Questions On Advanced Discrete Math And Algorithms
Homework 1 Solutions
Author: Aditeya Pandey, Collaborators: Micha Schwab,Supraja Krishnan
• Problems 13 are meant as a review of undergraduate discrete math and algorithms. They shouldn’t take you too long, but I recommend starting these right away to make sure that you have the appropriate background for this course.
• You must type your solutions using L A TEX. Please submit both the source and PDF files using the naming conventions lastname hw1.tex and lastname hw1.pdf.
• Strive for clarity and conciseness in your solutions, emphasizing the main ideas over lowlevel details. I recommend looking at the introduction in Jeff Erickson’s textbook for advice on writing up solutions to algorithms problems.
• Do not share written solutions, and remember to cite all collaborators and sources of ideas.
Sharing written solutions, and getting solutions from outside sources such as the Web or students not enrolled in the class is strictly forbidden.
1Review Problems
Problem 1 (Review of Asymptotic Growth). Arrange the following list of functions in ascending order of growth rate. That is, if function g(n) immediately follows function f (n) in your list, then it should be the case that f (n) is O(g(n)). (You do not need to provide proofs.)
2
f 1 (n) = 4n 2 + n log 28 (n)
√
f 4 (n) = n + 40 n f 2 (n) = 2 n f 3 (n) = 1024n log 2 (n) f 5 (n) = 10 n f 6 (n) = 3n log 2 (n) f 7 (n) = n 2 log 8 n f 8 (n) = 4096 log 42 (n) f 9 (n) = n log 2 (3)
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