Introduction to Algorithms, Second Edition

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The University of Texas at Austin Lecture 4 Department of Computer Sciences Professor Vijaya Ramachandran Quicksort; basic probability CS357: ALGORITHMS, Spring 2006 Quicksort Quicksort ( A, p, r ) Input. An array A [1 ..n ] of elements from a totally ordered set; p and r are integers with 1 p r n . Output. The elements in sub-array A [ p..r ] are rearranged in sorted order; the elements in array A outside of subarray A [ p..r ] are unchanged. if p < r then q := Partition ( A, p, r ) Quicksort ( A, p, q - 1) Quicksort ( A, q + 1 , r ) fi To sort the entire array A [1 ..n ] we call Quicksort ( A, 1 , n ). Partition ( A, p, r ) Let x be the element in A [ r ] when Partition is called; x is called the pivot element . Partition ( A, p, r ) returns an index q , p q r and rearranges the elements in subarray A [ p..r ] such that the following properties hold after execution: A [ q ] := x For p i < q , A [ i ] x For q < i r , A [ i ] > x It is easy to design an algorithm for Partition that runs in time linear in m = r - p + 1 ( m is the size of the subarray A [ p..r ]). It is also possible to design this algorithm to run
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