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

考察：完全二叉排序树，中序遍历递归算法。

答案如下：

---

#include<iostream>
#include<string>
#include<algorithm>
#include<vector>
#include<queue>
using namespace std;
int n, num[1010], TNode[1010], idx = 0;
void Inorder(int root) {
	if (root > n) return;
	else {
		Inorder(root * 2);
		TNode[root] = num[idx++];
		Inorder(root * 2 + 1);
	}
}
int main(){
	cin >> n;
	for (int i = 0; i < n; i++) {
		cin >> num[i];
	}
	sort(num, num + n);
	Inorder(1);
	for (int i = 1; i <= n - 1; i++) {
		cout << TNode[i]<<" ";
	}
	cout << TNode[n];
	return 0;
}