Lecture 4

# Introduction to Algorithms, Second Edition

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern