1115 Counting Nodes in a BST （30 分）建立二叉搜索树，求每层结点数目

Posted 2021-02-05 zhanghaijie

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;
}