PAT 1064 Complete Binary Search Tree [完全二叉搜索树] [中序遍历]

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本文介绍了一种根据给定的非负整数序列构造完全二叉搜索树的方法，并通过中序遍历输出该树的层次遍历序列。首先对输入序列进行排序，然后根据完全二叉树的特性进行中序遍历填充。

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

--------------------------------------这是题目和解题的分割线--------------------------------------

二叉搜索树有一个性质，其中序遍历是递增的。所以可以先把输入的数字进行递增排序，再按照完全二叉树左右子树和根结点的位置关系，进行中序遍历。

#include<cstdio>
#include<algorithm>

using namespace std;

int tmp[1010],a[1010],n,i,cnt = 0;

//中序遍历（index是位置不是数据） 
void inOrder(int index)
{
	if(index>n) return; //如果出界了，return 
	inOrder(index*2); //完全二叉树左子树的下标 = 根结点*2 
	a[index] = tmp[cnt++]; //赋值 
	inOrder(index*2+1); //右子树 
}

int main()
{	
	scanf("%d",&n);
	for(i=0;i<n;i++)
		scanf("%d",&tmp[i]);
	sort(tmp,tmp+n); //递增排序 
	inOrder(1); //完全二叉树的根结点位置为1 
	for(i=1;i<=n;i++)
	{
		printf("%d",a[i]);
		if(i!=n) printf(" ");
	}
	return 0;
}