ALGORITHM DESIGN & DATA STRUCTURES
ALGORITHMS
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An algorithm is a set of steps that can be carried out to perform a task.
•
It can be defined as a set of step by step procedures to be executed in order
to solve a problem.

Algorithms are not necessarily written in any specific language and can be
illustrated using the following:
a.
Descriptions
b.
Flowcharts
c.
Pseudocodes
d.
Structure diagrams.
Advantages of algorithms

They are not biased towards any programming language.

Easy to convert to a program code or flowchart.

Easy to determine logic errors.

Has finite steps which lead to a solution.
Disadvantages

Time consuming to design, i.e. first convert to flowchart, then to program
code .

Most people find them difficult to learn.
Properties of an algorithm
1.
Efficiency – a good algorithm should produce results in a reasonable amount
of time.
2.
Unambiguous – the instructions in an algorithm should be clear and have only
one meaning.
3.
Multiplicity – an algorithm should be represented in many different ways, e.g.
in pseudo code or flowchart.
4.
Finiteness – an algorithm should terminate or end or stop after performing a
task.
5.
An algorithm should have a specified range of input.
6.
Feasibility – an algorithm should be feasible with the available resources.
7.
Independence – an algorithm should have instructions which are independent
of any programming language.
Analysis of algorithms

Factors to consider when analysing algorithms are:
1. Time complexity – is the amount of time taken by the algorithm to run.
2. Space complexity – is the amount of space/memory taken by the algorithm
and this helps us to estimate whether the algorithm requires more or less
space.
3. Simplicity – this determines whether the sequence of steps are easy to
understand. Simple algorithms lead to simple programs , and simple programs
are easy to debug.
4. Range of input – input should be most natural to the corresponding problem.
a. Descriptions:

These are general statements that are followed in order to complete a specific
task.

They are not governed by any programming language. An example is as follows:

Enter the length of the rectangle.

Store length.

Enter the width of the rectangle.

Store width.

Calculate area of rectangle.

Store area of rectangle.

Display area

End program.
b. Pseudocodes:

These are English-like statements, closer to programming language that
indicate steps followed in performing a specific task.

They are however independent of any programming language. An example is
as follows:
Enter centigrade temperature, C
If C = 0, then stop.
Set F to 32 + (9C/5)
Print C and F
End
Control Structures in Pseudocode

A Control Structures is a code portion that specifies flow of control in
programs.

It basically analyses and chooses in which direction a program flows based on
certain parameters or conditions.

Control structures can be (1) sequence control structures,(2) conditional
control structures or (3) iterative control structures.

A number of control structures are used in designing Pseudocodes. These
includes:
1.
simple sequence
2.
selection and
3.
iteration (looping/repetition).
(1)Simple sequence:

This is whereby instructions are executed in the order they appear in a
program without jumping any one of them up to the end of the program.

Statements are executed one after another in the order they are.

It is simple and avoids confusion.

Example:

Enter first number, A

Enter second number, B

C=A+B

Print C

Stop
Statement 1
Simple sequence
Statement 2
Statement 3
Statement n
(2) Selection Structure:

This allows one to choose the route to follow in order to accomplish a specific
task.

Selection is written using the IF ....THEN...ELSE statement or the CASE
statement.
Question: Using the IF…THEN…ELSE write an algorithm which compares two
numbers and shows which one is greater.
Selection structure
False
Statement(s)
Condition?
True
Statement(s)
(a) IF… THEN… ELSE STRUCTURE

Is a two way selection structure, which allows a computer to choose one path for
execution out of two available options.

The IF… THEN… ELSE structure can accommodate more than two options through
nesting or cascading( placing one if statement inside another).

The general structure of the IF…THEN…ELSE statement/structure is as below:

IF< condition> THEN
statement(s)
ELSE
statement(s)
NB: Statements after the key word THEN are executed only if the condition is
TRUE, and those after the ELSE keyword are executed only if the condition is
FALSE.
(b) CASE STRUCTURE

Is a multi-way selection structure, where the computer must choose one
option to execute amongst many available options.

