An Analysis of Quicksort:

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Presentation transcript:

An Analysis of Quicksort: Average Case

Assumptions Average will be taken over Location of Pivot All Pivot Positions are equally likely Pivot positions in each call are independent of one another

Formulation I A(0) = 0 If the pivot appears at position i, 1£i£n then A(i-1) comparisons are done on the left hand list and A(n-i) are done on the right hand list. n-1 comparisons are needed to split the list

Recurrence Relation

Solve the Recurrence

Guessing the Solution Guess: a>0, b>0

Continuing ... By Integration:

And Finally ...