CS7800: Advanced Algorithms. Fall 2016 Homework 1 Solutions Author: Aditeya Pandey, Collaborators: Micha Schwab,Supraja Krishnan • Problems 1-3 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 low-level 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) Solution
Group the functions by complexity category. Find the complexity category for each function and sort the categories by increasing growth rate.
The data for Exercises 6 and 7 are in the data file named Lesson 20 Exercise File 1. Answer Exercises 6 and 7 based on the following
Complete the following problems from Chapter 7 and submit to your instructor. These problems will be graded for accuracy. Problems: 7-26, 7-27, 7-28
For this assignment I develop and either pseudo code or a flowchart for my following programming problem.
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b) It also consumes the least amount of time in all the cases (approx.) since its best and worst case performance are O(n log n)
This assignment consists of two (2) parts: a written paper and a PowerPoint presentation. You must submit both parts as separate files for the completion of this assignment. Label each file name according to the section of the assignment it is written for. Additionally, you may create and / or assume all necessary assumptions needed for the completion of this assignment.
This file contains the exercises, hints, and solutions for Chapter 1 of the book ”Introduction to the Design and Analysis of Algorithms,” 2nd edition, by A. Levitin. The problems that might be challenging for at least some students are marked by ; those that might be difficult for a majority of students are marked by .
2) Calculate following values recursively. ae + bg, af + bh, ce + dg and cf + dh.
Answer each problem thoroughly. Each problem is worth 10 points. Make sure to provide detailed explanations for each part of each problem.
We can list these numbers in the order 1, −1, 2, −2, 4, −4, 5, −5, 7, −7, ... , thereby establishing the desired correspondence.
F = { (1+2), (3+ 5), (4+7)} = { (3) + (8) + (11)} = 22
14 x C-H (412) + 4 x C-C (348) + 2 x C-O (360) + 2 x O-H (463) + 9 x O=O (498) 12 x C=O (805) + 16 x O=H (463)
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