Alogorithm & Prolem Solving

Algorithms Problem Solving

Topic & Structure of the lesson Design

In this chapter you will learn about: • Problem Solving • Algorithm • Pseudocodes • Flowcharts

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Key Terms you must be able to use Design

If you have mastered this topic, you should be able to use the following terms correctly in your assignments and exams: • program • pseudocode • flowchart • algorithm PSPD Using C

Problem Solving Techniques Design

In this chapter you will learn about:

 What problem solving is  The software development method of 

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problem solving using computers Basic algorithm control structures  The sequence structure  The selection structure  The repetition structure

Problem Solving Techniques Design

By the time you have completed this chapter,you will have acquired the ability to:

 Apply the software development method to solve problems

 Difference between the Algorithm & the Flowchart  Knowing about the control structures PSPD Using C

Problem Solving Design

UNDERSTANDING THE PROBLEM First:

What is the unknown? What are the data?What is the condition? You have to understand the Is it possible to satisfy the condition?Is the condition sufficient to determine the unknown?Or problem. is it sufficient?Or Redundant? Or Contradictory? Draw a figure.Introduce suitable notation.Separate the various parts of the condition.Can you write them down?

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Problem Solving Design

DEVISING A PLAN Second: Find the connection between the data and the unknown. Auxiliary problems may be devised if needed. You should obtain eventually a plan of the solution.

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Have you seen it before? Or have you seen the same problem in slightly different form? Do you know a related problem? Look at the unknown! Try to think of a familiar problem having the same or similar unknown. Split the problem into smaller, simple sub-problems. If you cannot solve the proposed problem try to solve first some related problem. Or solve more general problem. Or special case of the problem. Or solve the part of the problem.

Problem Solving Design

Third:

CARRYING OUT THE PLAN

Carry out your plan.

Carrying out your plan of the solution,check each step. Can you see clearly that step is correct? Can you prove that it is correct?

Fourth:

LOOKING BACK

Examine the solution obtained.

Can you check the result? Can you derive the result differently? Can you use the result, or the method, for some other problem?

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Problem Solving Design

The software development method The software development method consists of the following steps:  Requirements specification  Analysis  Design  Implementation  Testing and verification  Documentation PSPD Using C

Algorithmic Problem Solving Design

Algorithmic problem: Any problem whose solution can be expressed as a set of executable instructions. Algorithm: A well defined computational procedure consisting of a set of instructions, that takes some value or set of values, as input, and produces some value or set of values, as output.

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Algorithmic Problem Solving Design

Derived from the name of Mohammed alkhowarizmi, a Persian mathematician in the ninth century. Al-khowarizmi--Algorismus(in Latin)--Algorithm  An algorithm is like a recipe, that converts the ingredients into some culinary dish.  The formal written version is a program.  Algorithms/programs are the software.The machine that runs the programs is the hardware.

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Algorithmic Problem Solving Design

Ingredient

Recipe (software)

Cooking utensils (hardware)

Al-gong Bah-kut-the

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Characteristics of an Algorithm Design

 Each step of an algorithm must be exact, preciously and ambiguously described.

 It must terminate, i.e. it contains a finite number of steps.

 It must be effective, i.e.., produce the correct output.

 It must be general, i.e.. to solve every instance of the problem.

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Characteristics of an Algorithm Design

 An Algorithm is implemented in some programming language.

program = Algorithm + Data Structures.

 Data Structures refer to the types of data used and how the data are organized in the program.

 An algorithm is usually presented in the form of some

pseudo-code, which is a mixture of English statement,some mathematical notations,and selected keywords from a programming language.

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Characteristics of an Algorithm Design

 An Algorithm

should emphasize the WHAT’s and not the HOW’s. Consider the problem below: PROBLEM:

You are required to design a complete system which will enable the sum of two values to be calculated.

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Problem Solving Design

To grapple with this problem, we have to understand the problem from the human perspective. A question to ask yourself is this, “How Would You Calculate the Sum of Two Values?”

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Problem Solving Design

As the computer is also a device similar to the way in which the human brain functions, the process of calculating the sum of two values can also be easily performed by the computer.

