Analyze randomize quick-sort is to use a recurrence equation

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Reference no: EM131841550

Problem

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 for good and bad splits, we can write

T(n) ≤ 1/2 (T(3n/4) + T(n/4)) + (T(n - 1)) + 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(nlogn).

Reference no: EM131841550

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