Complete Binary Search Tree

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 (≤). 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 <cstdio> 
#include <math.h>
#include <algorithm> 

using namespace std;

int a[1010];
int T[1010];

int GetLeftLength(int n)
{
    int H=log(n+1)/log(2);
    int X=n+1-pow(2,H);
    if(X>pow(2,H-1))
        X=pow(2,H-1);
    int L=pow(2,H-1)-1+X;
    return L;
}

void solve(int ALeft,int ARight,int TRoot)
{
    int n=ARight-ALeft+1;
    if(n==0) return;
    int L=GetLeftLength(n);
    T[TRoot]=a[ALeft+L];
    int LeftTRoot=TRoot*2+1;
    int RightTRoot=LeftTRoot+1;
    solve(ALeft,ALeft+L-1,LeftTRoot);
    solve(ALeft+L+1,ARight,RightTRoot);
}

int main()
{
    int n;
    scanf("%d",&n);
    for(int i=0;i<n;i++)
    {
        scanf("%d",&a[i]);
    }
    sort(a,a+n);
    solve(0,n-1,0);
    for(int i=0;i<n;i++)
    {
        if(i==0)
            printf("%d",T[i]);
        else printf(" %d",T[i]);
    }
    return 0;
}