= PSPD Using C

Problem Solving Design

Processing (Brains)

Input Output PSPD Using C

Problem Solving Output Device

CPU (Brains)

Input Device PSPD Using C

Design

Problem Solving Design

Processing

10

5

5 + 10 = 15

15 Input Output Let us assume we are interested in calculating the sum of 5 and 10. PSPD Using C

Problem Solving Design

As shown previously, the example values (5 and 10) have been specified explicitly. As the brain is flexible enough in calculating a wide range of numbers, the two input values have to be generalised.

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Problem Solving Design

Value2 Value1

Sum = Value1 + Value2

Sum Notice that instead of using specific numbers, variables are used to represent these values. PSPD Using C

What Are Variables? Design

Variables are memory locations within the computer which allows pieces of data to be stored. The word variable comes from the word vary, which means that whatever you place within a variable can be changed. A variable can be viewed as a container used to store things.

Data (for example, name, age, salary) can be stored in these containers. PSPD Using C

What Are Variables? Design

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Problem Solving Design

Now that we have an exact idea about how the problem is solved, let us represent this in a clearer manner, using the defining diagram.

Input Value1 Value2

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Processing

Output Sum

Problem Solving Design

The next step is to identify the actual processing steps required to convert the input to become the output. Input

Processing

Value1

1) Read Value1, Value2

Value2

2) Calculate Sum 3) Display Sum

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Output Sum

Algorithm Development Once the defining diagram has been developed, the next logical step is to develop the algorithm (which is much more detailed).

Input

Processing

Value1

1) Read Value1, Value2

Value2

2) Calculate Sum

Output Sum

3) Display Sum

The developed processing steps have to be more detailed in the algorithm. PSPD Using C

Design

Algorithm Development Design

The basic mathematical operators used in algorithms are as follows:-

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+

addition

-

subtraction

*

multiplication

/

division

=

assignment

()

brackets for grouping calculations

Algorithm Development Design

Example of an algorithm (using pseudocodes) which can be used to carry out the tasks outlined in the defining diagram is as follows:1)

Read Value1, Value2

2)

Calculate Sum = Value1 + Value2

3) PSPD Using C

Display Sum

Pseudocoding Design

A Pseudocode language is semiformal, Englishlike language with a limited vocabulary that can be used to design and describe algorithms. The pseudocode language can be used for:  Designing algorithms  Communicating algorithms as programs  Implementing algorithms as programs  Debugging logic errors in program

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Pseudocode for the Control Structures Design

The Sequence Control Structure: The sequence control structure is a series of steps or statements that are executed in the order in which they are written in an algorithm. For Example: read taxable income read filing status compute income tax

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Cont’d Design

The Selection Control Structure: The selection control structure defines two courses of action, depending on the outcome of a condition. A condition is an expression that, when evaluated, computes to either true or false. Syntax is:

if condition then-part else else-part end-if

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Decision Making Design

Being able to mimic the way the human brain works, the computer also has the ability to make decisions. Decision making can be represented pseudocodes using the IF...THEN construct. IF (expression) THEN : : ENDIF PSPD Using C

in

Decision Making Design

The expression is a comparison between two values which evaluates to either true of false.

IF (expression) THEN : : ENDIF Statements are placed here. PSPD Using C

Decision Making Design

Example:We are looking for a job which pays more than RM4000. Example of an Expression

IF (Salary>4000) THEN Say "I Will Take The Job!!" ENDIF PSPD Using C

Decision Making Design

Commonly used relational operators in expressions:>

Greater Than

<

Less Than

=

Equals To



Not Equals To

>=

Greater Than or Equals To

4000) THEN Say “YES!” ELSE Say “NO!” ENDIF PSPD Using C

Decision Making Design

Certain conditions may give rise to more than one expression being evaluated. These are known as compound expressions. Example:You are interested in taking up a job which pays more than RM4000 and that the company must also provide a credit card. IF (Salary>4000) And (CreditCard=YES) THEN Take Job!! ENDIF PSPD Using C

Decision Making Design

Compound expressions can be represented using the following operators:AND

Every expression must evaluate to be true in order for the whole expression to be true.

OR

As long as any one of the expression can be true, the entire IF statement will be true.

