
60     }
61     printf("%d + %d = %d", n1,n2,n1+n2);
62 
63     return 0;
64 }

来源：https://www.cnblogs.com/blue-lin/p/11006098.html

标签

bst