04-树5 Complete Binary Search Tree

这题也是第二次做，本想第一次做时参考的算法会和老师讲的一样，不想老师讲的算法用在这题感觉还不如思雪园友的算法（http://www.cnblogs.com/sixue/archive/2015/04.html）来的简单，不过老师给的思路是一种挺通用的思路，可以用来解决一系列的问题，但我目前看着有点吃力。我坚持认为对全局变量的使用需十分谨慎，能不用就不用，所以为了不出现全局变量，就无辜多了一串参数。实现代码如下，题目在代码下方

#include <stdio.h>
#include <stdlib.h>

int compare(const void * a,  const void * b);
void inOrder(int * a, int n, int * in, int N);

int main()
{
//    freopen("in.txt", "r", stdin); // for test
    int i, N, n;
    scanf("%d", &N);
    int a[N];
    for(i = 0; i < N; i++)
    {
        scanf("%d", &n);
        a[i] = n;
    }
    
    qsort(a, N, sizeof(int), compare);
    int in[N + 1];
    inOrder(a, 1, in, N);
    for(i = 1; i <= N; i++)
    {
        printf("%d", in[i]);
        if(i < N)
            printf(" ");
        else
            printf("\n");
    }
//    fclose(stdin); // for test
    return 0;
}

int compare(const void * a, const void * b)
{
    return *(int *)a - *(int *)b;
}

void inOrder(int * a, int n, int * in, int N)
{
    static int i = 0;
    
    if(n * 2 <= N)
        inOrder(a, 2 * n, in, N);
    in[n] = a[i++];
    if(n * 2 + 1 <= N)
        inOrder(a, n * 2 + 1, in, N);
}

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