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.
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)
- Condition: n != 0 and n != 1
- Action: return 3 * factorial(2)
- Call: factorial(2)
- Condition: n != 0 and n != 1
- Action: return 2 * factorial(1)
- Call: factorial(1)
- Condition: n == 1
