CS107 - Lab 3
Given an algorithm that solves a problem, how do we measure its efficiency?
How do we know that one algorithm is more efficient than another? This lab
helps understand the measurement of algorithm efficiency and its
The (suggested) reading for this lab is (part of) Chapter 3 in the SG
Designing and analyzing algorithms
- Algorithms A and B perform the same task. On input of size n,
algorithm A executes 0.003n2 instructions, and
algorithm B executes 243n instructions. Write their efficiencies
using Theta-notation. Is algorithm B more efficient than algorithm A? Find
the approximate value of n above which algorithm B is more efficient .
- At about what value of n does an algorithm that does
100 n2 instructions become more efficient than one that
does 0.01x2n instructions? Use a calculator.
- An algorithm that is Theta(n) takes 10 seconds to execute
on a particular computer when n=100. How long would you expect it
to take when n=500?
- An algorithm that is Theta(n2) takes 10 seconds
to execute on a particular computer when n=100. How long would you
expect it to take when n=500?
- Here is a list of seven names:
Sherman, Jane, Ted, Elise, Raul, Maki, John
Search this list for each name in turn, using sequential search, and count
the number of comparisons for each name (Note: in class we counted
the total number of instructions; for simplicity, in this problems
you count comparisons). Now take the seven comparison counts and find their
average. Use this to find the (approximate) average number of comparisons
needed to find a name in an n-element list, and briefly explain why.
- If a list is already sorted in increasing order, a modified
sequential search algorithm can be used that compares against each element
in turn, stopping if a list element exceeds the target value. Write a
pseudocode version of this short sequential search.
- What is the worst-case number of comparisons of the short
sequential search algorithm above on a sorted list of n elements?
- Assume that we search once for each element in sorted input list
using the short sequential search algorithm above. What is the approximate
average number of comparisons to find an element?
- Is the short sequential search algorithm above ever more efficient
than regular sequential search? Explain.
- Consider the following problem (the bin-packing problem): Suppose we
have an unlimited number of bins of volume 1 unit, and n objects,
all of volume between 0.0 and 1.0. We would like to find
the minimum number of bins needed to store the n objects. A
solution algorithm for this problem would be of interest to any
manufacturer who ships sets of various items in standard-sized cartons, or
to anyone who wants to store image files on a set of CDs in the most
efficient way. Sketch an algorithm to solve this problem. For this
particular problem we do not care so much about writing the algorithm in
(correct) pseudocode, but rather on what the idea of the algorithm is. You
can describe your algorithm in a paragraph if you prefer, rather than use
What to turn in:
- The 10 problems in the Designing Algorithms section.
Be sure to justify your answers! You may do this work either with a
word processor or by hand. If you type your solutions, bring a hard copy of
your assignment and hand it in class. If you write by hand, do your best to
write legibly and leave space between problems.
You may choose to do this assignment either by yourself or in a
group. However, solutions should be written up individually and handed in
on the due date, at the beginning of class.
Once you are finished in the lab, if you want to save any
documents, you'll have to drag them to your network folder (mounted to
Files left on the desktop and in your local folder (on the local
machine) will be erased!