Implement three sorting algorithms – mergesort, quicksort, and heapsort in the language of your choice and investigate their performance on arrays of sizes n = 102, 103, 104, 105, and 106. For each of these sizes consider: randomly generated files of integers in the range [1..n]. increasing files of integers 1, 2, ..., n. decreasing files of integers n, n − 1, ..., 1.

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A:

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Merge sort

Merge Sort recursively sorts a given collection of numbers or elements by using the divide and conquer strategy in less time. It is one of the most used algorithms, with the worst-case time complexity of O (n log n). It was invented by John Von Neumann. The algorithm continuously divides an array into sub-arrays until each sub-array consists of a single element. It then merges those sub-arrays to produce a sorted array.