Homework 1

  • Assigned: Tuesday, September 6, 2011
  • Due: Friday, September 16, 2011
  • Required for Undergraduates: 4 of the following 5 problems 
  • Required for Graduate Students: 4 of the following 5 problems 
  • Points: 10 pts per problem
  • General Instructions: 
  1. Please review the homework and grading policy outlined in the course information and homework page.
  2. Mark your homework with your UNI, and use a separate page for each problem.
  3. On the first page of your solution write-up (with problem 1, whether or not you attempted it), you must make explicit which problems are to be graded for "regular credit", which problems are to be graded for "extra credit", and which problems you did not attempt. Please use a table something like the following

    Problem 01 02 03 04 05 06 07 08 09 ...
    Credit RC RC RC EC RC RC NA RC RC ...

    where "RC" is "regular credit", "EC" is "extra credit", and "NA" is "not attempted" (not applicable). Failure to do so will result in an arbitrary set of problems being graded for regular credit, no problems being graded for extra credit, and a five percent penalty assessment.

  4. You must also write down with whom you worked on the assignment. If this changes from problem to problem, then you should write down this information separately with each problem.
  5. Start early, be concise but rigorous, and enjoy!
  • Specific Instructions:
  1. Be sure to review any parts of Chapters 1-4 with which you are not familiar.
  2. All logs are base 2 unless otherwise specified.
  3. Unless otherwise specified, all problems and exercises are from CLRS, Introduction to Algorithms, 3rd edition.
  • Problems:
  1. Exercise 2-3-7. Finding numbers with a given sum.
  2. Problem 2-3. Horner's Rule
  3. Exercises 3.2-1, 3.2-5
  4. Problem 3-4 b, e, f, g. Big-O notation.
  5. Place the following functions by order of growth, from smallest to largest. For each adjacent pair in the list, give a proof that the earlier one is assymptotically smaller than the second, by giving a big-O proof.
    • n
    • n4
    • n.99
    • 2n
    • 3n/2
    • 2lg lg n
    • lg2 n
    • lg4 n
    • 16lg n
    • 16 n - 5 lg n
    • (lg n)lg n / lg lg n