Unit 11.4A · Term 4

Basic Algorithmic Structures

Every algorithm, no matter how complex, is built from just three fundamental structures: sequence, selection (branching), and iteration (loops). Understanding these building blocks is essential for designing correct and efficient programs.

Learning Objectives

11.5.3.9 Describe and apply the sequential structure
11.5.3.10 Describe and apply the branching structure
11.5.3.11 Describe and apply the loop structure

Lesson Presentation

11.4A-algorithmic-structures.pdf · Slides for classroom use

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Conceptual Anchor

The Recipe Analogy

Think of an algorithm as a cooking recipe. A sequence is doing steps in order (chop, mix, cook). A branch is a decision: "If the sauce is too thick, add water." A loop is repetition: "Stir every 2 minutes until golden." Every recipe — and every algorithm — uses combinations of these three structures.

Rules & Theory

1. Sequential Structure

Statements are executed one after another, in the order they appear. There are no decisions or repetitions — just straight-line execution.

Property	Description
Execution order	Top to bottom, left to right
Control flow	No branching or looping
Flowchart shape	Rectangles connected by straight arrows
Use case	Input → Process → Output

Pseudocode:

INPUT radius
area ← 3.14159 * radius * radius
OUTPUT "Area = ", area

C++:

#include <iostream>
using namespace std;

int main() {
    double radius;
    cout << "Enter radius: ";
    cin >> radius;
    double area = 3.14159 * radius * radius;
    cout << "Area = " << area << endl;
    return 0;
}

2. Branching Structure (Selection)

The program makes a decision based on a condition. If the condition is TRUE, one path is taken; otherwise, an alternative path is followed.

Type	Description	Keyword
Simple	One branch only	`IF...THEN...ENDIF`
Two-way	Two alternatives	`IF...THEN...ELSE...ENDIF`
Multi-way	Several alternatives	`CASE OF...ENDCASE`
Nested	Condition inside condition	`IF inside IF`

Pseudocode (IF/ELSE):

INPUT mark
IF mark >= 50 THEN
    OUTPUT "Pass"
ELSE
    OUTPUT "Fail"
ENDIF

Pseudocode (CASE):

INPUT grade
CASE OF grade
    "A": OUTPUT "Excellent"
    "B": OUTPUT "Good"
    "C": OUTPUT "Satisfactory"
    OTHERWISE: OUTPUT "Below standard"
ENDCASE

C++ (if/else):

int mark;
cin >> mark;
if (mark >= 50) {
    cout << "Pass" << endl;
} else {
    cout << "Fail" << endl;
}

C++ (switch):

char grade;
cin >> grade;
switch (grade) {
    case 'A': cout << "Excellent"; break;
    case 'B': cout << "Good";      break;
    case 'C': cout << "Satisfactory"; break;
    default:  cout << "Below standard";
}

3. Loop Structure (Iteration)

A group of statements is repeated while a condition is met (or a fixed number of times). There are three main loop types:

Loop type	Pseudocode	C++	When to use
Count-controlled	`FOR...NEXT`	`for`	Known number of iterations
Pre-condition	`WHILE...ENDWHILE`	`while`	May execute 0 times
Post-condition	`REPEAT...UNTIL`	`do...while`	Always executes at least once

FOR loop — Pseudocode:

FOR i ← 1 TO 5
    OUTPUT i
NEXT i
// Output: 1 2 3 4 5

FOR loop — C++:

for (int i = 1; i <= 5; i++) {
    cout << i << " ";
}
// Output: 1 2 3 4 5

WHILE loop — Pseudocode:

total ← 0
INPUT num
WHILE num <> -1
    total ← total + num
    INPUT num
ENDWHILE
OUTPUT "Total = ", total

REPEAT/UNTIL — Pseudocode:

REPEAT
    OUTPUT "Enter password: "
    INPUT password
UNTIL password = "secret123"
OUTPUT "Access granted"

Flowchart Shapes

Oval = Start/End · Rectangle = Process · Diamond = Decision · Parallelogram = Input/Output · Arrow = Flow direction. Branching uses a diamond with two exits (Yes/No). Loops use an arrow going back to the condition diamond.

