041/26
•
Algorithm costs: time, space, and energy
•
Best case, worst case, average case analysis
•
Counting instructions and asymptotic analysis
•
BigO, bigOmega, bigTheta notation
•
Introduction to algorithm measurement
CSE 12
Analysis and Measurement of Algorithms
Writing good software
•
Keep in mind the characteristics of good software:
–
robustness
: a program’s ability to spot exceptional
conditions and deal with them or shutdown
gracefully
–
correctness
: does the program do what it is
supposed to do?
–
efficiency
: all programs use resources (time and
space and energy, i.e. CPU cycles and memory
and battery or wall power); how can we measure
efficiency so that we can compare algorithms?
Cost functions
An algorithm’s performance can be described by:
–
time
complexity or cost – how long it takes to
execute. In general, less time is better!
–
space
complexity or cost – how much computer
memory it uses.
In general, less space is better!
–
energy
complexity or cost – how much energy
uses.
In general, less energy is better!
•
Costs are usually given
as functions of the size of the
input
to the algorithm
•
A big instance of the problem will probably take more
resources to solve than a small one, but how much
more?
Determining algorithm costs
•
For a given algorithm, if the size of the input
is
n
, we
would like to know:
x
T(
n
) , the time cost of solving the problem
x
S(
n
) , the space cost of solving the problem
x
E(
n
) , the energy cost of solving the problem
•
Two approaches:
–
We could implement the algorithm and run it and
measure
the time, memory, and energy usage
–
Or we can
analyze
the written algorithm
Algorithm cost analysis
•
To perform algorithm time cost analysis:
–
Write down the algorithm that solves the problem
–
Decide what “size of the problem” means for this kind of problem
–
Count
up the number of instructions the algorithm would execute,
as a function of
n
, the size of the problem it is solving
•
Note that different languages for writing the same
algorithm might require a different number of instructions
–
Java will probably require fewer than C which will require fewer
than assembly language, etc.
•
So, a
precise
count of the number of instructions is,
arguably, too much detail… we will need to consider how
to abstract away from nonessential detail
Algorithm cost cases
•
Sometimes it’s useful to distinguish among different
cases
that can occur when running a given algorithm to
solve a problem of size
n
•
Best case
:
for all inputs of size
n
, which one has the
lowest cost?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Summer '08
 Gary
 Algorithms, Big O notation, Analysis of algorithms, energy cost, time cost

Click to edit the document details