IB Computer Science Topic 5.1.2 Tracing Recursive Algorithms Revision Notes (HL)

IB Computer Science Topic 5.1.2 Tracing Recursive Algorithms Revision Notes (HL) | RevisionDojo

Tracing Recursive Algorithms

Tracing a recursive algorithm involves following each function call to understand how the algorithm progresses and eventually reaches a solution.
This process is crucial for debugging and gaining insight into the algorithm's behaviour.

Tip

Tips for tracing recursive algorithms:

Draw the Call Stack: Visualise each recursive call.
- Write down/draw each function call and its return value.
- This will help you see the overall structure and flow of the algorithm.
Identify the Base Case: Ensure you know when the recursion stops and what value is returned.
Track Return Values: Pay attention to how return values are combined to form the final solution.

Example: Factorial Calculation

Consider the following recursive algorithm to calculate the factorial of a number $n$:

def factorial(n):
    if n == 0 or n == 1:
        return 1
    else:
        return n * factorial(n - 1)

print(factorial(3))

Let's trace factorial(3):

Call: factorial(3)
1. Condition: n != 0 and n != 1

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Definition

Paywall

(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.

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Lorem ipsum dolor sit amet, consectetur adipiscing elit. Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

Duis aute irure dolor in reprehenderit

Duis aute irure dolor in reprehenderit in voluptate velit esse cillum dolore eu fugiat nulla pariatur. Excepteur sint occaecat cupidatat non proident, sunt in culpa qui officia deserunt mollit anim id est laborum.

Note

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam quis nostrud exercitation.

Excepteur sint occaecat cupidatat non proident

Nemo enim ipsam voluptatem quia voluptas sit aspernatur aut odit aut fugit, sed quia consequuntur magni dolores eos qui ratione voluptatem sequi nesciunt. Neque porro quisquam est, qui dolorem ipsum quia dolor sit amet, consectetur, adipisci velit.

Tip

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat.

Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.

Unlock the rest of this chapter with a free account

Tracing Recursive Algorithms

Tracing a recursive algorithm involves following each function call to understand how the algorithm progresses and eventually reaches a solution.
This process is crucial for debugging and gaining insight into the algorithm's behaviour.

Tip

Tips for tracing recursive algorithms:

Draw the Call Stack: Visualise each recursive call.
- Write down/draw each function call and its return value.
- This will help you see the overall structure and flow of the algorithm.
Identify the Base Case: Ensure you know when the recursion stops and what value is returned.
Track Return Values: Pay attention to how return values are combined to form the final solution.

Example: Factorial Calculation

Consider the following recursive algorithm to calculate the factorial of a number $n$:

def factorial(n):
    if n == 0 or n == 1:
        return 1
    else:
        return n * factorial(n - 1)

print(factorial(3))

Let's trace factorial(3):

Call: factorial(3)
1. Condition: n != 0 and n != 1

Definition

Paywall

(on a website) an arrangement whereby access is restricted to users who have paid to subscribe to the site.

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Note

Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam quis nostrud exercitation.

Excepteur sint occaecat cupidatat non proident

Tip

Lorem ipsum dolor sit amet, consectetur adipiscing elit.
Sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris.
Duis aute irure dolor in reprehenderit in voluptate velit esse cillum.

1. System fundamentals2 subtopics

2. Computer organization1 subtopic

3. Networks1 subtopic

4. Computational thinking, problem-solving and programming3 subtopics

5. Abstract data structures (HL)1 subtopic

6. Resource management (HL)1 subtopic

7. Control (HL)1 subtopic

A. Databases4 subtopics

B. Modelling and simulation4 subtopics

C. Web science6 subtopics

D. Object-oriented programming (OOP)4 subtopics

IB Computer Science 5.1.2 Tracing Recursive Algorithms Notes

1. System fundamentals2 subtopics

2. Computer organization1 subtopic

3. Networks1 subtopic

4. Computational thinking, problem-solving and programming3 subtopics

5. Abstract data structures (HL)1 subtopic

6. Resource management (HL)1 subtopic

7. Control (HL)1 subtopic

A. Databases4 subtopics

B. Modelling and simulation4 subtopics

C. Web science6 subtopics

D. Object-oriented programming (OOP)4 subtopics

Tracing Recursive Algorithms

Example: Factorial Calculation

Output

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account

Tracing Recursive Algorithms

Example: Factorial Calculation

Output

anim nostrud sit dolore minim proident quis fugiat velit et eiusmod nulla quis nulla mollit dolor sunt culpa aliqua

Duis aute irure dolor in reprehenderit

Excepteur sint occaecat cupidatat non proident

Unlock the rest of this chapter with a free account