NOT

The inverse (opposite) of the entire expression.

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Decision Making Design

IF statements can be nested, that is, placed within another IF statement. This is used in situations when the expression is more complex than the simple decisions (as seen earlier).

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Decision Making For example, this statement.........

Design

IF (Salary>4000) And (CreditCard=YES) THEN Say “Yes I Will Take The Job!!” ENDIF

can be represented like this......... IF (Salary>4000) THEN IF (CreditCard=YES) THEN Say “Yes I Will Take The Job!!” ELSE Say “No Credit Card?” Say “Sorry!!” ENDIF ELSE Say “Not Enough Pay!!” ENDIF

........ whereby more possibilities can be represented. PSPD Using C

Decision Making For good practice...........

Design

IF (Salary>4000) THEN IF (CreditCard=YES) THEN Say “Yes I Will Take The Job!!” ELSE Say “No Credit Card?” Say “Sorry!!” ENDIF ELSE Say “Not Enough Pay!!” ENDIF

........ ensure that statements are properly indented to indicate block of statements which belong together. PSPD Using C

Cont’d Design

For Example: if a is greater than b then print “A is greater” else print “B is greater” end if

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Cont’d Design

Repetition Control Structure: The repetition control structure specifies a block of one or more statements that are repeatedly executed until a condition is satisfied. Syntax is: while condition loop-body end-while

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Looping Constructs Design

Looping constructs (also known as repetition or iteration constructs) are a kind of construct found in pseudocodes which allows statements (or a group of statements) to be repeated. The main reason why looping constructs are provided is because most of the problems which we encounter everyday requires some degree of repetition.

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Looping Constructs Design

An example of a process which is iterative:-

Payroll processing is very much an iterative process as the person processing the payroll applies the same calculations for each employee to produce the pay slip.

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Looping Constructs Design

The looping constructs available in pseudocodes are as follows:-

DOWHILE...ENDDO FOR…NEXT REPEAT...UNTIL

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Looping Constructs Design

The format of the DOWHILE...ENDDO construct is shown below:DOWHILE (expression) : : : ENDDO Group of statements PSPD Using C

An expression which determines whether the loop will continue.

Looping Constructs Design

The format of the FOR...NEXT construct is shown below:FOR (initialze TO expression) STEP increment : : : ENDDO Group of statements PSPD Using C

An expression which determines whether the loop will continue.

Looping Constructs Design

The format of the REPEAT...UNTIL construct is shown below:REPEAT : : : UNTIL (expression) Group of statements PSPD Using C

An expression which determines whether the loop will continue.

Looping Constructs Design

Take a look at the following example:You are required to develop a complete system which will allow the total payroll to be calculated. The system is required to read in the amount to be paid for each employee. The moment the system receives an input value of -99, the system is required to stop and display the total payroll. PSPD Using C

Looping Constructs Design

The Defining Diagram Input Salary

Processing 1) Read Salary 2) Calculate Total 3) Display Total

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Output Total

Looping Constructs Algorithm (Using Pseudocodes) 1) Display "Enter Salary" 2) Read Salary 3) Total = 0 4) DOWHILE (Salary-99) Total = Total + Salary Display "Enter Salary" Read Salary ENDDO 5) Display "Total Payroll = ", Total PSPD Using C

Design

Cont’d Design

Example: Dowhile (income is less than 50000) print “Enter taxable income;should be greater than or equal to 50000” read income Enddo

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Desk Check Table Design

A desk check table is used to verify the correctness of the design. This is to ensure that the program which will eventually be developed is going to produce the answer which is required. The desk check table is developed based on the following steps:1) 2) 3) 4) PSPD Using C

Identify the data sets. Identify the expected results. Trace through the algorithm with the data sets using a trace table. Analyse & compare the results produced in step (3) and the expected results in step (2).