The general structure/syntax of the CASE statement/structure is as below:
CASE 1: <statement(s)>
CASE 2: <statement(s)>
CASE 3: <statement(s)>
….
CASE ELSE
<statement(s)>
NB: statements after the CASE ELSE are only executed if none of the cases above
it are true.

Write an algorithm for a program that accepts a mark scored by a learner in
computer science and grades it as follows:
70-100: A
60-69: B
50-59: C
45-49: D
40-44: E
0-39: 39
3 Repetition/Iteration/Looping:

A control structure that repeatedly executes part of a program or the whole
program until a certain condition is satisfied.

Iteration is in the following forms: FOR...NEXT loop, REPEAT... UNTIL Loop and
the WHILE...ENDWHILE Loop.
Iteration structure
FTru
Condition ?
Statement(s)
a. For...Next Loop

A looping structure that repeatedly executes the loop body for a specified number of times. The
general syntax of the For...Next loop is as follows:

A group of statements between the looping structures is called the loop body and is the one that
is repeatedly executed.

The For...Next loop is appropriate when the number of repetitions is known well in advance,
e.g. five times.

An example of a program that uses the For...Next loop is as follows:
b. Repeat...Until Structure

This is a looping structure that repeatedly executes the loop body when the
condition set is FALSE until it becomes TRUE.

The number of repetitions may not be known in advance and the loop body is
executed at least once. The general syntax is as follows:
Question:

Using the repeat until structure, write an algorithm for a program that
calculates the average of five numbers entered through the keyboard.
c. While ... End while loop

A looping structure in which the loop body is repeatedly executed when the
condition set is TRUE until it becomes FALSE.

It is used when the number of repetitions is not known in advance. The
condition set is tested first before execution of the loop body. Therefore the
loop body may not be executed at all if the condition set is FALSE from the
start.

The syntax of the WHILE…END WHILE structure is as follows:
question

Write an algorithm using the while loop that calculates the average of 10
numbers.
Differences between the Repeat...Until and
the While…ENDWHILE structures
4 Flowcharts

It is a diagram used to give details on how programs and procedures are
executed.

Flowcharts are drawn using specific symbols, each with its own meaning, as
given below:
question

Write an algorithm to add two numbers and display the sum using a flowchart.
Use of the Pre-defined Symbol and the
connector

This is used when drawing flowcharts of subprograms as given below:
d. Structure Diagrams

These are diagrams that show relationships between different modules as
given below:
Interpreting and Testing Programs
Dry running (desk checking): the process of manually testing the logic of a
program on paper before coding on the computer.

Dry running is done to determine the logic of a program (to check if it gives
intended results.)
Debugging: The process of finding and correcting errors in a program. Bugs are
errors in a program.

A debugger is a program used in aiding the finding and removal of errors in a
program.
Programming Errors

i.
Programming errors are grouped into:
Syntax error: this is an error of violating the grammatical rules governing
sentence construction in a certain programming language, for example,
leaving a semi-colon at the end of each line in Pascal.

Syntax errors are detected by the computer.

A program cannot run with syntax errors.
ii. Logic error (Semantic error):

refers to an error in the sequencing of instructions, modules and specifying
wrong formulae that will produce undesirable results.

For example, instructing the computer to display result before any processing
has been done.

Logic errors cannot be detected by the computer.

The user just finds wrong and unintended results of a process
iii. Runtime (execution) error:

These are errors that occur during program execution and can be generated
when the computer tries to read past an end of file marker or by dividing a
number by zero.
(iv) Arithmetic error:

occurs in an instruction which performs inappropriate arithmetic, e.g.
Dividing a number by zero is an arithmetic error.
(v) Type Mismatch error

A type Mismatch error occurs in a program when a variable has been declared
as one data type, but it is later assigned a value that is of an incompatible
data type. The following code will produce a ‘Type Mismatch’ error because
“Stella” is not an integer:
Dim Firstname As integer
Firstname= “Stella”
Sorting algorithms

Is an algorithm that is used to arrange a given list or array of elements into a
certain order, i.e. ascending or descending order.

