1064 Complete Binary Search Tree (30 point(s))

1064 Complete Binary Search Tree (30 point(s))

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

二叉排序树的中序遍历是递增的，左孩子的下标为root2，右孩子root2+1

#include<bits/stdc++.h>
using namespace std;
int n,t=0;
int in[1010],level[1010];
void inOrder(int root){
    
    
    if(root>n) return;
    inOrder(root*2);
    level[root]=in[t++];
    inOrder(root*2+1);
}
int main(){
    
    
    scanf("%d",&n);
    for(int i=0;i<n;++i)
        scanf("%d",&in[i]);
    sort(in,in+n);
    inOrder(1);
    for(int i=1;i<=n;++i){
    
    
        if(i!=1) printf(" ");
        printf("%d",level[i]);
    }
}