Introduction to Algorithms
Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 8, Problem 7P

(a)

Program Plan Intro

To argue that A[q]>A[p] so that B[p]=0 and B[q]=1 .

(b)

Program Plan Intro

To prove that algorithm X fails to sort array B correctly to prove the 0-1 sorting lemma.

(c)

Program Plan Intro

To argue that treating columnsort as an oblivious compare-exchange algorithm, even as it does not know the sorting method taken in odd steps.

(d)

Program Plan Intro

To prove that after steps1-3, the array consists of some clean row of 0’s at the top, some clean rows of 1’s at the bottom and at most s dirty rows between them.

(e)

Program Plan Intro

To prove that after step4, the array read in column-major order starts with a clean area of 0’s ends with a clean area of 1’s and has a dirty area of at most s2 elements in the middle.

(f)

Program Plan Intro

To prove that steps 5-8 produce a fully sorted 0-1 output.

(g)

Program Plan Intro

To find the value ofr that compared with s for column-sort to correctly sort when s does not divide r .

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