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Question: another way to analyze randomized quicksort is to use a...

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Another way to analyze randomized quick-sort is to use a recurrence equation. In this case, we let T(n) denote the expected running time of randomized quick-sort, and we observe that, because of the worst-case partitions of good and bad splits, we can write (20%) T(n) s (T(3n/4) +T(n/4)) (T(n1)bn, where bn is the time needed to partition a list for a given pivot and concatenate the result sublists after the recursive calls return. Show, by induction, that T(n) is O(n logn) Hint: You can show that T(n) cn log n for some constant c > 0, by induction, ie., show that the right hand side is less than or equal to cn log n

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