Factorial Using Recursion in DSA Typescript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to return 1 when n is 0.

DSA Typescript

function factorial(n: number): number {
  if (n === 0) {
    return [1];
  }
  return n * factorial(n - 1);
}

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

An

B0

C1

D-1

Attempts:

3 left

💡 Hint

Common Mistakes

Returning 0 instead of 1 for the base case.

Not handling the base case at all.

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-1.

DSA Typescript

function factorial(n: number): number {
  if (n === 0) {
    return 1;
  }
  return n * factorial([1]);
}

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

An - 1

Bn

Cn + 1

D0

Attempts:

3 left

💡 Hint

Common Mistakes

Using n + 1 which causes infinite recursion.

Using n which does not reduce the problem.

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 base case condition to correctly check for n equals zero.

DSA Typescript

function factorial(n: number): number {
  if (n [1] 0) {
    return 1;
  }
  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 = which assigns instead of compares.

Using != which checks for inequality.

In TypeScript, use === to check for equality without type coercion.

4fill in blank

hard

Fill both blanks to create a recursive factorial function with a base case and recursive step.

DSA Typescript

function factorial([1]: number): number {
  if ([2] === 0) {
    return 1;
  }
  return [2] * factorial([2] - 1);
}

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

An

Bnum

Cx

Dval

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variable names causing reference errors.

Using undefined variables inside the function.

Using the same variable name 'n' for the parameter and inside the function keeps the code clear and consistent.

5fill in blank

hard

Fill all three blanks to create a recursive factorial function with parameter, base case check, and recursive call.

DSA Typescript

function factorial([1]: number): number {
  if ([2] === 0) {
    return 1;
  }
  return [3] * factorial([3] - 1);
}

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

Anum

Bn

Dval

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing variable names causing errors.

Forgetting to decrement the variable in recursive call.

Using 'n' consistently as the parameter and variable name ensures the function works correctly.

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

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

3. Final Answer:

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

4. Quick Check:

   Factorial = product of integers [OK]

Hint: Factorial means multiply all numbers down to 1 [OK]

Common Mistakes:

• Confusing factorial with sum
• Thinking factorial divides
• Mixing factorial with doubling

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

easy

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

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

C. if (n === 0) return 0;

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

Solution

1. Step 1: Identify factorial base case

   Factorial of 0 is defined as 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 is 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 0 returns 1 [OK]

Common Mistakes:

• Returning 0 for base case
• Using wrong base condition
• Returning n+1 incorrectly

3. What is the output of this TypeScript code?

function factorial(n: number): number {
  if (n === 0) return 1;
  return n * factorial(n - 1);
}
console.log(factorial(4));

medium

A. 120

B. 10

C. 16

D. 24

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 D

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

4. Identify the error in this recursive factorial function:

function factorial(n: number): number {
  if (n === 1) return 1;
  return n * factorial(n - 1);
}
console.log(factorial(0));

medium

A. No error, output is 1

B. Infinite recursion for input 0

C. Syntax error due to missing semicolon

D. Returns 0 for input 0

Solution

1. Step 1: Analyze base case for input 0

   Base case triggers only when n === 1, so factorial(0) calls factorial(-1), then factorial(-2), and so on infinitely.

2. Step 2: Understand recursion behavior

   Without base case for 0, recursion never stops for input 0, causing infinite recursion (stack overflow).

3. Final Answer:

   Infinite recursion for input 0 -> Option B

4. Quick Check:

   Missing base case for 0 causes infinite recursion [OK]

Hint: Always include base case for 0 in factorial [OK]

Common Mistakes:

• Missing base case for 0
• Assuming 1 covers 0
• Ignoring negative inputs

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

hard

A. Return 0 for all negative inputs inside recursion

B. Remove the base case and let recursion handle negatives

C. Add a check to return -1 for negative inputs before recursion

D. Use a loop instead of recursion for negatives

Solution

1. Step 1: Understand factorial domain

   Factorial is not defined for negative numbers, so function should handle negatives before recursion.

2. Step 2: Add input validation

   Adding a condition to return -1 (or error) for negative inputs prevents invalid recursion calls.

3. Final Answer:

   Add a check to return -1 for negative inputs before recursion -> Option C

4. Quick Check:

   Validate input before recursion to handle negatives [OK]

Hint: Check negatives first, return error code [OK]

Common Mistakes:

• Ignoring negative inputs
• Letting recursion run on negatives
• Returning wrong values for negatives