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 = , n1, n2;
 void levelOrder(node* root){
     queue<node*> Q;
     root->level = ;
     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 + ;
             Q.push(temp->lchild);
         }
         if(temp->rchild != NULL){
             temp->rchild->level = temp->level + ;
             Q.push(temp->rchild);
         }
     }
 }
 void DFS(node * root){
     if(root == NULL)
         return;
     if(root->level == depth)
         n1++;
     else if(root->level == depth -)
         n2++;
     DFS(root->lchild);
     DFS(root->rchild);
 }
 int main(){
     int N, temp;
     node* root = NULL;
     scanf("%d", &N);
     for(int i = ; i < N; i++){
         scanf("%d", &temp);
         insert(root, temp);
     }
     levelOrder(root);
     DFS(root);
     printf("%d + %d = %d", n1, n2, n1 + n2);
     cin >> N;
     return ;
 }

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。