PAT 甲级 1064. Complete Binary Search Tree (30)

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

#include <iostream>
#include <vector>
#include <algorithm>
#include <string>
#include <set>
using namespace std;
const int maxn = 1010;
int n, number[maxn], cbt[maxn], index=0;
void inOrder(int root) {
if (root > n) return;
inOrder(root * 2);
cbt[root] = number[index++];
inOrder(root * 2 + 1);
}
int main() {
scanf("%d", &n);
for (int i = 0; i < n; i++) {
scanf("%d", &number[i]);
}
sort(number, number + n);
inOrder(1);
for (int i = 1; i <= n; i++) {
printf("%d", cbt[i]);
if (i < n) printf(" ");
}
return 0;
}