[二叉查找树] 1115. Counting Nodes in a BST (30)

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 <iostream>
#include <cstdio>
#include <cmath>
#include <cstring>
#include <algorithm>
#include <vector>
#include <queue>
using namespace std;const int maxn=;struct Node
{
int data;
int layer;
Node *lchild,*rchild;
};void insert(Node * & root,int data)
{
if(root==NULL)
{
root=new Node;
root->lchild=NULL;
root->rchild=NULL;
root->data=data;
return ;
}
if(root->data<data) insert(root->rchild,data);
else insert(root->lchild,data);
}int max_layer=;
int layer[maxn]={};void layerOrder(Node * root)
{
queue<Node *> q;
root->layer=;
q.push(root);
while(!q.empty())
{
Node * now=q.front();
q.pop();
if(now->layer>max_layer) max_layer=now->layer;
layer[now->layer]+=;
if(now->lchild!=NULL)
{
now->lchild->layer=now->layer+;
q.push(now->lchild);
}
if(now->rchild!=NULL)
{
now->rchild->layer=now->layer+;
q.push(now->rchild);
}
}
}int main()
{
int n;
cin>>n;
Node * root=NULL;
for(int i=;i<n;i++)
{
int input;
cin>>input;
insert(root,input);
}
layerOrder(root);
int a=layer[max_layer];
int b=layer[max_layer-];
cout<<a<<" + "<<b<<" = "<<a+b<<endl;
return ;
}