1115. Counting Nodes in a BST (30)

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 (<=1000) which is the size of the input sequence. Then given in the next line are the N integers in [-1000 1000] 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

建树，然后不断更新最大深度和次大深度，及相应点个数。
代码：

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <map>
using namespace std;
struct tree
{
    int data;
    tree *left,*right;
    tree()
    {
        data = 0;
        left = right = NULL;
    }
}*head;
int n;
int m,c1,c2;
tree *insert_(tree *r,int d,int h)
{
    if(r == NULL)
    {
        r = new tree();
        r -> data = d;
        if(h > m)
        {
            m = h;
            c2 = c1;
            c1 = 1;
        }
        else if(h == m)c1 ++;
        else if(h == m - 1)c2 ++;
    }
    else if(d > r -> data)
    {
        r -> right = insert_(r -> right,d,h + 1);
    }
    else
    {
        r -> left = insert_(r -> left,d,h + 1);
    }
    return r;
}
int main()
{
    int d;
    scanf("%d",&n);
    head = NULL;
    for(int i = 0;i < n;i ++)
    {
        scanf("%d",&d);
        head = insert_(head,d,1);
    }
    printf("%d + %d = %d",c1,c2,c1 + c2);
}

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