Factorial Using Recursion in DSA Python - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to return 1 when n is 0.

DSA Python

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

Drag options to blanks, or click blank then click option'

An

B1

C0

D-1

Attempts:

3 left

💡 Hint

Common Mistakes

Using 1 instead of 0 in the base case condition.

Not having a base case causing infinite recursion.

The factorial of 0 is defined as 1, so we check if n == 0.

2fill in blank

medium

Complete the recursive call to calculate factorial of n-1.

DSA Python

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

Drag options to blanks, or click blank then click option'

An - 1

B1

Cn

Dn + 1

Attempts:

3 left

💡 Hint

Common Mistakes

Using n + 1 causing infinite recursion.

Using n instead of n - 1.

To calculate factorial recursively, multiply n by factorial of n-1.

3fill in blank

hard

Fix the error in the base case condition to stop recursion correctly.

DSA Python

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

Drag options to blanks, or click blank then click option'

A==

B<

C>

D!=

Attempts:

3 left

💡 Hint

Common Mistakes

Using > or < instead of == causing wrong base case.

Using != causing infinite recursion.

The base case should check if n is equal to 0 to stop recursion.

4fill in blank

hard

Fill both blanks to create a dictionary of factorials for numbers 1 to 5.

DSA Python

factorials = {i: factorial(i) for i in range([1], [2])}

Drag options to blanks, or click blank then click option'

A1

B0

C6

D5

Attempts:

3 left

💡 Hint

Common Mistakes

Starting range at 0 causing unexpected keys.

Ending range at 5 excluding factorial of 5.

Range starts at 1 and goes up to but not including 6 to cover 1 to 5.

5fill in blank

hard

Fill all three blanks to create a dictionary of factorials for even numbers from 2 to 10.

DSA Python

even_factorials = {i: factorial(i) for i in range([1], [2], [3])}

Drag options to blanks, or click blank then click option'

A2

B11

D10

Attempts:

3 left

💡 Hint

Common Mistakes

Using 10 as end excludes 10 itself.

Using step 1 includes odd numbers.

Starting at 0 includes zero factorial.

Range starts at 2, ends before 11, stepping by 2 to get even numbers 2,4,6,8,10.

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