PAT Advanced Level 1064 Complete Binary Search Tree (30)（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
题解总是好使的，看了题解我一拍大腿，我怎么就没想到！！！

/**********************
author: yomi
date: 18.8.18
ps:
**********************/
#include <iostream>
#include <cmath>
#include <algorithm>

using namespace std;
const int maxn = 1010;
int CBT[maxn], s[maxn], cnt = 1, n;
void in(int index)
{
    if(index >  n)
        return;
    in(2*index);
    CBT[index] = s[cnt++];
    in(2*index+1);

}
int main()
{
    cin >> n;
    for(int i=1; i<=n; i++){
        cin >> s[i];
    }
    sort(s+1, s+n+1);
    in(1);
    for(int i=1; i<n; i++){
        cout << CBT[i] << ‘ ‘;
    }
    cout << CBT[n];
    return 0;
}
/**
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
**/