Computer Science 112 Spring 2015

Gregory M. Kapfhammer

Introduction to Computer Science II

Algorithms

Correctness

Performance

How fast is an algorithm?

Try some examples!

for loops

Constant

Linear

Quadratic

Cubic

git pull

CLASSPATH

Compile

Run!

Results?

Conclusions?

Algorithm

Function

Draw a Graph

Slow growing

Fast growing

Function Exploration

Add in exponential

Add in factorial

Plot the functions

Create a table of values

Fastest Growth?

Slowest Growth?

Conclusions?

Implications?

Take a step back

Limitations of empirical studies

Direct Comparison

Limited Inputs

Fully Implemented

Characterize programs as functions of input size

Hands-on Example

Largest Integer?

Largest Double?

How did you determine?

Computing Sums

Correct?

Incorrect?

Conduct an Experiment

Efficient?

Inefficient?

Why?

Pseudo code

When n gets big

Revisit computing sums

Best, Worst, Average

Worst-Case Graph

f(n) is O(g(n))

f(n) is O(g(n))

f(n) is O(g(n))

f(n) is O(g(n))

Does this really matter?

Composing Long Strings

String concatenation

Which is faster?

repeat1 vs. repeat2

Why?

Additional examples

ArrayMax

ArrayFind

Worst-Case time complexity?

Why?

Run an experiment

Analysis confirmed?