Insertion or Heap Sort

Insertion or Heap Sort

According to Wikipedia:

Insertion sort iterates, consuming one input element each repetition, and growing a sorted output list. Each iteration, insertion sort removes one element from the input data, finds the location it belongs within the sorted list, and inserts it there. It repeats until no input elements remain.

Heap sort divides its input into a sorted and an unsorted region, and it iteratively shrinks the unsorted region by extracting the largest element and moving that to the sorted region. it involves the use of a heap data structure rather than a linear-time search to find the maximum.

Now given the initial sequence of integers, together with a sequence which is a result of several iterations of some sorting method, can you tell which sorting method we are using?

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (≤ 100). Then in the next line, N integers are given as the initial sequence. The last line contains the partially sorted sequence of the N numbers. It is assumed that the target sequence is always ascending. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print in the first line either "Insertion Sort" or "Heap Sort" to indicate the method used to obtain the partial result. Then run this method for one more iteration and output in the second line the resulting sequence. It is guaranteed that the answer is unique for each test case. 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 1:

10
3 1 2 8 7 5 9 4 6 0
1 2 3 7 8 5 9 4 6 0

Sample Output 1:

Insertion Sort
1 2 3 5 7 8 9 4 6 0

Sample Input 2:

10
3 1 2 8 7 5 9 4 6 0
6 4 5 1 0 3 2 7 8 9

Sample Output 2:

Heap Sort
5 4 3 1 0 2 6 7 8 9

 

解题思路

　　和Insert or Merge一样，先挑简单的判断，也就是先判断是不是插入排序，如果不是则为堆排序。

　　如果是堆排序，从数组最后一个元素开始往前跟数组第一个元素比较。由于除去数组中已排好序的部分外（也就是数组中放在最后的那些元素），数组第一个元素是最大的。所以从后开始向前比较，如果发现某个元素比数组第一个元素要小，说明找到已排好序的元素个数。然后再进行一次堆排序，向下调整就好了。

　　AC代码：

#include <cstdio>
#include <algorithm>

int main() {
    int n;
    scanf("%d", &n);
    int a[n], ret[n];
    for (int i = 0; i < n; i++) {
        scanf("%d", a + i);
    }
    for (int i = 0; i < n; i++) {
        scanf("%d", ret + i);
    }
    
    int i, j;
    for (i = 0; i < n - 1 && ret[i] <= ret[i + 1]; i++);
    for (j = i + 1; j < n && a[j] == ret[j]; j++);
    if (j == n) {
        puts("Insertion Sort");
        std::sort(ret, ret + i + 2);
    }
    else {
        puts("Heap Sort");
        int k = n - 1;
        for ( ; k > 1 && ret[k] >= ret[0]; k--);
        
        std::swap(ret[0], ret[k]);
        int tmp = ret[0], parent = 0;
        for (int child = 2 * parent + 1; child < k; parent = child, child = 2 * parent + 1) {
            if (child != k - 1 && ret[child] < ret[child + 1]) child++;
            if (tmp >= ret[child]) break;
            else ret[parent] = ret[child];
        }
        ret[parent] = tmp;
    }
    
    for (int i = 0; i < n; i++) {
        if (i) putchar(' ');
        printf("%d", ret[i]);
    }
    
    return 0;
}