17  Algorithm Representation: Pseudocode & Struktogramme

Last week we described the GCD algorithm in three ways: natural language, a trace table, and Python code.

Today we add two more notations:

• Pseudocode — precise, structured, language-independent text
• Struktogramme (Nassi–Shneiderman diagrams) — visual block diagrams

By the end of this notebook you will be able to translate freely between Python and pseudocode.

17.1 What Is Pseudocode?

Pseudocode is a way of describing an algorithm using structured, human-readable language that resembles a programming language but is not tied to any specific one.

Advantage	Explanation
More precise than natural language	Avoids ambiguity
More readable than real code	No syntax details (colons, brackets, imports)
Language-independent	Anyone who knows any language can read it
Widely used	Textbooks, exams, professional documentation

17.2 Pseudocode Conventions

There is no single “official” pseudocode standard, but the conventions below are widely used and will be our standard for this course.

Element	Python	Pseudocode
Assignment	x = 5	x ← 5
Input	x = int(input())	READ x
Output	print(x)	PRINT x
Condition	if x > 0:	IF x > 0 THEN
Else	else:	ELSE
End block	(indentation)	END IF
While loop	while x > 0:	WHILE x > 0 DO
End loop	(indentation)	END WHILE
For loop	for i in range(n):	FOR i ← 0 TO n-1 DO
End for	(indentation)	END FOR
Function	def gcd(a, b):	FUNCTION gcd(a, b)
Return	return a	RETURN a
Not equal	!=	≠
Modulo	%	MOD

Key idea: Python uses indentation to show structure. Pseudocode uses keywords (THEN, DO, END IF, END WHILE) to show where blocks begin and end.

17.3 Worked Example: GCD in Pseudocode

Here is the GCD function you wrote last week in Python:

def gcd(a, b):
    while b != 0:
        r = a % b
        a = b
        b = r
    return a

And here is the same algorithm in pseudocode:

FUNCTION gcd(a, b)
    WHILE b ≠ 0 DO
        r ← a MOD b
        a ← b
        b ← r
    END WHILE
    RETURN a
END FUNCTION

Notice the correspondences: - def → FUNCTION … END FUNCTION - while → WHILE … DO … END WHILE - = (assignment) → ← - % → MOD - != → ≠

---

17.4 Exercise 1: Python → Pseudocode

Read the Python function below carefully. Then write the equivalent pseudocode on paper (or in a new markdown cell).

Use the conventions table above as a reference.

def max_of_three(a, b, c):
    if a >= b and a >= c:
        return a
    elif b >= a and b >= c:
        return b
    else:
        return c

Click to reveal the solution

FUNCTION max_of_three(a, b, c)
    IF a ≥ b AND a ≥ c THEN
        RETURN a
    ELSE IF b ≥ a AND b ≥ c THEN
        RETURN b
    ELSE
        RETURN c
    END IF
END FUNCTION

---

17.5 Exercise 2: Pseudocode → Python

The pseudocode below describes a linear search algorithm. It searches through a list for a given value and returns the index of the first occurrence, or -1 if the value is not found.

FUNCTION linear_search(lst, target)
    FOR i ← 0 TO length(lst) - 1 DO
        IF lst[i] = target THEN
            RETURN i
        END IF
    END FOR
    RETURN -1
END FUNCTION

Task: Implement this algorithm in Python in the cell below.

def linear_search(lst: list, target) -> int:
    pass  # TODO: implement the pseudocode above

# Test cases — all should print True
print(linear_search([10, 20, 30, 40, 50], 30) == 2)
print(linear_search([10, 20, 30, 40, 50], 10) == 0)
print(linear_search([10, 20, 30, 40, 50], 50) == 4)
print(linear_search([10, 20, 30, 40, 50], 99) == -1)
print(linear_search([], 5) == -1)

---

17.6 Exercise 3: Pseudocode → Python

The pseudocode below prints every integer from 1 to n. For multiples of 3 it prints "Fizz" instead of the number, for multiples of 5 it prints "Buzz", and for multiples of both 3 and 5 it prints "FizzBuzz".

FUNCTION fizzbuzz(n)
    FOR i ← 1 TO n DO
        IF i MOD 3 = 0 AND i MOD 5 = 0 THEN
            PRINT "FizzBuzz"
        ELSE IF i MOD 3 = 0 THEN
            PRINT "Fizz"
        ELSE IF i MOD 5 = 0 THEN
            PRINT "Buzz"
        ELSE
            PRINT i
        END IF
    END FOR
END FUNCTION

Task: Implement this algorithm in Python.

def fizzbuzz(n: int):
    pass  # TODO: implement the pseudocode above

# Run this cell to test — expected output:
# 1, 2, Fizz, 4, Buzz, Fizz, 7, 8, Fizz, Buzz,
# 11, Fizz, 13, 14, FizzBuzz
fizzbuzz(15)

---

17.7 Structure Diagrams (Struktogramme)

A Struktogramm (Nassi–Shneiderman diagram) is a visual way of representing an algorithm using nested rectangles. Each rectangle represents one instruction or control structure.

Advantage	Explanation
Visual	Structure is visible at a glance
No arrows	Forces structured programming (no “goto”)
Widely used	Common in German-speaking CS education and exams

17.7.1 The Three Building Blocks

Every Struktogramm is built from just three elements:

17.7.1.1 1. Sequence

Instructions are executed one after another, top to bottom.

┌─────────────────────────┐
│ Instruction 1           │
├─────────────────────────┤
│ Instruction 2           │
├─────────────────────────┤
│ Instruction 3           │
└─────────────────────────┘

17.7.1.2 2. Selection (IF / ELSE)

A condition splits execution into two branches.

┌─────────────────────────┐
│      condition?         │
├────────────┬────────────┤
│   TRUE     │   FALSE    │
│   block    │   block    │
└────────────┴────────────┘

17.7.1.3 3. Iteration (WHILE loop)

A block is repeated as long as a condition holds.

┌─────────────────────────┐
│ WHILE condition         │
│  ┌──────────────────────┤
│  │ loop body            │
│  └──────────────────────┤
└─────────────────────────┘

17.7.2 Worked Example: GCD Struktogramm

┌──────────────────────────────┐
│ READ a, b                    │
├──────────────────────────────┤
│ WHILE b ≠ 0                  │
│  ┌───────────────────────────┤
│  │ r ← a MOD b               │
│  ├───────────────────────────┤
│  │ a ← b                     │
│  ├───────────────────────────┤
│  │ b ← r                     │
│  └───────────────────────────┤
├──────────────────────────────┤
│ PRINT a                      │
└──────────────────────────────┘

Reading the diagram: - Top to bottom = execution order (sequence) - The indented box = the loop body (iteration) - READ at the top = input, PRINT at the bottom = output

17.7.3 Drawing Task (on Paper)

Now draw Struktogramme on paper for the algorithms you translated above:

1. max_of_three(a, b, c) — uses sequence and selection.
2. linear_search(lst, target) — uses sequence, selection, and iteration.
3. Sum of all integers from 1 to n.

Compare your diagrams with a partner when you’re done.

---

17.8 Summary: Comparing Notations

Notation	Precise?	Executable?	Visual?	Language-independent?
Natural language	✗	✗	✗	✓
Pseudocode	✓	✗	✗	✓
Struktogramm	✓	✗	✓	✓
Python	✓	✓	✗	✗

No single notation is “best” — each has strengths. Good computer scientists can switch between notations fluently.