Cambridge International A Level Computer Science

slide1. Cambridge International A Level Computer Science (9618) – Revision Notes This pack is intended for students to who are taking CIE A Level in Computer Science, either in preparation for their A Level exam, or more likely alongside year 2 of the course to improve fluency, recall and pace on AS & A topics. It could be used as lesson starters, or supplied to students for independent use. Recursion<br>
slide2. Recursion AS & A Level Computer Science 9618 Chapter 24<br>
slide3. Chapter
Outline The Recursive Approach to Problem Solving 24.1 Building and Visualising Recursive Functions 24.2 Executing Recursive Calls in Programs Evaluating the Pros and Cons of Recursion 24.4 24.3<br>
slide4. 24.1 The Recursive Approach to Problem Solving What is a recursive routine? A recursive routine is a function or algorithm that calls itself during its execution, either directly or indirectly, to solve a smaller instance of the same problem. Eg. The factorial problem 4! = 4 x 3 x 2 x 1<br>
slide5. What is a recursive routine? A recursive routine is a function or algorithm that calls itself during its execution, either directly or indirectly, to solve a smaller instance of the same problem. Eg. The factorial problem 4! = 4 x 3 x 2 x 1 4! = 4 x 3! = 24.1 The Recursive Approach to Problem Solving<br>
slide6. What is a recursive routine? A recursive routine is a function or algorithm that calls itself during its execution, either directly or indirectly, to solve a smaller instance of the same problem. Eg. The factorial problem 4! = 4 x 3! 3! = 3 x 2! 2! = 2 x 1! 1! = 1 x 0! 0! = 1 24.1 The Recursive Approach to Problem Solving<br>
slide7. What is a recursive routine? A recursive routine is a function or algorithm that calls itself during its execution, either directly or indirectly, to solve a smaller instance of the same problem. Eg. The factorial problem 4! = 4 x 3! 3! = 3 x 2! 2! = 2 x 1! 1! = 1 x 0! 0! = 1 Base Case n! = n x (n-1)! General Case 24.1 The Recursive Approach to Problem Solving<br>
slide8. Subtopic 1 24.2 Building and Visualising Recursive Functions Python code for calculating factorial (Recursive method) def factorial(n):
if n == 0 or 1:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 5
result = factorial(number)
print(f"The factorial of {number} is: {result}") factorial (5)<br>
slide9. Subtopic 1 Python code for calculating factorial (Recursive method) def factorial(n):
if n == 0 or 1:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 5
result = factorial(number)
print(f"The factorial of {number} is: {result}") factorial (5) 5*factorial (4) call 24.2 Building and Visualising Recursive Functions<br>
slide10. Subtopic 1 Python code for calculating factorial (Recursive method) def factorial(n):
if n == 0 or 1:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 5
result = factorial(number)
print(f"The factorial of {number} is: {result}") factorial (5) 5*factorial (4) 4*factorial (3) call call 24.2 Building and Visualising Recursive Functions<br>
slide11. Subtopic 1 Python code for calculating factorial (Recursive method) def factorial(n):
if n == 0 or 1:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 5
result = factorial(number)
print(f"The factorial of {number} is: {result}") factorial (5) 5*factorial (4) 4*factorial (3) 3*factorial (2) call call call 24.2 Building and Visualising Recursive Functions<br>
slide12. Subtopic 1 Python code for calculating factorial (Recursive method) def factorial(n):
if n == 0 or 1:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 5
result = factorial(number)
print(f"The factorial of {number} is: {result}") factorial (5) 5*factorial (4) 4*factorial (3) 3*factorial (2) 2*factorial (1) call call call call 24.2 Building and Visualising Recursive Functions<br>
slide13. Subtopic 1 Python code for calculating factorial (Recursive method) def factorial(n):
if n == 0 or 1:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 5
result = factorial(number)
print(f"The factorial of {number} is: {result}") factorial (5) 5*factorial (4) 4*factorial (3) 3*factorial (2) 2*factorial (1) factorial (1) call call call call call 24.2 Building and Visualising Recursive Functions<br>
slide14. Subtopic 1 Python code for calculating factorial (Recursive method) def factorial(n):
if n == 0 or 1:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 5
result = factorial(number)
print(f"The factorial of {number} is: {result}") factorial (5) 5*factorial (4) 4*factorial (3) 3*factorial (2) 2*factorial (1) factorial (1) call call call call call return 1 24.2 Building and Visualising Recursive Functions<br>
