1064. Complete Binary Search Tree (30)-PAT甲级真题(树的层序遍历)

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:
1 2 3 4 5 6 7 8 9 0
Sample Output:
6 3 8 1 5 7 9 0 2 4
1. 因为二叉搜索树的中序满足:是一组序列的从小到大排列,所以只需将所给序列排序即可得到中序数组in
2. 假设把树按从左到右、从上到下的顺序依次编号,根节点为0,则从根结点root = 0开始中序遍历,root结点的左孩子下标是root*2+1,右孩子下标是root*2+2
3. 因为是中序遍历,所以遍历结果与中序数组in中的值从0开始依次递增的结果相同,即in[t++](t从0开始),将in[t++]赋值给level[root]数组
4. 因为树是按从左到右、从上到下的顺序依次编号的,所以level数组从0到n-1的值即所求的层序遍历的值,输出level数组即可~

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