1064complete binary search tree (30 points)

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 integerN(≤1000). ThenNdistinct 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`

### thinking

- Use arrays to construct a complete binary tree.
- A complete binary tree can construct the only complete binary search tree (CBST).
- The middle order sequence of binary search tree (BST) is an increasing sequence, so the CBST of middle order sequence is constructed in the middle order traversal of complete binary tree. Finally, the sequential output of CBT is the hierarchical traversal sequence of CBST.

### code

```
#include <cstdio>
#include <algorithm>
using namespace std;
const int maxn = 1010;
int n, number[maxn], cbt[maxn];
int index = 0;
void inOrder(int root)
{
if (root > n) return;
inOrder(root * 2);
cbt[root] = number[index ++];
inOrder(root * 2 + 1);
}
int main()
{
scanf("%d", &n);
for (int i = 0; i < n; i ++)
{
scanf("%d", &number[i]);
}
sort(number, number + n);
inOrder(1);
for (int i = 1; i <= n; i ++)
{
printf("%d", cbt[i]);
if (i < n)
printf(" ");
}
return 0;
}
```