1064 Complete Binary Search Tree (30分)

1064 Complete Binary Search Tree (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 the node's key.
• The right subtree of a node contains only nodes with keys greater than or equal to the node's key.
• Both the left and right subtrees must also be binary search trees.

A Complete Binary Tree (CBT) is a tree that is completely filled, with the possible exception of the bottom level, which is filled from left to right.

Now given a sequence of distinct non-negative integer keys, a unique BST can be constructed if it is required that the tree must also be a CBT. You are supposed to output the level order traversal sequence of this BST.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (≤1000). Then N distinct non-negative integer keys are given in the next line. All the numbers in a line are separated by a space and are no greater than 2000.

Output Specification:

For each test case, print in one line the level order traversal sequence of the corresponding complete binary search tree. All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line.

Sample Input:

10
1 2 3 4 5 6 7 8 9 0

Sample Output:

6 3 8 1 5 7 9 0 2 4

#include <iostream>
#include <algorithm>
#include<vector>
#include<map>
#include<string>
#include<cmath>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<set>
#include<unordered_map>
#include<queue>
#include<climits>
#include<stack>
using namespace std;
const int maxn= 10000+10;


int num[maxn],in[maxn];

int n,k=0;

void inorder(int root){
	if(root>n) return;
	inorder(2*root);
	in[root]=num[k++];
	inorder(2*root+1);
}


int main(){
	cin>>n;
	for(int i=0;i<n;i++){
		cin>>num[i];		
	}	
	sort(num,num+n);
	inorder(1); 
	for(int i=1;i<=n;i++) {
		if(i!=1) cout<<" ";
		cout<<in[i];
	} 
    return 0;
}