1064 Complete Binary Search Tree

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

对于BST，其中序遍历是非递减数列，所以先从小到大排序，按照中序遍历来建树，然后按序号输出（即层序遍历）即可： 

#include <iostream>
#include <algorithm>
using namespace std;
int a[1010], n, ans[1010], cnt;

void dfs(int x) {
	if (x <= n) {
		dfs(x * 2);
		ans[x] = a[cnt++];
		dfs(x * 2 + 1);
	}
}

int main() {
	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> a[i];
	}
	sort(a, a + n);
	dfs(1);
	for (int i = 1; i <= n; i++) {
		cout << ans[i];
		if (i != n) {
			cout << ' ';
		}
	}
	return 0;
}