Desk Check Table Identify Data Sets Input

Processing

Value1

1) Read Value1, Value2

Value2

2) Calculate Sum

Design

Output Sum

3) Display Sum

Focus on the input section of the defining diagram and identify some possible values (data sets) which can be used to test the system. PSPD Using C

Desk Check Table Design

Identify Expected Results Input

Processing

Value1

1) Read Value1, Value2

Value2

2) Calculate Sum

Output Sum

3) Display Sum

Focus on the output section of the defining diagram and identify some possible values which the system will produce based on the data sets. PSPD Using C

Desk Check Table Design

Trace Table - Data Set 1 Value1 Read

5

Value2

Sum

3

Calculate

8

Display



Do the results match the expected results? PSPD Using C

Desk Check Table Design

Trace Table - Data Set 2 Value1 Read

8

Value2

Sum

13

Calculate

21

Display



Do the results match the expected results? PSPD Using C

Desk Check Table Design

Trace Table - Data Set 3 Value1 Read

15

Value2

Sum

9

Calculate

24

Display



Do the results match the expected results? PSPD Using C

Program Flowcharts Design

As humans are more inclined towards understanding diagrams and pictures rather than words, pseudocodes tends to become tedious to understand if too lengthy. Program flowcharts, because they are represented graphically, makes understanding easier.

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Program Flowcharts The following are the commonly used symbols for drawing program flowcharts. terminator

off-page connector

process

storage

decision making

document

input/output

connector

arrowheads PSPD Using C

Design

Program Flowcharts Begin Read Value1, Value2

Calculate Sum = Value1 + Value2

Display Sum

End PSPD Using C

Design

Program Flowcharts Begin

Design

Read Amount

YES

Amount>20.00?

Calculate Actual=Amount * 0.80

Calculate Actual=Amount

End PSPD Using C

NO

Flowcharting Design

 Another technique used in designing and representing algorithms.

 Alternative to pseudocoing  A pseudocode description is verbal, a flowchart is graphical in nature.

Definition:

 A flowchart is a graph consisting of geometrical shapes that are connected by flow lines.

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Sequence Structure Design

Pseudocode: statement_1

Flowchart:

Statement -1

statement_2 ------------

Statement -2

statement_n

Statement -n

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Selection Structure Design

Pseudocode:

Flowchart:

if condition then-part else

false

else-part end_if

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else-part

condition

true

then-part

Selection Structure Design

Pseudocode:

Flowchart:

if condition then-part end_if

Y

condition N

false

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true

then-part

Repetition Structure Design

Pseudocode:

Flowchart:

while condition loop-body

T

end-while

condition F N

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Y

loop-body

Summary Design

 Problem Solving– the process of transforming the  

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description of a problem to its solution. To Solve complex problems, we use computers as a tool and develop computer programs that give us solutions. A commonly used method for problem solving using computers is the software development method,which consists of six steps.

Summary Design

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1.

The Requirements specification, provides us with a precise definition of the problem.

2.

In the analysis phase we identify problem inputs,outputs,special constraints, and formulas and equations to be used.

3.

The design phase is concerned with developing an algorithm for the solution of the problem.

Summary Design

4.

The implementation of an algorithm is a computer program.When executed, it should produce the solution to the problem.

5.

Program Verification is the process of ensuring that a program meets user requirements.

6.

Program testing, on the other hand, is the process of executing a program to demonstrate its correctness.

7.

Program Documentation facilitates the use of the program,future program maintenance efforts,and program debugging.

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Summary Design

 An algorithm is a sequence of a finite number of steps arranged in a specific logical order that, when executed, produce the solution for a problem.

 A pseudocode language is a semiformal,English-like language with a limited vocabulary that can be used to design and describe algorithms.

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Summary Design

 Any algorithm can be described in terms of three basic

control structures.They are the sequence,selection and repetition structures.

 The top-down stepwise refinement of algorithms is a fundamental problem-solving strategy.

 A Flowchart is a graphical representation of an algorithm.

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Quick Review Question Design

1. State the difference between the Dowhile – Enddo structure and the Repeat – Until structure. 2. Write an algorithm that will display the first hundred even numbers using the Do-While loop.

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Follow Up Assignment Design

• This is an individual piece of work. • Your source code will be discussed at the end of the next lesson.

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Summary of Main Teaching Points Design

•

Problem Solving • Pseudocodes • Flowcharts

•

Basic control structures • The sequence structure • The selection structure • The repetition structure

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