Introduction To Algorithms, Third Edition (international Edition)
Introduction To Algorithms, Third Edition (international Edition)
3rd Edition
ISBN: 9780262533058
Author: Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein
Publisher: TRILITERAL
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Chapter 17, Problem 5P

(a)

Program Plan Intro

To argue that if heuristic H does not know the access sequence in advance then the worse-case cost of H on an access sequence σ is CH(σ)=Ω(mn) .

(b)

Program Plan Intro

To show that if σi accesses element x in list L using the move-to-front heuristic the ci=2.rankL(x)1.

(c)

Program Plan Intro

To explain that equation ci=rankLi1(x)+ti.

(d)

Program Plan Intro

To argue the transposition either increases the potential by 2 or decrease the potential by 2.

(e)

Program Plan Intro

To argue that rankLi1(x)=|A|+|B|+1 and rankL*i1(x)=|A|+|C|+1 .

(f)

Program Plan Intro

To show that access σi causes a change in potential of Φ(Li)=Φ(Li1)2(|A||B|+ti) .

(g)

Program Plan Intro

To show that the amortized cost of access is bound by 4ci .

(h)

Program Plan Intro

To show the cost CMTF(σ) of access σ sequence with move-to-front is at most 4 times the cost CH(σ) of σ with any other heuristic H .

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