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=0,n1=0,n2=0;
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+1)
            n2++;
        else if(deep == height-1)
        {
            deep++;
            n2 = n1;
            n1 = 1;
        }
        root = new node;
        root->data = x;
        root->lchild = root->rchild = NULL;
    }
    else if(x <= root->data)
        Insert(root->lchild, x, height+1);
    else
        Insert(root->rchild, x, height+1);
}

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=0; i<n; i++)
    {
        scanf("%d", &x);
        Insert(root,x,1);
    }
    printf("%d + %d = %d", n1,n2,n1+n2);

    return 0;
}