# 04-树6 Complete Binary Search Tree

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

### 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
 1 #include <iostream>
2 #include <cstdio>
3 #include <algorithm>
4 using namespace std;
5
6 #define MaxSize 1005
7 int sortNum[MaxSize] = {0};
8 int CBTreeNode[MaxSize] = {0};
9 int countNum = 0;
10 void CreatCBTree(int root,int N)
11 {
12     if(root > N)
13         return;
14     int left = root * 2;
15     int right = root * 2 + 1;
16     CreatCBTree(left,N);        //中序遍历LGR从小到大 小的先
17     CBTreeNode[root] = sortNum[countNum++];
18     CreatCBTree(right,N);
19 }
20
21 int main()
22 {
23     int N;
24     scanf("%d",&N);
25     for(int i = 0; i < N; i++)
26         scanf("%d",&sortNum[i]);
27
28     sort(sortNum,sortNum + N);//按从小到大排序
29     CreatCBTree(1,N);
30     for(int i = 1; i <= N; i++) {
31         if(i != N)
32             printf("%d ",CBTreeNode[i]);
33         else
34             printf("%d",CBTreeNode[i]);
35     }
36     return 0;
37 }

posted on 2016-03-26 16:15  kuotian  阅读(437)  评论(0编辑  收藏  举报