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a (15 pts) Recall merge sort algorithm explained in the lecture. It recursively divides a given input array into two halves then uses “merge” to combine the two sorted halves into a solution. Suppose you revise a this algorithm to recursively divides an input into four parts of equal length. Derive a recurrence equation of this revised merge sort algorithm and solve it by using 1) back-substitution and 2) Master's theorem. Suppose that the merge function can also be revised to combine the four parts in O(n) runtime. Explain how big-O time complexity you derive relates to that of the original merge sort.
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