PAT A1115 Counting Nodes in a BST （30 分）——二叉搜索树，层序遍历或者dfs

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 [−10001000] 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 <stdio.h>
 #include <algorithm>
 #include <set>
 #include <vector>
 #include <queue>
 using namespace std;
 int height;
 struct node{
     int data,h,lvl;
     node* l,*r;
 };
 node* newnode(int x){
     node* root = new node;
     root->data=x;
     root->l=NULL;
     root->r=NULL;
     root->h=;
     return root;
 }
 int geth(node* root){
     if(root==NULL) return ;
     return root->h;
 }
 void updateh(node* root){
     root->h = max(geth(root->l),geth(root->r))+;
 }
 void insert(node* &root,int x){
     if(root==NULL) {
         root=newnode(x);
         return;
     }
     if(x>root->data){
         insert(root->r,x);
         updateh(root);
     }
     else if(x<=root->data){
         insert(root->l,x);
         updateh(root);
     }
 }
 int main(){
     int n;
     scanf("%d",&n);
     node* root = NULL;
     for(int i=;i<n;i++){
         int x;
         scanf("%d",&x);
         insert(root,x);
     }
     height=root->h;
     int n1=,n2=;
     queue<node*> q;
     root->lvl=;
     q.push(root);
     while(!q.empty()){
         node* now=q.front();
         q.pop();
         //printf("%d %d\n",now->data,now->lvl);
         if(now->l!=NULL){
             now->l->lvl=now->lvl+;
             q.push(now->l);
         }
         if(now->r!=NULL){
             now->r->lvl=now->lvl+;
             q.push(now->r);
         }
         if(now->lvl==height)n1++;
         if(now->lvl==height-)n2++;
     }
     printf("%d + %d = %d",n1,n2,n1+n2);
 }

注意点：二叉搜索树的建立与层序遍历。不过好像做麻烦了，用dfs会更简洁。又好像dfs都不用，可以直接在插入时候加个lvl数组算