Problem solving

Algorithms and
Problem Solving

• Learn about problem solving skills
• Explore the algorithmic approach for
problem solving
• Learn about algorithm development
• Become aware of problem solving process
Lecture Objectives

Problem Solving
• Programming is a process of problem
solving
• Problem solving techniques
 Analyze the problem
 Outline the problem requirements
 Design steps (algorithm) to solve the problem
• Algorithm:
 Step-by-step problem-solving process
 Solution achieved in finite amount of time

Problem Solving Process
• Step 1 - Analyze the problem
 Outline the problem and its requirements
 Design steps (algorithm) to solve the problem
• Step 2 - Implement the algorithm
 Implement the algorithm in code
 Verify that the algorithm works
• Step 3 - Maintenance
 Use and modify the program if the problem
domain changes

Analyze the Problem
• Thoroughly understand the problem
• Understand problem requirements
 Does program require user interaction?
 Does program manipulate data?
 What is the output?
• If the problem is complex, divide it into
subproblems
 Analyze each subproblem as above

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

• Before a computer can perform a task, it must
have an algorithm that tells it what to do.
• Informally: “An algorithm is a set of steps that
define how a task is performed.”
• Formally: “An algorithm is an ordered set of
unambiguous executable steps, defining a
terminating process.”
 Ordered set of steps: structure!
 Executable steps: doable!
 Unambiguous steps: follow the directions!
 Terminating: must have an end!
What is an algorithm? (Cont’d)

What is an algorithm? (Cont’d)

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

Representation of Algorithms
• A single algorithm can be represented in
many ways:
 Formulas: F = (9/5)C + 32
 Words: Multiply the Celsius by 9/5 and add 32.
 Flow Charts.
 Pseudo-code.
• In each case, the algorithm stays the same;
the implementation differs!

 A program is a representation of an algorithm
designed for computer applications.
 Process: Activity of executing a program, or execute
the algorithm represented by the program
  Process: Activity of executing an algorithm.
Representation of Algorithms (Cont’d)

Expressing Algorithms
• English description
• Pseudo-code
• High-level
programming
language
More
precise
More easily
expressed

• Pseudocode is like a programming language
but its rules are less stringent.
• Written as a combination of English and
programming constructs
 Based on selection (if, switch) and iteration (while,
repeat) constructs in high-level programming
languages
• Design using these high level primitives
 Independent of actual programming language
Pseudocode

Example: The sequential search algorithm in
pseudocode
Pseudocode (Cont’d)

Algorithm Discovery
• The Two Steps of Program Development:
 1. Discover the algorithm.
 2. Represent the algorithm as a program.
• Step 2 is the easy step!
• Step 1 can be very difficult!
• To discover an algorithm is to solve the
problem!

Problem Solving: A creative process
• Problem solving techniques are not unique
to Computer Science.
• The CS field has joined with other fields to
try to solve problems better.
• Ideally, there should be an algorithm to
find/develop algorithms.
• However, this is not the case as some
problems do not have algorithmic solutions.
• Problem solving remains an art!

Problem Solving Strategies
• Working backwards
 Reverse-engineer
 Once you know it can be done, it is much easier to do
 What are some examples?
• Look for a related problem that has been solved before
 Java design patterns
 Sort a particular list such as: David, Alice, Carol and Bob
to find a general sorting algorithm
• Stepwise Refinement
 Break the problem into several sub-problems
 Solve each subproblem separately
 Produces a modular structure
• K.I.S.S. = Keep It Simple Stupid!

Stepwise Refinement
• Stepwise refinement is a top-down methodology
in that it progresses from the general to the
specific.
• Bottom-up methodologies progress from the
specific to the general.
 These approaches complement each other
• Solutions produced by stepwise refinement
posses a natural modular structure - hence its
popularity in algorithmic design.

Object-Oriented Design Methodology
• Four stages to the decomposition process
 Brainstorming
 Filtering
 Scenarios
 Responsibility algorithms

Class-Responsibility-Collaboration (CRC) Cards

Brainstorming
• A group problem-solving technique that
involves the spontaneous contribution of
ideas from all members of the group
 All ideas are potential good ideas
 Think fast and furiously first, and ponder later
 A little humor can be a powerful force
• Brainstorming is designed to produce a list
of candidate classes

Filtering
• Determine which are the core classes in the
problem solution
• There may be two classes in the list that
have many common attributes and behaviors
• There may be classes that really don’t belong
in the problem solution

Scenarios
• Assign responsibilities to each class
• There are two types of responsibilities
 What a class must know about itself (knowledge)
 What a class must be able to do (behavior)
• Encapsulation is the bundling of data and
actions in such a way that the logical
properties of the data and actions are
separated from the implementation details

Responsibility Algorithms
• The algorithms must be written for the
responsibilities
 Knowledge responsibilities usually just return the
contents of one of an object’s variables
 Action responsibilities are a little more complicated,
often involving calculations

Computer Example
• Let’s repeat the problem-solving process for
creating an address list
• Brainstorming and filtering
 Circling the nouns and underlining the verbs

• First pass at a list of classes
Computer Example (Cont’d)

• Filtered list
Computer Example (Cont’d)

Problem solving

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