Factorial Using Recursion in DSA C# - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is recursion in programming?

Recursion is when a function calls itself to solve smaller parts of a problem until it reaches a simple case it can solve directly.

beginner

What is the base case in a recursive factorial function?

The base case is when the input number is 0 or 1, and the factorial is 1. This stops the recursion from continuing forever.

intermediate

Explain how factorial of 4 is calculated using recursion.

Factorial(4) calls Factorial(3), which calls Factorial(2), which calls Factorial(1). Factorial(1) returns 1. Then results multiply back: 1 * 2 = 2, 2 * 3 = 6, 6 * 4 = 24.

beginner

What happens if a recursive function does not have a base case?

Without a base case, the function keeps calling itself forever, causing a stack overflow error and crashing the program.

beginner

Write the recursive formula for factorial n!

Factorial(n) = n * Factorial(n - 1), with Factorial(0) = 1 as the base case.

What is the factorial of 0?

A 1

B 0

C Undefined

D Factorial of 0 does not exist

By definition, factorial of 0 is 1.

In recursion, what stops the function from calling itself infinitely?

A Base case

B Loop

C Variable

D Return type

The base case provides a condition to stop recursion.

What does factorial(3) return?

A 3

B 9

C 6

D 1

3! = 3 * 2 * 1 = 6.

Which of these is the correct recursive call in factorial function?

A Factorial(n) = Factorial(n + 1)

B Factorial(n) = n * Factorial(n - 1)

C Factorial(n) = n + Factorial(n - 1)

D Factorial(n) = n / Factorial(n - 1)

Factorial is calculated by multiplying n with factorial of n-1.

What error occurs if recursion has no base case?

A Type error

B Syntax error

C Null pointer exception

D Stack overflow

Without base case, recursion calls itself endlessly causing stack overflow.

Explain how recursion works in calculating factorial with an example.

Think about how factorial(4) breaks down into smaller factorial calls.

Describe the importance of the base case in a recursive factorial function.

What happens if the base case is missing?

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