CPS 120: Introduction to Computer Science

Algorithm Design

and

Problem Solving

Session Goals

• Determine whether a problem is suitable for a computer solution

• Describe the computer problem-solving process

• Distinguish between following an algorithm and developing one

• Apply top-down design methodology to develop an algorithm to solve a problem

Analyze the problem

Design the solution algorithm

Design the user interface

Write the code

Test and debug the program

Complete the documentation

The Program Development Cycle

Problem Solving

• Problem solving is the act of finding a solution to a perplexing, distressing, vexing, or unsettled question

Problem Solving

• In 1945 George Polya wrote How to Solve It: A New Aspect of Mathematical Method

• His How to Solve It list is quite general – Written in the context of solving

mathematical problems– The list becomes applicable to all

types of problems

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?

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

Divide and Conquer

• Break up a large problem into smaller units that we can handle

– Applies the concept of abstraction

– The divide-and-conquer approach can be applied over and over again until each subtask is manageable

Computer Problem-Solving

The computer problem-solving process

The Interactions Between Problem-Solving Phases

Analyze the problem

Design the solution algorithm

Design the user interface

Write the code

Test and debug the program

Complete the documentation

The Program Development Cycle

Algorithms

• Muhammad ibn Musa Al'Khowarizmi, a Tashkent cleric who in the twelfth century developed the concept of a written process to be followed to achieve some goal, and published a book on the subject that gave it is modern name -- algorithm.

What is an Algorithm?

• An algorithm is merely the sequence of steps taken to solve a problem– Two parts

• Actions to be executed • Order in which those actions are to be done

– Computational steps that transform the input data into useful output data.

• Algorithms are not programs– They need to be coded in a programming language like

C++, Visual Basic, COBOL, Java, etc.

Algorithms

• An algorithm is set of instructions for solving a problem or sub-problem in a finite amount of time using a finite amount of data

• The instructions are unambiguous

Following an Algorithm

• Preparing a Hollandaise sauce

Following an Algorithm (cont.)

• Preparing a Hollandaise sauce

Programs are Solutions to Problems

• Programmers arrive at these solutions by using one or more of these devices:

• Structured Programming

• Structure charts

• Logic flowcharts

• Pseudocode (sue-dough'-code)

• Solutions to problems need to be developed before code is written

Developing an Algorithm

• The plan must be suitable in a suitable form

• Two methodologies that currently used– Top-down design – Object-oriented design

Structured Programming

• Structured program languages lend themselves to flowcharts, structure charts, and pseudocode.

• Structured programming languages work best where the instructions have been broken up into small, manageable parts.

Top-Down Design

• Breaking the problem into a set of sub-problems called modules

• Creating a hierarchical structure of problems and sub-problems

Structure Charts

• Structure charts illustrate the structure of a program by showing independent hierarchical steps.

• Major divisions are subdivided into smaller pieces of information.

Top-Down Design

• 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

An example of top-down design

A General Example

• Planning a large party

Subdividing the party planning

Flowcharts and Pseudocode

• Forms of documentation used to build and communicate the detailed parts your structured designs

Flowchart

• A graphical representation of an algorithm.

Pseudocode

• Uses a mixture of English and formatting to make the steps in the solution explicit

Flowcharts & Pseudocode are Important

• Flowcharts – – A graphical layout of the algorithm is often very useful

in spotting “illogical” logic!

• Pseudocode – – Make a detailed description of your algorithm’s logic

before worrying about syntax and data layout.

– An algorithm you develop using pseudocode should be capable of implementation in any procedural programming language

• Pseudocode is generally independent of the implementation language

Reasons Programmers Draw Flowcharts

• Drawing a flowchart gives the programmer a good visual reference of what the program will do

• Flowcharts serve as program documentation• Flowcharts allow a programmer to test alternative

solution to a problem before coding • Flowcharts provide a method for easy desk

checking

Logic Flowcharts

• These represent the flow of logic in a program and help programmers “see” program design.

Terminator. Shows the starting and ending points of the program. A terminator has flow lines in only one direction, either in (a stop node) or out (a start node).

Data Input or Output. Allows the user to input data and results to be displayed.

Processing. Indicates an operation performed by the computer, such as a variable assignment or mathematical operation. With a heading – an internal subroutine

Decision. The diamond indicates a decision structure. A diamond always has two flow lines out. One flow lineout is labeled the “yes” branch and the other is labeled the “no” branch.

