A1064. Complete Binary Search Tree (30)

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 <stdio.h>
#include <stdlib.h>
#include <iostream>
#include <string.h>
#include <math.h>
#include <algorithm>
#include <string>
#include <stack> 
#include <queue>
using namespace std;
const int maxn=1010; 
int n,number[maxn],CBT[maxn];
int shuzucount=0;

void inOrder(int root)//这里中序遍历的目的是，
{//将中序的结果数组num与过程结合，得到CBT 
   if(root>n)return;
   inOrder(root*2);
   CBT[root]=number[shuzucount++];
   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;
}