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=1;
    return root;
}
int geth(node* root){
    if(root==NULL) return 0;
    return root->h;
}
void updateh(node* root){
    root->h = max(geth(root->l),geth(root->r))+1;
}
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=0;i<n;i++){
        int x;
        scanf("%d",&x);
        insert(root,x);
    }
    height=root->h;
    int n1=0,n2=0;
    queue<node*> q;
    root->lvl=1;
    q.push(root);
    while(!q.empty()){
        node* now=q.front();
        q.pop();
        //printf("%d %d
",now->data,now->lvl);
        if(now->l!=NULL){
            now->l->lvl=now->lvl+1;
            q.push(now->l);
        }
        if(now->r!=NULL){
            now->r->lvl=now->lvl+1;
            q.push(now->r);
        }
        if(now->lvl==height)n1++;
        if(now->lvl==height-1)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