Predefined Process. One statement denotes a group of previously defined statements. Such as a function or a subroutine created externally

Connector. Connectors avoid crossing flow lines, making the flowchart easier to read. Connectors indicate where flow lines are connected. Connectors come in pairs, one witha flow line in and the other with a flow line out.

Off-page connector. Even fairly small programs can have flowcharts that extend severalpages. The off-page connector indicates the continuation of the flowchart on another page. Just like connectors, off-page connectors come in pairs.

Flow line. Flow lines connect the flowchart symbols and show the sequence of operations during the program execution.

Common Flowchart Symbols

Common Flowchart Symbols

How to Draw a Flowchart• Five steps which can be used as a guide for

completing flowcharts. 1. Start with a 'trigger' event (it may be the beginning of

the program)

2. Initialize any values that need to be defined at the start of the program

3. Note each successive action concisely and clearly

4. Go with the main flow (put extra detail in other charts -- this is the basis of structured programming)

5. Follow the process through to a useful conclusion (end at a 'target' point -- like having no more records to process)

Rules for Drawing Flowcharts

• Top to bottom and left to right– Draw the flowchart the way you like to read– Use arrowheads on flow lines whenever the

flow is not top to bottom, left to right

• Be neat ! Use graphics software

• Avoid intersecting lines

Start

Variables =

Open Files

Moreitems?

ProcessRecord

(Detail Time)

WriteRecord

Stop

No

Yes

Sample Program FlowchartTerminal Symbol

I/O Symbol

Process Symbol

Decision Symbol

Preparation Symbol or Initialize Variables

Read aRecord

CloseFiles

ProcessRecord

(Total Time)

Disadvantages to Flowcharts

• Time consuming

• A program flowchart shows how the input becomes output, but it does not show why a particular step is done

• Flowcharts are subjective

Pseudocode

• Pseudocode is an artificial and informal language that helps programmers develop algorithms. – Pseudocode is a "text-based" detail

(algorithmic) design tool. – An English description of an algorithm in

sufficient detail to allow its implementation to be easily written.

Pseudocode

• This device is not visual but is considered a “first draft” of the actual program.

• Pseudocode is written in the programmer’s native language and concentrates on the logic in a program—not the syntax of a programming language.

General Rules for Pseudocode

• There is no standard pseudocode

• The rules of Pseudocode are generally straightforward– Should be easily read and understood by non-

programmers – All statements showing "dependency" are to be

indented. • These include while, do, for, if, switch

Writing Pseudocode

• You need to reach a balance between excessive and insufficient detail. – Write only what is necessary to understand and

communicate the essential parts of your algorithm

Pseudocode Statement Rules– Statements are written in a simple English-like

language– Each instruction is started on a separate line– Logic-showing keywords are written in UPPER CASE

or typed in BOLD UPPERCASE• (e.g. IF, THEN, FOR, DO etc.)• These are the only uppercase words in this form of

pseudocode.

– Indentation is used to show structure– Instructions are written from top to bottom, with only

one entry point and one exit point– Logically related groups of instructions can be formed

into modules and given a name

STARTIntialize variablesLOOPWhile More records do READ record PROCESS record PRINT detail recordENDLOOPCALCULATE TOTALSPRINT total recordEND

Pseudocode for a Generalized Program

Rules for Pseudocode1. Make the pseudocode language-independent

2. Indent lines for readability

3. Make keywords stick out by showing them capitalized, in a different color or a different font

4. Punctuation is optional

5. End every IF with ENDIF

6. Begin loop with LOOP and end with ENDLOOP

7. Show MAINLINE first; all others follow

8. TERMINATE all routines with an END instruction

A Computer Example

• Problem

– Create an address list that includes each person’s name, address, telephone number, and e-mail address

– This list should then be printed in alphabetical order

– The names to be included in the list are on scraps of paper and business cards

A Computer Example

A Computer Example

A Computer Example

A Computer Example

A Computer Example

Relation of Flowcharts & Pseudocode

Analyze the problem

Design the solution algorithm

Design the user interface

Write the code

Test and debug the program

Complete the documentation

The Program Development Cycle

Data Processing

• Facts enter the computer

• They are:– Checked for accuracy– Organized– Calculated with– Stored