Recall that an inversion in a list of distinct integers (a,..., an) is a pair ai,...

 

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Recall that an inversion in a list of distinct integers (a,..., an) is a pair ai, aj such that i < j and ai > aj. The problem here is to find the value of the biggest difference among inversion pairs. Example: for the sequence [11, 7, 1, 17, 4, 3, 6, 2, 13, 20, 15, 9], the greatest difference among all inversion pairs is 15 coming from the pair (17,2) (a) Design a divide and conquer type algorithm that finds the value of the greatest difference between all inversion pairs in a list of distinct integers. Your algorithm should take O(n log n) runtime. (No justification for correctness needed. Please give a justification of the runtime.) (b) By keeping track of some more information, design a Divide and Conquer algorithm that runs in O(n) time. (No justification for correctness needed. Please give a justification of the runtime.) Recall that an inversion in a list of distinct integers (a,..., an) is a pair ai, aj such that i < j and ai > aj. The problem here is to find the value of the biggest difference among inversion pairs. Example: for the sequence [11, 7, 1, 17, 4, 3, 6, 2, 13, 20, 15, 9], the greatest difference among all inversion pairs is 15 coming from the pair (17,2) (a) Design a divide and conquer type algorithm that finds the value of the greatest difference between all inversion pairs in a list of distinct integers. Your algorithm should take O(n log n) runtime. (No justification for correctness needed. Please give a justification of the runtime.) (b) By keeping track of some more information, design a Divide and Conquer algorithm that runs in O(n) time. (No justification for correctness needed. Please give a justification of the runtime.)