Question

Make a function called merge - insertion sort that utilizes both merge sort and iteration sort. The function will use the header void sort merge _ insert _ sort (int * array, int size). Instead of merge sort breaking the array down to subarrays of length 1, you ’ re going to try larger subarrays. You ’ ll then call insertion sort once the subarrays are less than the given length. Code in C.

Options:
a. Implementing merge-insertion sort is not feasible.
b. Combining merge sort and insertion sort doesn't make sense.
c. Implementing merge-insertion sort is a good strategy.
d. Merge sort and insertion sort cannot be used together.

Answer 1

Merge-Insertion Sort combines the recursive divide-and-conquer approach of merge sort with the efficient sorting of small-sized arrays by insertion sort. It is feasible and can be implemented in C to improve the efficiency of sorting algorithms by optimizing the approach for smaller subarrays.

Step-by-step explanation:

Merge-Insertion Sort is a hybrid sorting algorithm that combines the concepts of both merge sort and insertion sort. As requested, the provided function sort_merge_insert_sort(int *array, int size) utilizes a modified merge sort algorithm that breaks down the array until subarrays reach a certain size threshold. Instead of reducing the subarrays to single elements, the algorithm employs insertion sort for sorting these smaller subarrays. The sorted subarrays are then merged together to form a fully sorted array. This is a good strategy as insertion sort performs efficiently on smaller or nearly sorted datasets.

The implementation of such a function in C would follow the principles of both sorting methods. Merge sort divides the array into smaller parts recursively, and insertion sort efficiently sorts these small parts before they are merged back together. This combination can in some cases outperform traditional merge sort due to the more efficient sorting of small arrays by insertion sort.

Here's a basic sketch of how part of the algorithm would work in C:

void insertion_sort(int *array, int length) {
// Insertion sort logic here
}

void merge(int *left, int leftSize, int *right, int rightSize, int *array) {
// Merging logic here
}

void sort_merge_insert_sort(int *array, int size) {
if (size < THRESHOLD) {
insertion_sort(array, size);
} else {
int mid = size / 2;
int *left = (int *)malloc(mid * sizeof(int));
int *right = (int *)malloc((size - mid) * sizeof(int));
// Copy and sort each half
// Merge sorted halves
free(left);
free(right);
}
}

This approach is feasible and does make sense as it effectively combines the robustness of merge sort with the efficiency of insertion sort for smaller data sets.