Lecture 6

# Introduction to Algorithms, Second Edition

• Notes
• davidvictor
• 3

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The University of Texas at Austin Lecture 6 Department of Computer Sciences Professor Vijaya Ramachandran Randomized Quicksort CS357: ALGORITHMS, Spring 2006 Randomized Partition and Randomized Quicksort Randomized-Partition is a simple modification of Partition (which was defined earlier) in which a random element in the subarray being considered is moved to the last position in the subarray (hence this element becomes the pivot), and then Partition is invoked. Rand-Partition ( A, p, r ) i := Random ( p, r ) interchange A [ i ] and A [ r ] return Partition ( A, p, r ) Correctness of Rand-Partition is immediate once we assume correctness of Partition , since A [ i ] is guaranteed to be an element in the subarray A [ p..r ]. The running time remains linear in the size of subarray. We now use Rand-Partition in the randomized version of Quicksort given below. Rand-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. (So initial call is to A [1 ..n ].) if p < r

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• Spring '06
• Ramachandran
• Algorithms, Sort, Probability theory, Pivot element, Rand-Partition

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