Worked Examples

1 Temperature Classifier (All Three Structures)

Read 5 temperatures and classify each as Cold, Warm, or Hot.

// Sequential: variable declaration
// Loop: FOR to repeat 5 times
// Branching: IF/ELSE to classify

FOR i ← 1 TO 5
    OUTPUT "Enter temperature: "
    INPUT temp
    IF temp < 10 THEN
        OUTPUT "Cold"
    ELSE IF temp < 25 THEN
        OUTPUT "Warm"
    ELSE
        OUTPUT "Hot"
    ENDIF
NEXT i

// C++ equivalent
#include <iostream>
using namespace std;

int main() {
    for (int i = 1; i <= 5; i++) {
        double temp;
        cout << "Enter temperature: ";
        cin >> temp;
        if (temp < 10)
            cout << "Cold" << endl;
        else if (temp < 25)
            cout << "Warm" << endl;
        else
            cout << "Hot" << endl;
    }
    return 0;
}

2 Sum Until Sentinel (WHILE loop + branching)

Keep reading numbers until the user enters 0. Output the sum and count of positive numbers.

sum ← 0
count ← 0
OUTPUT "Enter a number (0 to stop): "
INPUT num
WHILE num <> 0
    IF num > 0 THEN
        sum ← sum + num
        count ← count + 1
    ENDIF
    OUTPUT "Enter a number (0 to stop): "
    INPUT num
ENDWHILE
OUTPUT "Sum = ", sum, " Count = ", count

3 Menu-Driven Calculator (REPEAT + CASE)

REPEAT
    OUTPUT "1. Add  2. Subtract  3. Quit"
    INPUT choice
    CASE OF choice
        1: INPUT a, b
           OUTPUT "Result = ", a + b
        2: INPUT a, b
           OUTPUT "Result = ", a - b
        3: OUTPUT "Goodbye!"
        OTHERWISE: OUTPUT "Invalid choice"
    ENDCASE
UNTIL choice = 3

Common Pitfalls

Infinite Loops

Forgetting to update the loop variable leads to an infinite loop. Always ensure the condition will eventually become false.

Off-by-One Errors

Using < instead of <= (or vice versa) can cause your loop to run one time too many or too few. Trace the first and last iterations carefully.

Missing ELSE / Default

Forgetting to handle the "otherwise" case in branching means unexpected inputs produce no output. Always include ELSE or OTHERWISE.

Pro Tips

Use FOR when you know how many times to repeat
Use WHILE when the condition is checked before each iteration
Use REPEAT/UNTIL when you need at least one execution (e.g., menu)
Draw a flowchart first — it helps you see the logic clearly before coding

Tasks

Remember

Name the three basic algorithmic structures and give one real-life example of each.

Understand

Explain the difference between a pre-condition loop (WHILE) and a post-condition loop (REPEAT/UNTIL). When would you use each?

Apply

Write pseudocode that reads 10 numbers and outputs how many are even and how many are odd.

Analyze

A student wrote: FOR i ← 1 TO 10 ... NEXT i but inside the loop also has i ← i + 1. Trace the execution and explain what goes wrong.

Create

Design a number-guessing game: the program picks a random number 1–100, the user guesses, and the program says "Higher" or "Lower" until correct. Use all three structures.

Self-Check Quiz

Q1: Which structure executes statements one after another with no decisions?

Sequential structure

Q2: What flowchart shape represents a decision?

Diamond (rhombus)

Q3: Which loop type always executes at least once?

Post-condition loop (REPEAT...UNTIL / do...while)

Q4: What is the C++ equivalent of pseudocode CASE OF?

switch statement