参考：http://blog.csdn.net/iaccepted/article/details/20726067

题目来源：

04-树8. Complete Binary Search Tree (30)

时间限制

100 ms

内存限制

65536 kB

代码长度限制

8000 B

判题程序

Standard

作者

CHEN, Yue

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:

101 2 3 4 5 6 7 8 9 0

Sample Output:

6 3 8 1 5 7 9 0 2 4

要求构造完全二叉搜索树。基本思路时：

1. 将输入的序列node 进行排序

2. 中序遍历结果树tree，用排序后的序列node构造tree

3.  输出tree 

import java.math.BigInteger;import java.util.Arrays;import java.util.Hashtable;import java.util.LinkedList;import java.util.Scanner;import java.util.concurrent.ConcurrentHashMap;import java.util.concurrent.locks.ReentrantLock;/** *  * */public class Main {static int nodeIndex;public static void buildTree(int i,int N,int[] node,int[] tree){if(i >N) return ;int leftChild = i<<1;int rightChild = (i<<1)+1;buildTree(leftChild,N,node,tree);tree[i] = node[nodeIndex++];buildTree(rightChild,N,node,tree);}public static void main(String[] args) {Scanner scanner = new Scanner(System.in);int N = scanner.nextInt(); int[] node = new int[N+1];int [] tree = new int[N+1];nodeIndex =1;for(int i=1;i<=N;i++){node[i]= scanner.nextInt();}Arrays.sort(node);buildTree(1,N,node,tree);for(int i=1;i<=N-1;i++){System.out.print(tree[i]+" ");}System.out.println(tree[N]);}}