There are many sorting algorithms which include:
1.
Bubble sort/sinking sort
2.
Quick sort
3.
Bucket sort
4.
Heap sort
5.
insertion sort
6.
Radix sort
7.
Selection sort
8.
Merge sort.
(i) Bubble sort algorithm

Is an algorithm that works by comparing adjacent pairs of elements, and if
they are out of order, they are swapped.

The process is repeated for all the remaining elements until the whole array
is sorted.

It is named bubble sort to describe the way larger elements “bubble” to their
rightful positions in the sorted list.
Bubble sort algorithm
1.
Compare the first two elements in the list, if they are out of order, swap
them.
2.
Compare the second element with its neighbour on the right, if they are out
of order, swap them.
3.
Compare the third element with its neighbour on the right, if they are out of
order, swap them.
4.
Repeat this process throughout the list until all the elements have been
sorted.
- the comparison of elements is called a pass.
example

Use bubble sort algorithm to arrange the following elements in ascending
order:
7
2
8
5
4
(ii) Quick sort

Is a highly efficient algorithm and is based on partitioning the array of
elements/data into smaller sub arrays.

A large array is partitioned into two sub arrays, one of which holds values
smaller than the specified value called the pivot and the other which holds
values greater than the pivot.

The quick sort algorithm is quite efficient for a large data set.

It is a divide and conquer algorithm.
Steps in quick sort
1.
pick the right most element as the pivot.
2.
Partition the array using the pivot value.
3.
Quick sort the left sub array recursively.
4.
Quick sort the right sub array recursively.
Searching algorithms

These are algorithms that are used to locate a certain item form a list of
elements.

The element being searched for may be in the list or may not be in the list.

A search can be successful or unsuccessful, a successful search is when a
search item is found in a list, and an unsuccessful search is when an element
is not found after going through the whole list.

There are principally many searching algorithms, but we will look at linear
search and binary search.
Linear search algorithm

A linear search or sequential search is a method for finding an element
within a list.

It sequentially checks each element of the list until a match is found or the
whole list has been searched.

If the item is found, the index where the element is located is returned.

If it does not find the element after searching the whole array, then the index
-1 is returned, which means element does not exist since -1 is an invalid
index.

NB: Linear search works on both sorted or unsorted arrays of elements.
Steps in linear search (algorithm)
1.
check if the search item is equal to the first element in the list.
2.
If it is a match, end the search and return the index in which search item is
found.
3.
If it is not a match, check if the next item in the list matches the search
item, if it matches, end search and return the index, otherwise continue until
end of list, and if element is not found after searching all the elements, end
the search and return -1.
Binary search

binary search, also known as half-interval search, logarithmic search, or
binary chop, is a search algorithm that finds the position of a target value
within a sorted array.

Binary search compares the target value to the middle element of the array.

If they are not equal, the half in which the target cannot lie is eliminated and
the search continues on the remaining half, again taking the middle element
to compare to the target value, and repeating this until the target value is
found.

If the search ends with the remaining half being empty, the target is not in
the array.

Binary search is implemented using following steps...
•
Step 1 - Read the search element from the user.
•
Step 2 - Find the middle element in the sorted list.
•
Step 3 - Compare the search element with the middle element in the sorted list.
•
Step 4 - If both are matched, then display "Given element is found!!!" and terminate the function.
•
Step 5 - If both are not matched, then check whether the search element is smaller or larger than the
middle element.
•
Step 6 - If the search element is smaller than middle element, repeat steps 2, 3, 4 and 5 for the left sub
list of the middle element.
•
Step 7 - If the search element is larger than middle element, repeat steps 2, 3, 4 and 5 for the right sub
list of the middle element.
•
Step 8 - Repeat the same process until we find the search element in the list or until sub list contains
only one element.
•
Step 9 - If that element also doesn't match with the search element, then display "Element is not found
in the list!!!" and terminate the search.