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<bits/stdc++.h>
using namespace std;

const int N = 1010;
int n, node[N], level[N], index = 0;

void bct(int root){
	if(root > n)
		return;
	bct(root * 2);
	level[root] = node[index++];
	bct(root * 2 + 1);
}

int main(){
	scanf("%d", &n);
	for(int i = 0; i < n; i++)
		scanf("%d", &node[i]);
	sort(node, node + n);
	bct(1);
	for(int i = 1; i <= n; i++)
	if(i != n)
		printf("%d ", level[i]);
	else
		printf("%d", level[i]);
	return 0;
}