题目描述

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

求解思路

• 题意：给定一棵完全二叉搜索树，要求我们输出其层次遍历序列。
• 根据完全二叉搜索树的定义，我们可以知道该树的中序遍历序列一定是一个非递减序列。所以我们可以预先对输入序列进行升序排列，然后根据中序遍历建树。假设层次遍历从下标0开始，故根节点的下标为0。对于第i个结点其左节点为2i+1，其右节点为2i+2。每次递归都需要判断当前索引是否大于等于n，如果是的则回溯到上一层。

代码实现(AC)

#include<cstdio>
#include<algorithm>
using namespace std;
int n,index=0;
int ans[1001],num[1001];
void create(int root)
{
	if(root>=n)	return;
	create(2*root+1);
	ans[root]=num[index++];
	create(2*root+2);
}
int main()
{
	scanf("%d",&n);
	for(int i=0;i<n;i++)
		scanf("%d",&num[i]);
	sort(num,num+n);
	create(0);
	for(int i=0;i<n;i++)
	{
		printf("%d",ans[i]);
		if(i!=n-1)	printf(" ");
	}
}