PAT A1064

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

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#include "stdio.h"
#include "math.h"
#include "string.h"
//#include "iostream"
//#include "stdlib.h"
#include "vector"
//#include "set"
//#include "map"
//#include "stack"
#include "queue"
#include "algorithm"
using namespace std;

//typedef long long LL;
const int maxn = 1010;
//n为结点数,number用以存放结点权值,CBT用以存放完全二叉树
//index从小到大枚举number数组
int n, number[maxn], CBT[maxn], indexs = 0;
void inOrder(int root){
if(root > n) return;//空结点 返回
inOrder(2*root);//左子树
CBT[root] = number[indexs++];
inOrder(2*root +1);//右子树
}
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;
}