Transcript Problem Solving and Algorithm Design Problem Solving Problem solving The act of finding a solution to a perplexing, distressing, vexing, or unsettled question. Problem Solving G.

Problem Solving
and Algorithm Design
Problem Solving
Problem solving
The act of finding a solution to a
perplexing, distressing, vexing, or
unsettled question.
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Problem Solving
G. Polya wrote How to Solve It: A New
Aspect of Mathematical Method
His “How to Solve It” list is quite general.
– It’s written in the context of solving
mathematical problems.
– With simple wording changes the list becomes
applicable to all types of problems.
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1 - Ask Questions...
…to understand the problem:
– What do I know about the problem?
– What is the information that I have to process
in order the find the solution?
– What does the solution look like?
– What sort of special cases exist?
– How will I recognize that I have found
the solution?
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2 - Look for Familiar
Things
You should never “reinvent the wheel”.
In computing, you see certain problems again
and again in different guises.
A good programmer sees a task,
or perhaps part of a task (a subtask),
that has been solved before and plugs
in the solution.
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3 - Divide and Conquer
Break up a large problem into smaller units
that can be handled more easily.
– Abstraction plays an important role.
– The divide-and-conquer approach can be
applied over and over again until each subtask
is manageable.
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Abstraction
Abstraction (n.) - A mental model that
removes complex details.
This is a key concept. Abstraction will
reappear throughout the course – be sure
you understand it!
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Algorithms
Algorithm:
A set of instructions for solving a problem
or subproblem in a finite amount of time
using a finite amount of data.
The instructions must be unambiguous.
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Example of an Algorithm
Preparing a Hollandaise sauce
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Pseudocode
… uses a mixture of English and formatting to make
the steps in the solution explicit.
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Developing an Algorithm
Since implementing the algorithm involves
making it computer-readable, the plan
must be in a suitable form.
The methodology (set of working methods)
used to make the plan must begin with a
problem statement and conclude with a
plan that can be easily coded.
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Developing an Algorithm
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Two methodologies are currently used,
both based on the divide-and-conquer
strategy:
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Top-Down Design
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(functional decomposition)
Object-Oriented Design
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(OOD)
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Top-Down Design
… consists of breaking the problem into a set of
subproblems called modules.
It creates a hierarchical structure of problems and
subproblems (modules).
This process continues for as many levels as it takes
to expand every task to the smallest details.
A step that needs to be expanded is an abstract step.
One that doesn’t need expansion is a concrete step.
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Top-Down Design
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Object-Oriented Design
Object-oriented design is the process of
planning a system of interacting objects
for the purpose of solving a software
problem.
An object is an exemplar of a class.
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Object-Oriented Design
A class defines the abstract characteristics of
a thing (object), including it's properties
and the things it can do, or methods.
One might say that a class is a blueprint that
describes the nature of something.
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Object-Oriented Design
Assume a class called DOG, which defines
all possible dogs by listing the
characteristics and behaviours they have.
The object Lassie is one particular dog, with
particular versions of the characteristics.
A Dog has fur; Lassie has fur.
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Object-Oriented Design
Notice that fur is also an object.
It has characteristics of its own.
Lassie’s is long, and brown and white.
But fur is also a class!
- a blueprint for anything that can be called fur.
There is no heirarchical organisation of the Object
Oriented concepts.
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Object-Oriented Design
Programming techniques include features such as:
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information hiding,
data abstraction,
encapsulation,
modularity,
polymorphism,
and inheritance.
We will see examples of many of these in the
exercises.
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Testing the Algorithm
Regardless of the design methodology, the
algorithm itself must be tested.
Testing at the algorithm development phase
involves looking at each part of the design
independently, and at how they are
coupled.
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Testing the Algorithm
Large scale programming is conducted in teams.
Divide-and-Conquer strategies makes it possible
to assign subtasks to team members, who
independently develop solutions.
In this environment, design testing is often done in
team meetings, using the method of Inspection.
Inspection: One person (not the designer) reads the design
(handed out in advance) line by line while the others
point out problems.
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Testing the Algorithm
Modern languages have been designed to reduce the
time it takes use them, but any powerful language
requires significant time to become an effective
programmer.
VB allows us to use a prototype approach –
to try code segments and see how they work,
without a lot of Desk Checking of algorithms.
Desk checking: Working through a design at a desk
with a pencil and paper.
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Testing the Algorithm
Unfortnately, our prototypes don’t always
work the first time. So even though it’s
easy to get started, we often need to test
our designs to find their errors.
A useful technique here is the Walk-through.
Walk-through: Manual simulation of the design,
taking sample data values and tracing them
through its steps to see what actually happens.
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