1064 Complete Binary Search Tree (30分)

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

Code:

#include
#include
using namespace std;
#define maxn 1010
int number[maxn],CBT[maxn];
int sum,temp = 0;
void inOrder(int index){
    if(index > sum){
        return;
    }
    inOrder(2 * index);
    CBT[index] = number[temp++];
    inOrder(2 * index + 1);
}

int main(){
    int i;
    scanf("%d",&sum);
    for(i=0;i<sum;i++){
        scanf("%d",&number[i]);
    }
    sort(number,number + sum);
    inOrder(1);
    for(i=1;i<=sum;i++){
        printf("%d",CBT[i]);
        if(i < sum){
            printf(" ");
        }
    }
    return 0;
}