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

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

This is the second time to do, I wanted to do for the first time when the reference algorithm will be the same as the teacher said, do not want the teacher to talk about the algorithm used in this question feel better than sixueyuanyou algorithm (http://www.cnblogs.com/sixue/archive/2015/04.html) this is simple, but the idea given by the teacher is quite generic and can be used to solve a series of problems, but I am a little hard at present. I insist that the use of global variables should be very careful, so you don't need to use them if you don't need them. In order not to show global variables, there will be a series of additional parameters. The implementation code is as follows:

 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 test10     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         else28             printf("\n");29     }30 //    fclose(stdin); // for test31     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:

101 2 3 4 5 6 7 8 9 0

Sample Output:

6 3 8 1 5 7 9 0 2 4