Problem: Develop an improved implementation of insertion sort for integer vector (insertion_sort_im) that precomputes the length of each vector before the sorting. Keep in mind that the vectors are sorted according to their length (see ivector_length function). You can test the correctness of your sorting algorithm using the provided check_sorted function.
Implement a merge sort for an array of integer vectors. For this implementation of the merge sort, as is the case for the improved insertion sort algorithm, you should precompute the length of the vectors before the sorting, and the sorting is done according to the vector lengths. Test the correctness of your merge sort implementation using the provided check_sorted function.