## Problem #

Source: [PAT 1064]

### Description #

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`

## Solution #

## Code #

```
#include <iostream>
#include <algorithm>
#define max_size 1001
using namespace std;
int n, flag = 1, origin_order[max_size];
int tree[max_size];
void inOrder(int index)
{
if (index > n)
{
return;
}
else
{
inOrder(index * 2);
tree[index] = origin_order[flag++];
inOrder(index * 2 + 1);
}
}
bool cmp(int a, int b)
{
return a < b;
}
int main()
{
int t;
cin >> n;
for (int i = 1; i <= n; i++)
{
cin >> t;
origin_order[i] = t;
}
sort(origin_order + 1, origin_order + n + 1, cmp);
inOrder(1);
for (int i = 1; i <= n; i++)
{
if (i != 1)
cout << " ";
cout << tree[i];
}
return 0;
}
```