slide15. Subtopic 1 Python code for calculating factorial (Recursive method) def factorial(n):
if n == 0 or 1:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 5
result = factorial(number)
print(f"The factorial of {number} is: {result}") factorial (5) 5*factorial (4) 4*factorial (3) 3*factorial (2) 2*factorial (1) factorial (1) call call call call call return 1 return 2x1 = 2 24.2 Building and Visualising Recursive Functions<br>
slide16. Subtopic 1 Python code for calculating factorial (Recursive method) def factorial(n):
if n == 0 or 1:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 5
result = factorial(number)
print(f"The factorial of {number} is: {result}") factorial (5) 5*factorial (4) 4*factorial (3) 3*factorial (2) 2*factorial (1) factorial (1) call call call call call return 1 return 2x1 = 2 return 3x2 = 6 24.2 Building and Visualising Recursive Functions<br>
slide17. Subtopic 1 Python code for calculating factorial (Recursive method) def factorial(n):
if n == 0 or 1:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 5
result = factorial(number)
print(f"The factorial of {number} is: {result}") factorial (5) 5*factorial (4) 4*factorial (3) 3*factorial (2) 2*factorial (1) factorial (1) call call call call call return 1 return 2x1 = 2 return 3x2 = 6 return 4x6 = 24 24.2 Building and Visualising Recursive Functions<br>
slide18. Subtopic 1 Python code for calculating factorial (Recursive method) def factorial(n):
if n == 0 or 1:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 5
result = factorial(number)
print(f"The factorial of {number} is: {result}") factorial (5) 5*factorial (4) 4*factorial (3) 3*factorial (2) 2*factorial (1) factorial (1) call call call call call return 1 return 2x1 = 2 return 3x2 = 6 return 4x6 = 24 return 5 x 24 = 120 24.2 Building and Visualising Recursive Functions<br>
slide19. 24.3 Executing Recursive Calls in Programs def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 3
result = factorial(number)
print(f"The factorial of {number} is: {result}") 0
1
2
3
4
567
8
9<br>
slide20. def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 3
result = factorial(number)
print(f"The factorial of {number} is: {result}") 0
1
2
3
4
567
8
9 24.3 Executing Recursive Calls in Programs<br>
slide21. def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 3
result = factorial(number)
print(f"The factorial of {number} is: {result}") 0
1
2
3
4
567
8
9 factorial(3) 24.3 Executing Recursive Calls in Programs<br>
slide22. def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 3
result = factorial(number)
print(f"The factorial of {number} is: {result}") 0
1
2
3
4
567
8
9 Line number Current content of the local variable factorial(3) stack frame 24.3 Executing Recursive Calls in Programs<br>
slide23. def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 3
result = factorial(number)
print(f"The factorial of {number} is: {result}") 0
1
2
3
4
567
8
9 factorial(2) Line number Current content of the local variable 24.3 Executing Recursive Calls in Programs<br>
slide24. def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 3
result = factorial(number)
print(f"The factorial of {number} is: {result}") 0
1
2
3
4
567
8
9 factorial(2) 24.3 Executing Recursive Calls in Programs<br>
slide25. def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 3
result = factorial(number)
print(f"The factorial of {number} is: {result}") 0
1
2
3
4
567
8
9 factorial(1) 24.3 Executing Recursive Calls in Programs<br>
slide26. def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 3
result = factorial(number)
print(f"The factorial of {number} is: {result}") 0
1
2
3
4
567
8
9 factorial(0) - base case reached! 24.3 Executing Recursive Calls in Programs<br>
slide27. def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 3
result = factorial(number)
print(f"The factorial of {number} is: {result}") 0
1
2
3
4
567
8
9 Return the value to call #3 24.3 Executing Recursive Calls in Programs<br>
slide28. def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 3
result = factorial(number)
print(f"The factorial of {number} is: {result}") 0
1
2
3
4
567
8
9 Return the value to call #2 24.3 Executing Recursive Calls in Programs<br>
slide29. def factorial(n):
if n == 0:
return 1
else:
return n * factorial(n - 1)

# Example usage:
number = 3
result = factorial(number)
print(f"The factorial of {number} is: {result}") 0
1
2
3
4
567
8
9 Return the value to call #1 24.3 Executing Recursive Calls in Programs<br>
slide30. 24.4 Evaluating the Pros and Cons of Recursion<br>