04-樹5 Complete Binary Search Tree，04-binary

04-樹5 Complete Binary Search Tree，04-binary

這題也是第二次做，本想第一次做時參考的算法會和老師講的一樣，不想老師講的算法用在這題感覺還不如思雪園友的算法（http://www.cnblogs.com/sixue/archive/2015/04.html）來的簡單，不過老師給的思路是一種挺通用的思路，可以用來解決一系列的問題，但我目前看著有點吃力。我堅持認為對全局變量的使用需十分謹慎，能不用就不用，所以為了不出現全局變量，就無辜多了一串參數。實現代碼如下，題目在代碼下方

 1 #include <stdio.h>
 2 #include <stdlib.h>
 3 
 4 int compare(const void * a,  const void * b);
 5 void inOrder(int * a, int n, int * in, int N);
 6 
 7 int main()
 8 {
 9 //    freopen("in.txt", "r", stdin); // for test
10     int i, N, n;
11     scanf("%d", &N);
12     int a[N];
13     for(i = 0; i < N; i++)
14     {
15         scanf("%d", &n);
16         a[i] = n;
17     }
18     
19     qsort(a, N, sizeof(int), compare);
20     int in[N + 1];
21     inOrder(a, 1, in, N);
22     for(i = 1; i <= N; i++)
23     {
24         printf("%d", in[i]);
25         if(i < N)
26             printf(" ");
27         else
28             printf("\n");
29     }
30 //    fclose(stdin); // for test
31     return 0;
32 }
33 
34 int compare(const void * a, const void * b)
35 {
36     return *(int *)a - *(int *)b;
37 }
38 
39 void inOrder(int * a, int n, int * in, int N)
40 {
41     static int i = 0;
42     
43     if(n * 2 <= N)
44         inOrder(a, 2 * n, in, N);
45     in[n] = a[i++];
46     if(n * 2 + 1 <= N)
47         inOrder(a, n * 2 + 1, in, N);
48 }

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