UMBC CMSC441, Design & Analysis of Algorithms, Fall 2014


Homework 2

Due Thursday, September 11, 2014

  1. For each pair of functions below, use O( ), Ω( ), Θ( ), o( ) or ω( ) to describe the relationship between the two functions. E.g., say "n2 + 3n is O(n2)". Make the most accurate statement. E.g., "n2 is o(n3)" is more accurate than "n2 is O(n3)". Briefly justify your answers.

  2. Consider the recurrence relation:
    T(n) = 6 T(n/3) + 3 n
    Use the substitution method to show that:

    1. T(n) ≤ n2

    2. T(n) ≥ n1.5

    Show all of your work.

  3. Use the recursion tree method to find an upper bound for
    T(n) = 7 T(n/2) + n2
    Show all of your work.


Last Modified: 3 Sep 2014 13:16:09 EDT by Richard Chang
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