A1115. Counting Nodes in a BST

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

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<string>
#include<queue>
using namespace std;
typedef struct NODE{
    struct NODE *lchild, *rchild;
    int data;
    int level;
}node;
void insert(node* &root, int x){
    if(root == NULL){
        node* temp = new node;
        temp->lchild = NULL;
        temp->rchild = NULL;
        temp->data = x;
        root = temp;
        return;
    }
    if(x <= root->data)
        insert(root->lchild, x);
    else insert(root->rchild, x);
}
int depth = 0, n1, n2;
void levelOrder(node* root){
    queue<node*> Q;
    root->level = 1;
    Q.push(root);
    while(Q.empty() == false){
        node* temp = Q.front();
        depth = temp->level;
        Q.pop();
        if(temp->lchild != NULL){
            temp->lchild->level = temp->level + 1;
            Q.push(temp->lchild);
        }
        if(temp->rchild != NULL){
            temp->rchild->level = temp->level + 1;
            Q.push(temp->rchild);
        }
    }
}
void DFS(node * root){
    if(root == NULL)
        return;
    if(root->level == depth)
        n1++;
    else if(root->level == depth -1)
        n2++;
    DFS(root->lchild);
    DFS(root->rchild);
}
int main(){
    int N, temp;
    node* root = NULL;
    scanf("%d", &N);
    for(int i = 0; i < N; i++){
        scanf("%d", &temp);
        insert(root, temp);
    }
    levelOrder(root);
    DFS(root);
    printf("%d + %d = %d", n1, n2, n1 + n2);
    cin >> N;
    return 0;
}

 总结：

1、注意最下面两层，和叶节点+叶节点上一层节点个数是不一样的。