1115 Counting Nodes in a BST （30 分）
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思路： 通过先序遍历建立二叉树，然后使用先序遍历求每层结点数。#include<iostream>
#include<vector>
#include<algorithm>
#include<queue>
#include<string>
#include<map>
#include<set>
#include<stack>
using namespace std;
struct Node
{
int data;
Node *lchild,*rchild;
};
void insertBST(Node *&root,int key)
{
if(root==nullptr)
{
root=new Node;
root->data=key;
root->lchild=root->rchild=nullptr;
return;
}
if(key>root->data)
insertBST(root->rchild,key);
else
insertBST(root->lchild,key);
}
int level[1001];
int maxLevel=0;
void dfs(int depth,Node *root)
{
if(root==nullptr)
return;
level[depth]++;
maxLevel=max(depth,maxLevel);
dfs(depth+1,root->lchild);
dfs(depth+1,root->rchild);
}
int main()
{
int n;
cin>>n;
//int a[n+1];
Node *root=nullptr;
for(int i=0;i<n;i++)
{
int temp;
cin>>temp;
insertBST(root,temp);
}
dfs(1,root);
// for(int i=1;i<=maxLevel;i++)
// cout<<level[i]<<" ";
// cout<<endl;
cout<<level[maxLevel]<<" + "<<level[maxLevel-1]<<" = "<<level[maxLevel]+level[maxLevel-1];
return 0;
}
原文地址：https://www.cnblogs.com/zhanghaijie/p/10308812.html