(a) Program Explanation The classification of the classes in decreasing order of the complexity is given in below table: 2 2 n + 1 2 2 n ( n + 1 ) ! n ! e n n .2 n 2 n ( 3 / 2 ) n n lg ( lg n ) = ( lg n ) lg n ( lg n ) ! n 3 4 lg n = n 2 n lg n and lg ( n ! (b) Program Plan Intro Give an example of a single nonnegative function such that f ( n ) is neither O ( g i ( n ) ) nor Ω ( g i ( n ) ) .

Partition list into equivalence classes such that functions are in same class if f ( n ) = θ ( g ( n ) ) .

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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Question

Chapter 3, Problem 3P

(a)

Program Plan Intro

Partition list into equivalence classes such that functions are in same class if f(n)=θ(g(n)) .

(b)

Program Plan Intro

Give an example of a single nonnegative function such that f(n) is neither O(gi(n)) nor Ω(gi(n)) .

Expert Solution & Answer

Partition list into equivalence classes such that functions are in same class if f ( n ) = θ ( g ( n ) ) .

Solution Summary: The author explains the classification of equivalence classes based on the decreasing complexity from bottom to top: 1 has lowest complexity and 22n+1 is largest.

Partition list into equivalence classes such that functions are in same class if f(n)=θ(g(n)) .

Give an example of a single nonnegative function such that f(n) is neither O(gi(n)) nor Ω(gi(n)) .

Chapter 3 Solutions