Algorithm Design

What is an Algorithm?

An algorithm is a step-by-step set of instructions to solve a problem or complete a task. Algorithms are the foundation of all computer programs.

Real-life example: A recipe is an algorithm. It has a sequence of steps, decisions ("if the sauce is too thick, add water"), and repetition ("stir for 5 minutes").

Properties of Good Algorithms

Clear - Unambiguous instructions that can be followed
Finite - Must eventually end (not run forever)
Effective - Each step can actually be performed
Input - Takes zero or more inputs
Output - Produces at least one result

Control Structures

All algorithms are built using three fundamental control structures:

Sequence

Steps executed one after another, in order.

Step 1
Step 2
Step 3

Selection

Making decisions based on conditions.

IF condition THEN
do this
ELSE
do that

Iteration

Repeating steps (loops).

WHILE condition
do something
ENDWHILE

Flowcharts

A flowchart is a visual representation of an algorithm using standard symbols.

Flowchart Symbols

Symbol	Name	Purpose
○	Terminator	Start or End of the algorithm
□	Process	An action or calculation
◇	Decision	Yes/No question (branching)
▱	Input/Output	Getting input or showing output
●	Connector	Links parts of flowchart
→	Flow Line	Shows direction of flow

Flowchart Example

Algorithm to check if a number is positive, negative, or zero:

Start

Input: number

number > 0?

Yes

Output: "Positive"

number < 0?

End

Pseudocode

Pseudocode is a way to describe an algorithm using structured English. It's not a real programming language but is easy to translate into code.

Pseudocode Conventions

Keywords in CAPITALS: IF, THEN, ELSE, WHILE, FOR, INPUT, OUTPUT
Use indentation to show structure
One instruction per line
Use meaningful variable names

Selection in Pseudocode

// Simple IF
IF age >= 18 THEN
    OUTPUT "You can vote"
ENDIF

// IF-ELSE
IF temperature > 30 THEN
    OUTPUT "It's hot!"
ELSE
    OUTPUT "It's comfortable"
ENDIF

// IF-ELSEIF-ELSE
IF score >= 80 THEN
    grade = "A"
ELSEIF score >= 60 THEN
    grade = "B"
ELSEIF score >= 40 THEN
    grade = "C"
ELSE
    grade = "D"
ENDIF

Iteration in Pseudocode

// WHILE loop (condition checked first)
count = 0
WHILE count < 5
    OUTPUT count
    count = count + 1
ENDWHILE

// FOR loop (known number of iterations)
FOR i = 1 TO 10
    OUTPUT i
NEXT i

// FOR EACH (iterate through a collection)
FOR EACH item IN shoppingList
    OUTPUT item
NEXT item

Example: Finding the Maximum

Algorithm to find the largest number in a list:

BEGIN FindMaximum
    INPUT numbers[]
    max = numbers[0]

    FOR EACH num IN numbers
        IF num > max THEN
            max = num
        ENDIF
    NEXT num

    OUTPUT "The maximum is: " + max
END

Trace Tables

A trace table tracks how variable values change as an algorithm executes. It helps verify that an algorithm works correctly.

Trace table for counting from 1 to 3:

Step	count	count < 4	Output
1	1	TRUE	1
2	2	TRUE	2
3	3	TRUE	3
4	4	FALSE	-

Key Terminology

Algorithm - Step-by-step instructions to solve a problem
Flowchart - Visual representation of an algorithm
Pseudocode - Structured English description of an algorithm
Sequence - Steps executed in order
Selection - Making decisions (IF statements)
Iteration - Repeating steps (loops)
Trace table - Tracking variable values through execution

Learning Objectives