Algorithms and Problem Solving

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TK 1914 C Programming

• Algorithms and Problem Solving

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WHAT IS AN ALGORITHM?

• An algorithm is a set of ordered steps for
  solving a problem.
• Examples
• An algorithm for preparing breakfast.
• An algorithm for converting Gregorian dates to
  Islamic dates.
• An algorithm for calculating moon phase.
• An algorithm for drawing a curve.

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Algorithm in Real Life

• Consider the following
• Problem Baking a Cake
• How to solve
• Start
• Preheat the oven at 180oC
• Prepare a baking pan
• Beat butter with sugar
• Mix them with flour, eggs and essence vanilla
• Pour the dough into the baking pan
• Put the pan into the oven
• End

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Divide and Conquer Strategy in Algorithm

• Problem Prepare a Breakfast

1. Start 2. Prepare a Breakfast 3. End
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Divide and Conquer Strategy in Algorithm

• 1. Start
• 2. Prepare a Breakfast
• 2.1 Prepare a tuna sandwich
• 2.2 Prepare some chips
• 2.3 Make a cup of coffee
• 3. End

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Divide and Conquer Strategy in Algorithm

• 1. Start
• 2. Prepare a Breakfast
• 2.1 Prepare a tuna sandwich
• 2.1.1 Take 2 slices of bread
• 2.1.2 Prepare tuna paste
• 2.2 Prepare some chips
• 2.3 Make a cup of coffee
• 3. End

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Divide and Conquer Strategy in Algorithm
1. Start 2. Prepare a Breakfast 2.1 Prepare a
tuna sandwich 2.1.1 Take 2 slices of
bread 2.1.2 Prepare tuna paste
2.2 Prepare some chips 2.2.1 Cut
potatoes into slices 2.2.2 Fry the
potatoes 2.3 Make a cup of coffee 3. End
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Divide and Conquer Strategy in Algorithm
1. Start 2. Prepare a Breakfast 2.1. Prepare
a tuna sandwich 2.1.1 Take 2 slices of
bread 2.1.2 Prepare tuna paste
2.2. Prepare some chips 2.2.1 Cut
potatoes into slices 2.2.2 Fry the
potatoes 2.3. Make a cup of coffee
2.3.1 Boil water 2.3.2 Add water with
sugar and coffee 3. End
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CLASS ACTIVITY 5.1

• Write a simple algorithm for withdrawing a sum of
  money at an ATM.

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WHY DO WE NEED TO BUILD ALGORITHMS?

• If we wish to build a house, we need to design it
  first.
• Can you think of some possible consequences of
  not designing a house before building it?
• Similarly, computer programs (especially large
  and complex ones) need to be designed before they
  are written.
• Can you think of some possible consequences of
  not designing a program before building it?
• One of the things considered when designing a
  computer program is the algorithm which it will
  be based on.

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ALGORITHMS IN PROGRAM DESIGN

• A computer program is built to solve a certain
  problem.
• Examples
• 1. A program to calculate the grade obtained
  given a mark.
• 2. A program to convert a Gregorian date to an
  Islamic date.
• 3. A program to produce a document.

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• Below are steps (in fact, an algorithm) for
  building a program to solve a particular problem
• Analyse the problem
• Design a computer solution to the problem by
  developing an algorithm.
• Write a computer program based on the algorithm.
• Test the program.

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HOW TO SPECIFY AN ALGORITHM?

• An algorithm must be specific enough so that it
  can be conveniently translated into a computer
  program (using C, for example).
• An algorithm can be specified
• Textually
• For example, using pseudo code (see later)
• Graphically
• For example, using flowcharts or UML activity
  charts

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FLOWCHARTS

• A flowchart is a graphical representation of the
  sequence of operations in a program.
• An algorithm can be represented graphically using
  a flowchart.

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Flowchart notations
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FLOWCHART EXAMPLE 1
Start
Input Gregorian date
Convert Gregorian date to Islamic date
Display Islamic date
End
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Pseudocode

• An outline of a program, written in a form that
  can easily be converted into real programming
  statements. It resembles the actual program that
  will be implemented later. However, it cannot be
  compiled nor executed.
• Pseudocode normally codes the following actions
• Initialisation of variables
• Assignment of values to the variables
• Arithmetic operations
• Relational operations

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Example of Pseudocode

• 1. Start
• 2. Read quantity
• 3. Read price_per_kg
• 4. price ? quantity price_per_kg
• 5. Print price
• 6. End

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CLASS ACTIVITY 5.2

• Draw a flowchart which represents the algorithm
  built in CA5.1.

