1 Foundations of Software Design Fall 2002 Marti Hearst Lecture 9: Algorithms and Pseudo-code

1

Foundations of Software DesignFall 2002Marti Hearst

Lecture 9: Algorithms and Pseudo-code

2

The central role of algorithms in computer science

From Brookshear; Copyright 2003 Pearson Education

3

What is an algorithm?

• The idea behind the computer program• Stays the same independent of

– Which kind of hardware it is running on– Which programming language it is written in

• Solves a well-specified problem in a general way• Is specified by

– Describing the set of instances (input) it must work on– Describing the desired properties of the output

Adapted from http://www.cs.sunysb.edu/~algorith/lectures-good/node1.html

4

Brookshear: The definition of an algorithm


The terminating part comes from theoretical considerations.

5

Important Properties of Algorithms

• Correct– always returns the desired output for all legal

instances of the problem.

• Unambiguous• Precise • Efficient

– Can be measured in terms of• Time• Space

– Time tends to be more important


6

Algorithms

• Hand-waving not allowed!

• Specifying algorithms requires you to say what is really involved in making it work.

• Example:– How does a computer work?– Hand-wave: zeros & ones – Real answer: see first three weeks of class.

• You learn to know when you don’t know– “I know nothing except the fact of my ignorance.”– Socrates, from Diogenes Laertius, Lives of Eminent Philosophers

7

Expressing Algorithms

• English description

• Pseudo-code

• High-level programming language

More precise

More easily expressed


8

Pseudo-code

• A shorthand for specifying algorithms• Leaves out the implementation details• Leaves in the essence of the algorithm

<

Code corrected from Brookshear; Copyright 2003 Pearson Education

9

Sequential search algorithm in pseudo-code


10

Origami as Algorithm: Folding a bird from a square piece of paper.


11From Brookshear; Copyright 2003 Pearson Education

Origami as Algorithm: Folding a bird from a square piece of paper.

12

Origami primitivesSyntax vs. Semantics


13

Origami primitivesSyntax vs. Semantics


14

Primitive Operations

• Assign a value to a variable• Call a method• Arithmetic operation• Comparing two numbers• Indexing into an array• Following an object reference• Returning from a method

15

The RAM Model

• Random Access Machine (not Memory)• An idealized notion of how the computer works

– Each "simple" operation (+, -, =, if) takes exactly 1 step.

– Each memory access takes exactly 1 step– Loops and method calls are not simple operations,

but depend upon the size of the data and the contents of the method.

• Measure the run time of an algorithm by counting the number of steps.


16

Counting Primitive Operations

Algorithm ArrayMax(A,n)Input: An array A storing N integersOutput: The maximum element in A.

currentMax A[0]for i 1 to n-1 do

if currentMax < A[i] then currentMax A[i]

return currentMax

Adapted from Goodrich & Tamassia

17

Counting Primitive Operations

Algorithm ArrayMax(A,n)Input: An array A storing N integersOutput: The maximum element in A.

currentMax A[0]for i 1 to n-1 do

if currentMax < A[i] then currentMax A[i]

return currentMax

2 steps + 1 to initialize i

2 steps

2 steps

1 step

2 step each time (compare i to n, inc i)n-1 times

How often done??

It depends on the order the numbers appear in in A[]

Between 4(n-1) and 6(n-1) in the loop

Adapted from Goodrich & Tamassia

18

Algorithm Complexity

• Worst Case Complexity:– the function defined by the maximum number of

steps taken on any instance of size n

• Best Case Complexity:– the function defined by the minimum number of

steps taken on any instance of size n

• Average Case Complexity:– the function defined by the average number of steps

taken on any instance of size n


19

Problem Solving

• Polya’s Advice– Understand the problem– Devise a plan for solving the problem– Carry out the plan– Evaluate the solution for accuracy

• Reality– They are intermixed– Sometimes don’t know the full problem statement

until a solution is found!

20

Problem Solving Strategies

• Try to work the problem backwards – Reverse-engineer– Once you know it can be done, it is much easier to do– What are some examples?

• Stepwise Refinement– Break the problem into several sub-problems– Solve each subproblem separately– Produces a modular structure

• Look for a related problem that has been solved before– Java design patterns

21

Example of Stepwise RefinementSpiderman

• Peter Parker’s goal: Make Mary Jane fall in love with him

• To accomplish this goal:– Get a cool car– To accomplish this goal:

• Get $3000• To accomplish this goal:

– Appear in a wrestling match …

• Each goal requires completing just one subgoal

22

Example of Stepwise RefinementStar Wars Episode IV

• Luke Skywalker’s goal: Make Princess Leia fall in love with him (they weren’t siblings yet)

• To accomplish this goal:– Rescue her from the death star– To accomplish this goal:

1. Land on Death Star2. Remove her from her Prison Cell3. Disable the Tractor Beam4. Get her onto the Millennium Falcon

– To accomplish subgoal (2)• Obtain Storm Trooper uniforms

– Have Wookie pose as arrested wild animal• Find Location of Cell

– Have R2D2 communicate coordinates– To accomplish subgoal (3)

• Have last living Jedi walk across catwalks – To accomplish subgoal (4)

• Run down hall• Survive in garbage shoot

– Fight garbage monster – Have R2D2 stop compaction …

23

Practice Stepwise Refinement + Pseudo-code

• Recipe for Strawberry Rhubarb Pie• Define Pseudo-code at different levels of

description

24

Pair Programming

• Two people programming together• Both are engaged• Only one keyboard and mouse• NOT working separately and then joining

results.• Advantages?

– Prevent bugs– Better code– Mutual learning– Almost as fast as two independent programmers

Documents

1 Foundations of Software Design Fall 2002 Marti Hearst Lecture 9: Algorithms and Pseudo-code