Factorial Using Recursion in DSA Python - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Recursive Factorial Function Call

What is the output of the following Python code that calculates factorial recursively?

DSA Python

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

print(factorial(4))

A 10

B 120

C 24

D 1

💡 Hint

Remember factorial of 4 is 4 * 3 * 2 * 1.

The factorial function multiplies n by factorial of n-1 until it reaches 0, where it returns 1. So factorial(4) = 4*3*2*1 = 24.

❓ Predict Output

intermediate

Output When Calling Factorial with Zero

What will be printed when the factorial function is called with 0?

DSA Python

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

print(factorial(0))

A None

B 1

C 0

D Error

💡 Hint

Factorial of zero is defined as 1.

By definition, factorial(0) returns 1 as the base case in recursion.

🔧 Debug

advanced

Identify the Error in Recursive Factorial Code

What error will this code produce when calling factorial(3)?

DSA Python

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

print(factorial(3))

A RecursionError: maximum recursion depth exceeded

B ValueError: invalid literal for int()

C TypeError: unsupported operand type(s)

D Output: 6

💡 Hint

Check how the recursive call changes the argument.

The recursive call increases n instead of decreasing it, causing infinite recursion until Python stops it.

❓ Predict Output

advanced

Output of Factorial with Negative Input

What happens when factorial is called with a negative number?

DSA Python

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

print(factorial(-1))

A RecursionError: maximum recursion depth exceeded

B -1

C 1

D TypeError

💡 Hint

Think about the base case and how negative numbers affect recursion.

Since n never reaches 0 when starting negative and decreasing, recursion never stops causing RecursionError.

🧠 Conceptual

expert

Why is a Base Case Necessary in Recursive Factorial?

Why must a recursive factorial function have a base case like 'if n == 0: return 1'?

A To convert the recursion into iteration

B To speed up the calculation by caching results

C To handle negative inputs correctly

D To stop the recursion and prevent infinite calls

💡 Hint

Think about what happens if recursion never stops.

The base case stops recursion by providing a simple answer, preventing infinite calls and errors.

Practice

1. What does the factorial of a number represent in mathematics?

easy

A. The product of all positive integers up to that number

B. The sum of all positive integers up to that number

C. The number multiplied by 2

D. The number divided by 2

Solution

1. Step 1: Understand factorial definition

   Factorial of a number n (written as n!) is the product of all positive integers from 1 to n.

2. Step 2: Compare options with definition

   Only The product of all positive integers up to that number correctly states this product definition.

3. Final Answer:

   The product of all positive integers up to that number -> Option A

4. Quick Check:

   Factorial = product sequence [OK]

Hint: Factorial multiplies numbers down to 1 [OK]

Common Mistakes:

• Confusing factorial with sum
• Thinking factorial doubles the number
• Mixing factorial with division

2. Which of the following is the correct base case for a recursive factorial function in Python?

easy

A. if n == 1: return n + 1

B. if n == 1: return 0

C. if n == 0: return 0

D. if n == 0: return 1

Solution

1. Step 1: Identify base case for factorial

   Factorial of 0 is defined as 1, so base case should return 1 when n is 0.

2. Step 2: Check options for correct base case

   if n == 0: return 1 returns 1 when n == 0, which is correct. Others return wrong values.

3. Final Answer:

   if n == 0: return 1 -> Option D

4. Quick Check:

   Base case n=0 returns 1 [OK]

Hint: Base case factorial(0) = 1 [OK]

Common Mistakes:

• Returning 0 for factorial(0)
• Using wrong base case condition
• Returning n+1 instead of 1

3. What is the output of the following code?

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

print(factorial(4))

medium

A. 10

B. 16

C. 24

D. 120

Solution

1. Step 1: Trace recursive calls for factorial(4)

   factorial(4) = 4 * factorial(3) factorial(3) = 3 * factorial(2) factorial(2) = 2 * factorial(1) factorial(1) = 1 * factorial(0) factorial(0) = 1 (base case)

2. Step 2: Calculate values bottom-up

   factorial(1) = 1 * 1 = 1 factorial(2) = 2 * 1 = 2 factorial(3) = 3 * 2 = 6 factorial(4) = 4 * 6 = 24

3. Final Answer:

   24 -> Option C

4. Quick Check:

   4! = 24 [OK]

Hint: Multiply down from n to 1 recursively [OK]

Common Mistakes:

• Stopping recursion too early
• Adding instead of multiplying
• Wrong base case causing infinite recursion

4. Find the error in this recursive factorial function:

def factorial(n):
    if n == 1:
        return 1
    else:
        return n * factorial(n+1)

print(factorial(3))

medium

A. The recursive call should use n-1, not n+1

B. The print statement should be outside the function

C. The function should return n + factorial(n-1)

D. The base case should be n == 0, not n == 1

Solution

1. Step 1: Analyze recursive call parameter

   The function calls factorial(n+1), which increases n each time, causing infinite recursion.

2. Step 2: Correct recursive call to decrement n

   It should call factorial(n-1) to move towards base case and stop recursion.

3. Final Answer:

   The recursive call should use n-1, not n+1 -> Option A

4. Quick Check:

   Recursion must approach base case by decreasing n [OK]

Hint: Recursive calls must reduce n to reach base case [OK]

Common Mistakes:

• Increasing n in recursive call causing infinite loop
• Wrong base case value
• Adding instead of multiplying in return

5. How can you modify the recursive factorial function to handle negative inputs gracefully?

hard

A. Change base case to n == -1

B. Add a check to return None or error if n < 0 before recursion

C. Use absolute value of n in recursive call

D. Ignore negative inputs and proceed as usual

Solution

1. Step 1: Understand factorial domain

   Factorial is not defined for negative numbers, so function should handle this case explicitly.

2. Step 2: Add input validation before recursion

   Check if n < 0 and return None or raise error to avoid invalid recursion.

3. Final Answer:

   Add a check to return None or error if n < 0 before recursion -> Option B

4. Quick Check:

   Validate input before recursion [OK]

Hint: Check for negative input before recursion [OK]

Common Mistakes:

• Using absolute value hides invalid input
• Changing base case to negative number
• Ignoring invalid inputs causes wrong results