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FLOWCHART EXAMPLE 2
Start

• length, width and area are referred to as
  variables.
• A variable is like a box in which a value can be
  stored

Input length, width
area ? length X width
Output area
End
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FLOWCHART EXAMPLE 3
Start

• Selection

Input height
false
true
height gt 1.6?
Output You are short!
Output You are tall!
End
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FLOWCHART EXAMPLE 4

• Repetition (looping)

Start
Output Thank you!
Input stop
false
true
End
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Problem solving
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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

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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

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Example 1 Rectangle

• Problem
• Design an algorithm to find the perimeter and
  area of a rectangle.
• Information
• The perimeter and area of the rectangle are
  given by the following formulas
• perimeter 2 (length width)
• area length width

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Example 1

• Requirements
• Input length and width of the rectangle
• Output perimeter and area of the rectangle
• Process perimeter ???, area ???

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Example 1

• Algorithm
• Get length of the rectangle
• Get width of the rectangle
• Find the perimeter using the following equation
• perimeter 2 (length width)
• Find the area using the following equation
• area length width
• Display the result perimeter and area

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Example 2 Calculate Car Park Charge
A car park has the following charges The 1st
hour costs RM2.00. The subsequent hours cost
RM1.00 per hour. Write an algorithm to calculate
the charges based on a vehicles entry and exit
time.
Process
Input
Output

• Entry_time
• Exit_time

Charge
????
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Example 2 Flowchart
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Example 2 Flowchart
cin gtgt entry_time gtgt exit_time
period exit_time entry_time
if (period gt 1) charge 2 ( period
1) else charge 2 cout ltltcharge
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Example 2 C Program
void main() int entry_time, exit_time, period,
charge cin gtgtentry_time gtgtexit_time period
exit_time entry_time if (period gt
1) charge 2 (period 1) else charge
2 cout ltltcharge
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Example 3 Paycheck

• Problem
• Design an algorithm to calculate a paycheck of a
  salesperson.
• Information
• Every salesperson has a base salary.
• Salesperson receives 10 bonus at the end of the
  month for each year worked if he or she has been
  with the store for five or less years.
• The bonus is 20 for each year that he or she has
  worked there if over 5 years.

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Example 3

• Information (continue)
• Additional bonuses are as follows
• If total sales for the month are 5,000-10,000,
  he or she receives a 3 commission on the sale
• If total sales for the month are at least
  10,000, he or she receives a 6 commission on
  the sale

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Example 3

• Requirements
• Input base salary, number of years work, total
  sale
• Output amount of paycheck (total salary)
• Process ???

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Example 3

• Algorithm
• Get baseSalary
• Get noOfServiceYears
• Calculate bonus using the following formula
• if (noOfServiceYears lt 5)
• bonus 10 noOfServiceYears
• otherwise
• bonus 20 noOfServiceYears
• Get totalSale

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Example 3

• Calculate additionalBonus as follows
• if (totalSale lt 5000)
• additionalBonus 0
• otherwise
• if (totalSalegt5000 and totalSalelt10000)
• additionalBonus totalSale x(0.03)
• otherwise
• additionalBonus totalSale x (0.06)

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Example 3

• Calculate payCheck using the equation
• payCheck baseSalary bonus
  additionalBonus

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Example 4 Average Test Score

• Problem
• 10 students in a class
• Each student has taken five tests and each test
  is worth 100 points.
• Design an algorithm to calculate the grade for
  each student as well as the class average.
• Design an algorithm to find the average test
  score.
• Design an algorithm to determine the grade.
• Data consists of students names and their test
  scores.

