Natural mergesort. Determine empirically the number of passes needed in a natural mergesort (see exercise) for random Long keys with N=103, 106, and 109. Hint: You do not need to implement a sort (or even generate full 64-bit keys) to complete this exercise
Exercise
Natural mergesort. Write a version of bottom-up mergesort that takes advantage of order in the array by proceeding as follows each time it needs to find two arrays to merge: find a sorted subarray (by incrementing a pointer until finding an entry that is smaller than its predecessor in the array), then find the next, then merge them. Analyze the running time of this algorithm in terms of the array size and the number of maximal increasing sequences in the array.
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