Factorial Using Recursion in DSA C# - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to return 1 when n is 0 in the factorial function.

DSA C#

if (n == 0) return [1];

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

A1

B0

Cn

D-1

Attempts:

3 left

💡 Hint

Common Mistakes

Returning 0 instead of 1 for the base case.

Returning n which causes infinite recursion.

The factorial of 0 is defined as 1, so the function should return 1 when n is 0.

2fill in blank

medium

Complete the recursive call to calculate factorial of n.

DSA C#

return n * Factorial([1]);

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

A1

Bn - 1

Cn + 1

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Calling factorial with n instead of n-1 causing infinite recursion.

Calling factorial with n+1 which increases n and causes infinite recursion.

The factorial function calls itself with n-1 to reduce the problem size until it reaches 0.

3fill in blank

hard

Fix the error in the factorial function header to make it recursive.

DSA C#

public static int Factorial([1] n) {

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

Adouble

Bbool

Cstring

Dint

Attempts:

3 left

💡 Hint

Common Mistakes

Using double or string as parameter type which is incorrect for factorial.

Using bool which is not suitable for numeric calculations.

The factorial function should take an integer parameter because factorial is defined for integers.

4fill in blank

hard

Fill both blanks to complete the factorial function with base case and recursive call.

DSA C#

if (n == [1]) return [2];
return n * Factorial(n - 1);

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

A0

B1

Cn

D-1

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong base case value.

Returning n instead of 1 in base case.

The base case is when n is 0, return 1. Otherwise, multiply n by factorial of n-1.

5fill in blank

hard

Fill all three blanks to complete the factorial function with parameter, base case, and recursive call.

DSA C#

public static int Factorial([1] n) {
    if (n == [2]) return [3];
    return n * Factorial(n - 1);
}

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

Aint

B0

C1

Ddouble

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong parameter type.

Incorrect base case condition or return value.

The function takes an int parameter n, returns 1 if n is 0, else returns n times factorial of n-1.

Practice

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

easy

A. The number multiplied by 2

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

C. The number divided by 2

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

Solution

1. Step 1: Understand factorial definition

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

2. Step 2: Compare options

   Only The product of all positive integers up to that number correctly describes factorial as a product, not sum or division.

3. Final Answer:

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

4. Quick Check:

   Factorial = product of integers [OK]

Hint: Factorial multiplies numbers down to 1 [OK]

Common Mistakes:

• Confusing factorial with sum
• Thinking factorial divides the number
• Assuming factorial doubles the number

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

easy

A. if (n == 0) return 1;

B. if (n == 1) return 1;

C. if (n == 2) return 2;

D. if (n == -1) return 1;

Solution

1. Step 1: Identify factorial base case

   By definition, 0! = 1, so the base case should return 1 when n is 0.

2. Step 2: Check options

   Only if (n == 0) return 1; returns 1 when n == 0, which is correct base case for recursion.

3. Final Answer:

   if (n == 0) return 1; -> Option A

4. Quick Check:

   Base case: 0! = 1 [OK]

Hint: Base case for factorial is n == 0 returning 1 [OK]

Common Mistakes:

• Using n == 1 as base case
• Returning wrong value in base case
• Not handling negative inputs

3. What is the output of the following C# code?

static int Factorial(int n) {
    if (n == 0) return 1;
    return n * Factorial(n - 1);
}

Console.WriteLine(Factorial(4));

medium

A. 24

B. 10

C. 16

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 A

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
• Misunderstanding base case

4. Identify the error in this recursive factorial function:

static int Factorial(int n) {
    if (n == 1) return 1;
    return n * Factorial(n);
}

medium

A. Return type should be void

B. Missing base case for n == 0

C. Recursive call uses same n, causing infinite recursion

D. Multiplication operator is incorrect

Solution

1. Step 1: Analyze recursive call

   The function calls Factorial(n) inside itself without changing n, causing infinite recursion.

2. Step 2: Identify fix

   Recursive call should be Factorial(n - 1) to reduce n and reach base case.

3. Final Answer:

   Recursive call uses same n, causing infinite recursion -> Option C

4. Quick Check:

   Recursive call must reduce n [OK]

Hint: Recursive call must change parameter to approach base case [OK]

Common Mistakes:

• Calling function with same argument
• Forgetting base case
• Wrong return type

5. How would you modify the recursive factorial function to handle negative inputs by returning -1 for any negative number?

static int Factorial(int n) {
    if (n == 0) return 1;
    return n * Factorial(n - 1);
}

hard

A. No change needed; factorial works for negatives

B. Add if (n < 0) return -1; before base case

C. Add if (n == 1) return -1; after base case

D. Change base case to if (n <= 0) return 1;

Solution

1. Step 1: Understand negative input handling

   Factorial is undefined for negative numbers, so function should return -1 for n < 0.

2. Step 2: Modify function

   Add a check at start: if (n < 0) return -1; before base case to handle negatives properly.

3. Final Answer:

   Add if (n < 0) return -1; before base case -> Option B

4. Quick Check:

   Return -1 for negatives before recursion [OK]

Hint: Check negatives first, return -1 before recursion [OK]

Common Mistakes:

• Changing base case incorrectly
• Not handling negatives at all
• Returning wrong value for negatives