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Example 4

• Algorithm 1 to find test score
• Get the five test scores.
• Add the five test scores. Suppose sum stands for
  the sum of the test scores.
• Suppose average stands for the average test
  score. Then
• average sum / 5

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Example 4

• Algorithm 2 to determine the grade.
• if average gt 90
• grade A
• otherwise
• if average gt 80 and lt 90
• grade B
• otherwise
• if average gt 70 and lt 80
• grade C
• otherwise
• if average gt 60 and lt 70
• grade D
• otherwise
• grade F

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Example 4

• Main algorithm
• totalAverage 0
• Repeat the following steps for each student in
  the class.
• Get students name.
• Use algorithm 1.
• Use the algorithm 2.
• Update totalAverage by adding current students
  average test score.
• Determine the class average as follows
• classAverage totalAverage / 10

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Program style and Form
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USE OF WHITESPACE

• Insert white space characters (such as blanks,
  tabs and newlines) if necessary to increase the
  readability of your source code.
• Example
• int matrix3 1, 0, 0, 0, 1, 0, 0, 0, 1
• int matrix3 1, 0, 0,
• 0, 1, 0,
• 0, 0, 1
• White space characters are ignored by the
  compiler during compilation.
• Remember to separate reserved words and
  identifiers from each other and other symbols.
• Example inta, b, c

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COMMAS AND SEMICOLONS

• Commas separate items in a list.
• Example int a, b, c
• All C statements end with a semicolon.
• Example area length width
• Semicolon is also called a statement terminator.

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DOCUMENTATION

• Programs are easier to read and maintain if they
  are well-documented.
• Comments can be used to document code
• Single line comments begin with // anywhere in
  the line
• Multiple line comments are enclosed between /
  and /

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DOCUMENTATION

• Avoid putting in useless comments such as shown
  below

int main() min elapsed_time / 60 //
assign elapsed_time / 60 to min sec
elapsed_time 60 // assign elapsed_time 60 to
sec hr min / 60 // assign min / 60 to
hr min min 60 // assign min 60 to
min
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DOCUMENTATION

• The program comments below are more useful

int main() // Convert elapsed_time to
minsec min elapsed_time / 60 sec
elapsed_time 60 // Convert minsec to
hrminsec hr min / 60 min min 60
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DOCUMENTATION

• Name identifiers with meaningful names.
• For example, which of the statements below is
  more meaningful?
• a l w
• area length width

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Form and Style

• Consider two ways of declaring variables
• Method 1
• int feet, inch
• double x, y
• Method 2
• int a,bdouble x,y
• Both are correct, however, the second is hard to
  read

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Syntax and logical error
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SYNTAX ERRORS

• Syntax errors are errors in the source code which
  are related to the syntax of the language.
• Syntax errors are detected by the compiler. An
  executable file will be generated by the compiler
  only if the source code it compiles has no syntax
  errors.
• Syntax errors are reported by the compiler in the
  form of error messages.

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include ltiostreamgt using namespace std int
main() cout ltlt "This program has
errors return
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LOGICAL ERRORS

• Logical errors are errors which are related to
  program logic.
• Normally, logical errors are not detectable by
  the compiler.
• Logical errors are usually detected during
  program runtime. For example, a program
  producing unexpected results is an indication
  that it has logical errors.
• It is important to remember that if the compiler
  does not produce any error messages, it does not
  mean that your program is free of logical errors.

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LOGICAL ERRORS

• Possible to remove all syntax errors in a program
  and still not have it run
• Even if it runs, it may still not do what you
  meant it to do
• For example,
• 2 3 5 and (2 3) 5
• are both syntactically correct expressions, but
  have different meanings

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• Write a program to calculate the area of the
  region in blue.

include ltiostreamgt using namespace std int
main() float radius, length, width cout ltlt
"Enter radius, length and width " cin gtgt
radius gtgt length gtgt width cout ltlt "Area of blue
region " ltlt length width - 3.14radiusradius
return 0
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• Suppose we test the program with these inputs
• radius 7 length 2 width 3
• Area of circle 3.14 7 7 153.86
• Area of rectangle 2 3 6
• This means that the rectangle is enclosed by the
  circle. The area of the region should not be
  negative.

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• The following output is generated when the
  program is executed with those inputs.
• The program should be checked for logical errors.

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include ltiostreamgt using namespace std int
main() float radius, length, width cout ltlt
"Enter radius, length and width " cin gtgt
radius gtgt length gtgt width cout ltlt "Area of
blue region " ltlt lengthwidth -
3.14radiusradius return 0
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YOU SHOULD NOW KNOW

• what an algorithm is.
• when an algorithm should be developed when
  building a computer program.
• the basic steps in building a computer program to
  solve a problem.
• what flowcharts are.
• how to represent algorithms graphically using
  flowcharts.

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YOU SHOULD NOW KNOW

• importance of program readability
• using whitespace characters
• inserting comments
• using meaningful names for identifiers
• syntax and logical errors