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 3.1, Problem 8E
Program Plan Intro

To describe the definitions for Ω(g(n,m)) and θ(g(n,m)) for the function g(n,m) .

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Simplify the following Boolean functions by means of K-map:a) f(A,B,C) =∑m(0,2,3,4,6)b) f(A,B,C,D) = ∑ m(0,2,3,7,8,10,12,13)c) F(X,Y,Z) = Y’Z+YZ+X’Y’Z’
Consider the following for loops in R. For each for loop, list the values (in order) that the variable i takes on in the body of the loop. Briefly (in no more than a few sentences) explain why. a) for(i in 1+2:3.4*5) { } b) for(i in dim(matrix(0, nr = 7, nc = 8))) { } c) for(i in rnorm(3)) { } d) for(i in iris[1:3,3]) { } e) for(j in c(1, 2, 3, 4, 5)) { } f) for(i in (function(x) x*x)(c(1, 2, 3))) { } g) for(i in NULL) { } h) for(i in strsplit(as.character(4*atan(1)),’’) [[1]][1:10]) { }
Simplify the following Boolean expressions, using four-variable K-maps: x′z+w′xy′+w(x′y+xy′)
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