CMPSCI 250: Introduction to Computation

David Mix Barrington

Fall, 2010

Homework Assignment #4

Posted Wednesday 27 October 2010

Due on paper in (lecture) class, Tuesday 9 November 2010

There are fifteen questions for 100 total points plus 10 extra credit. All are from the textbook, Mathematical Foundation for Computer Science, some from Volume I and some from Volume II. Note that the book has both Exercises and Problems -- make sure you are doing a Problem and not the Exercise with the same number. The number in parentheses following each problem is its individual point value.

Students are responsible for understanding and following the academic honesty policies indicated on this page.

Errors in Problem 9.4.5 corrected on 2 November 2010.

Typos corrected 3 November 2010 -- 9.1.1 and 9.1.5 are assigned, not 9.11.1 and 9.11.5.

Errors in Problems 9.3.1 and 9.6.3 corrected 8 November 2010.

• Problem 4.3.4 (10)

• Problem 4.4.4 (5)

• Problem 4.7.5 (10)

• Problem 4.9.3 (5)

• Problem 4.11.1 (5)

• Problem 4.11.2 (10)

• Problem 9.1.1 (5)

• Problem 9.1.5 (10)

• Problem 9.3.1 (5) The return type of foo should be integer rather than natural, because this function does (and should) return some negative values.

• Problem 9.3.2 (10) Instead of "Exercise T.2.2" it should say "Exercise 9.3.2".

• Problem 9.4.3 (10)

• Problem 9.4.4 (5XC)

• Problem 9.4.5 (5XC) Here "positions" means "Rubik's cube positions", as in Problem 9.4.4. The problem is actually not correctly stated. The expression should be "1 + 18 + 18(15) + 18(15²) + ... + 18(15^k-1)" and the bound should be 16 moves rather than 18. The bound of 18 requires a more careful analysis that I don't want to make you do.

• Problem 9.5.3 (5)

• Problem 9.6.3 (10) There is a mistake in the problem statement. Instead of "no edges between siblings", it should say "no edges between nodes at the same depth". See the Q and A page for more.