1. Algorithms and Problem Solving
TK 1914 : C++ Programming
Algorithms and Problem Solving

2. 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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3. 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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4. ‘Divide and Conquer’ Strategy in Algorithm
Problem: Prepare a Breakfast
1. Start
2. Prepare a Breakfast
3. End
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5. ‘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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6. ‘Divide and Conquer’ Strategy in Algorithm
1. Start 2. Prepare a Breakfast 2.1 Prepare a tuna sandwich Take 2 slices of bread Prepare tuna paste 2.2 Prepare some chips 2.3 Make a cup of coffee 3. End
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7. ‘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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8. ‘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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9. CLASS ACTIVITY 5.1
Write a simple algorithm for withdrawing a sum of money at an ATM.
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10. 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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11. 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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12. 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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13. 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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14. 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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15. Flowchart notations Semantic Symbol Start/End Process Input/Output
Test
Connector
Flow of activities
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16. FLOWCHART: EXAMPLE 1 Start Algorithm starts here Input Gregorian date
Input data from user
Convert Gregorian
date to Islamic date
Perform the date conversion
Display
Islamic date
Display the result
End
Algorithm ends here
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17. 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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18. 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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19. CLASS ACTIVITY 5.2
Draw a flowchart which represents the algorithm built in CA[5.1].
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20. 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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21. FLOWCHART: EXAMPLE 3 Selection Start Input height false true
Output
“You are short!”
Output
“You are tall!”
End
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22. FLOWCHART: EXAMPLE 4 Repetition (looping) Start Output “Thank you!”
Input
stop
stop = 1?
false
true
End
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23. Problem solving
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24. 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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25. 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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26. 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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27. Example 1 Requirements: Input: length and width of the rectangle
Output: perimeter and area of the rectangle
Process: perimeter = ???, area =???
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28. 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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29. 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 vehicle’s entry and exit time.
Input
Process
Output
Entry_time
Exit_time
????
Charge
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30. Period  Exit_time – Entry_time
Example 2: Flowchart
Input Entry_time
Input Exit_time
Start
Output
Charge
End
Period  Exit_time – Entry_time
Period > 1?
Yes
Charge  2 + (Period * 1)
Charge 2 No
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31. Period  Exit_time – Entry_time
Example 2: Flowchart
Input Entry_time
Input Exit_time
Start
Output
Charge
End
Period  Exit_time – Entry_time
Period > 1?
Yes
Charge  2 + (Period * 1)
Charge 2 No
cin >> entry_time >> exit_time;
period = exit_time – entry_time;
if (period > 1)
charge = 2 + ( period *1);
else
charge = 2;
cout <<charge;
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32. Example 2: C++ Program void main() {
int entry_time, exit_time, period, charge;
cin >>entry_time >>exit_time;
period = exit_time – entry_time;
if (period > 1)
charge = 2 + (period * 1);
else
charge = 2;
cout <<charge; }
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33. Example 3: Paycheck Problem: Information:
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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34. 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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35. Example 3 Requirements:
Input: base salary, number of years work, total sale
Output: amount of paycheck (total salary)
Process: ???
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36. Example 3 Algorithm: Get baseSalary Get noOfServiceYears
Calculate bonus using the following formula:
if (noOfServiceYears <= 5)
bonus = 10 * noOfServiceYears
otherwise
bonus = 20 * noOfServiceYears
Get totalSale
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37. Example 3 Calculate additionalBonus as follows:
if (totalSale < 5000)
additionalBonus = 0
otherwise
if (totalSale>=5000 and totalSale<10000)
additionalBonus = totalSale x(0.03)
additionalBonus = totalSale x (0.06)
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38. Example 3 Calculate payCheck using the equation
payCheck = baseSalary + bonus + additionalBonus
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39. 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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40. Example 4 average = sum / 5; 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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41. Example 4 Algorithm 2: to determine the grade. if average > 90
grade = A
otherwise
if average >= 80 and < 90
grade = B
if average >= 70 and < 80
grade = C
if average >= 60 and < 70
grade = D
grade = F
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42. Example 4 Main algorithm: totalAverage = 0;
Repeat the following steps for each student in the class.
Get student’s name.
Use algorithm 1.
Use the algorithm 2.
Update totalAverage by adding current student’s average test score.
Determine the class average as follows:
classAverage = totalAverage / 10
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43. Program style and Form
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44. 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 matrix[][3] = {1, 0, 0, 0, 1, 0, 0, 0, 1};
int matrix[][3] = { 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;
This statement
is syntactically
incorrect.
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45. Example: area = length * width;
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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46. 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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47. 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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48. DOCUMENTATION The program comments below are more useful: int main() {…
// Convert elapsed_time to min:sec
min = elapsed_time / 60;
sec = elapsed_time % 60;
// Convert min:sec to hr:min:sec
hr = min / 60;
min = min % 60; }
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49. 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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50. Form and Style Consider two ways of declaring variables:
Method 1
int feet, inch;
double x, y;
Method 2
int a,b;double x,y;
Both are correct, however, the second is hard to read
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51. Syntax and logical error
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52. 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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53. #include <iostream> using namespace std; int main() {
cout << "This program has errors
return; }
Error messages displayed by the compiler
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54. 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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55. 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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56. Write a program to calculate the area of the region in blue.
#include <iostream>
using namespace std;
int main() {
float radius, length, width;
cout << "Enter radius, length and width: ";
cin >> radius >> length >> width;
cout << "Area of blue region: " << length * width *radius*radius;
return 0; }
Example of logical error
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57. Suppose we test the program with these inputs:
radius: 7 length: 2 width: 3
Area of circle = 3.14 * 7 * 7 =
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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58. The program should be checked for logical errors.
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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59. #include <iostream> using namespace std; int main() {
float radius, length, width;
cout << "Enter radius, length and width: ";
cin >> radius >> length >> width;
cout << "Area of blue region: "
<< length*width *radius*radius;
return 0; }
Example of logical error
The formula should be
3.14*radius*radius – length*width
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60. 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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61. YOU SHOULD NOW KNOW… importance of program readability
using whitespace characters
inserting comments
using meaningful names for identifiers
syntax and logical errors
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