VCSG 800 Algorithms
Homeworks, Dates
Spring 2013

Homework 1 ( pdf ), due Thursday, March 21

Homework 2, due Tuesday, April 2

  1. Exercise 2.3-7 page 39. Be brief, but to the point.
  2. Exercise 3.2-5 page 60 (lg*).
  3. Solve exercise 3.2-7 page 60 from CLRS (Fibonacci).
  4. Solve exercise 4.2-1 page 82 from CLRS (Strassen).
  5. Solve exercise 4.2-4 page 82 from CLRS (Strassen).
  6. Determine all LCS's of the sequences BACBCAB and ABCCBA.
    Draw a diagram similar to that in Figure 15.8 page 395, but mark also all the ties.
  7. Solve exercise 15.4-5 page 397 from CLRS (LCS-like).


Homework 3, due Thursday, April 11

This homeworks is to be handed in right before the midterm exam.

Solve the following exercises and problems:

  1. Find an optimal parenthesization of a matrix-chain product whose sequence of dimensions is < 6, 20, 50, 12, 3, 22, 25>. Show triangular matrices m[i,j] and s[i,j]. Show the details of computation for m[1,6], and how to use s[1,6] to obtain the final result.
  2. Exercise 15.3-2 page 389. Be brief, but justify your answer.
  3. Exercise 15.3-5 page 390.
  4. Given
    C_n = \frac{1}{n+1}{2n\choose n} = \frac{(2n)!}{(n+1)!\,n! } \qquad\mbox{ for }n\ge 0,

    show that the following hold for Catalan numbers:

    C_0 = 1 \quad \mbox{and} \quad C_{n+1}=\frac{2(2n+1)}{n+2} C_n,
    and
    C_n = {2n\choose n} - {2n\choose n-1} \quad\mbox{ for }n\g e 1.
  5. Trace the behaviour of the recursive Hirschberg's quadratic-time linear-space Algorithm C on the strings ABACBB and ABABBBC. It is enough to show in detail only the main level of recursion of Algorithm C.


Midterm Exam, Thursday, April 11, in class


Homework 4 ( pdf ) due Thursday, May 2


Final Exam, Monday, May 13, 12:30-2:30pm, 70-1455


Back to the course page