pseudocode using the three basic constructs of sequence, decision, and iteration

9.2 Algorithms

Objective

To understand how to write clear pseudocode using the three basic programming constructs: sequence, decision, and iteration.

1. What is an Algorithm?

An algorithm is a finite, well‑defined set of instructions that solves a problem or performs a computation. It must be:

• Unambiguous – each step is clear.
• Finite – it terminates after a limited number of steps.
• Effective – each step can be carried out in a reasonable amount of time.

2. The Three Basic Constructs

All algorithms can be built from three fundamental control structures. In pseudocode they are expressed as follows:

READ a
READ b
SET sum ← a + b
WRITE sum

IF a > b THEN
SET max ← a
ELSE
SET max ← b
ENDIF

SET i ← 1
WHILE i ≤ n DO
WRITE i
SET i ← i + 1
ENDWHILE

3. Pseudocode Conventions

• Keywords are written in upper case (e.g., IF, WHILE, ENDWHILE).
• Indentation shows the block structure.
• Variables are given meaningful names; type is not required.
• Mathematical symbols may be written using LaTeX, e.g., \$a \le b\$, \$i \leftarrow i + 1\$.
• Input and output are represented by READ and WRITE (or INPUT/OUTPUT).

4. Detailed Examples

4.1 Sequence Example – Computing the Area of a Circle

Given a radius \$r\$, compute the area \$A = \pi r^2\$.

READ r
SET A ← 3.14159 * r * r
WRITE "Area =", A

4.2 Decision Example – Grade Classification

Assign a grade based on a mark \$m\$ (0–100).

READ m
IF m >= 80 THEN
SET grade ← 'A'
ELSE IF m >= 70 THEN
SET grade ← 'B'
ELSE IF m >= 60 THEN
SET grade ← 'C'
ELSE IF m >= 50 THEN
SET grade ← 'D'
ELSE
SET grade ← 'F'
ENDIF
WRITE "Grade:", grade

4.3 Iteration Example – Sum of the First \$n\$ Natural Numbers

Calculate \$S = 1 + 2 + \dots + n\$.

READ n
SET i ← 1
SET S ← 0
WHILE i <= n DO
SET S ← S + i
SET i ← i + 1
ENDWHILE
WRITE "Sum =", S

4.4 Combined Example – Finding the Maximum in a List

Given \$n\$ integers stored in an array \$A[1..n]\$, determine the maximum value.

READ n
FOR i ← 1 TO n DO
READ A[i]
ENDFOR
SET max ← A[1]
FOR i ← 2 TO n DO
IF A[i] > max THEN
SET max ← A[i]
ENDIF
ENDFOR
WRITE "Maximum =", max

5. Common Pitfalls

• Forgetting to update the loop variable (causes infinite loops).
• Using the wrong relational operator in a decision (e.g., = instead of ==).
• Placing statements outside the intended block due to incorrect indentation.
• Not handling edge cases such as \$n = 0\$ in loops.

6. Summary

1. All algorithms can be expressed using sequence, decision, and iteration.
2. Pseudocode provides a language‑independent way to describe algorithms.
3. Clear structure, consistent indentation, and meaningful variable names improve readability.
4. Testing with a range of inputs helps verify correctness and reveals hidden errors.

7. Practice Questions