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<algorithm>
    using namespace std;
    const int maxn = ; int n;
    int index = ;
    int CBT[maxn],num[maxn]; void inOrder(int root){
    if(root > n) return;
    inOrder(root*);
    CBT[root] = num[index++];
    inOrder(root*+);
    } int main(){ scanf("%d",&n);
    for(int i = ; i < n; i++){
    scanf("%d",&num[i]);
    }
    sort(num,num+n);
    inOrder();
    for(int i = ; i <= n; i++){
    printf("%d",CBT[i]);
    if(i < n) printf(" ");
    }
    return ;
    }

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