Factorial Using Recursion in DSA Javascript - Interactive Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to return 1 when n is 0.

DSA Javascript

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

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

A1

B0

C-1

Dnull

Attempts:

3 left

💡 Hint

Common Mistakes

Using 1 instead of 0 in the base case condition.

Not having a base case leading to infinite recursion.

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

2fill in blank

medium

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

DSA Javascript

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

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

An - 1

Bn

Cn + 1

D1

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 correctly check for zero.

DSA Javascript

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

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

A0

B1

Cnull

Dundefined

Attempts:

3 left

💡 Hint

Common Mistakes

Using '=' instead of '===' in the if condition.

Checking for 1 instead of 0.

The base case must check if n equals 0 using '===' operator, not assignment '='.

4fill in blank

hard

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

DSA Javascript

function factorial(n) {
  if (n [1] 0) {
    return 1;
  }
  return n [2] factorial(n - 1);
}

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

A===

B*

C==

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using '==' instead of '==='.

Using '+' instead of '*' in recursive multiplication.

The base case uses strict equality '===' to check if n is 0, and the recursive call multiplies n by factorial(n-1).

5fill in blank

hard

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

DSA Javascript

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

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

Anum

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variable names causing errors.

Not subtracting 1 in recursive call.

The function parameter is 'num'. The base case checks if 'num' is 0. The recursive call multiplies 'num' by factorial of 'num - 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 product of all positive integers up to that number

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 matches this definition exactly.

3. Final Answer:

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

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 JavaScript?

easy

A. if (n === 1) return n * factorial(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 is 0, which is correct. Others either return wrong values or recursive calls.

3. Final Answer:

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

4. Quick Check:

   Base case n=0 returns 1 [OK]

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

Common Mistakes:

• Returning 0 for factorial(0)
• Using recursive call in base case
• Confusing base case with recursive step

3. What will be the output of the following JavaScript code?

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

• Adding instead of multiplying
• Stopping recursion too early
• Misunderstanding base case

4. Find the error in this recursive factorial function:

function factorial(n) {
  if (n === 1) return 1;
  return n * factorial(n + 1);
}

medium

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

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

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

D. There is no error; the function is correct

Solution

1. Step 1: Analyze recursive call direction

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

2. Step 2: Correct recursive call

   To reach base case, n should decrease by 1 each call: factorial(n - 1).

3. Final Answer:

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

4. Quick Check:

   Recursion must move toward base case [OK]

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

Common Mistakes:

• Increasing n in recursive call
• Wrong base case value
• Using addition instead of multiplication

5. Consider this modified factorial function that returns the factorial of n only if n is even, otherwise returns 0:

function evenFactorial(n) {
  if (n === 0) return 1;
  if (n % 2 !== 0) return 0;
  return n * evenFactorial(n - 2);
}
console.log(evenFactorial(6));

What is the output of this code?

hard

A. 48

B. 720

C. 0

D. 120

Solution

1. Step 1: Understand function behavior

   Function returns 0 if n is odd. For even n, it multiplies n by factorial of n-2 recursively.

2. Step 2: Calculate evenFactorial(6)

   evenFactorial(6) = 6 * evenFactorial(4) evenFactorial(4) = 4 * evenFactorial(2) evenFactorial(2) = 2 * evenFactorial(0) evenFactorial(0) = 1 (base case) So, 2 * 1 = 2 4 * 2 = 8 6 * 8 = 48

3. Final Answer:

   48 -> Option A

4. Quick Check:

   Product of even numbers down to 0 = 48 [OK]

Hint: Multiply even numbers down by 2 recursively [OK]

Common Mistakes:

• Calculating full factorial instead of even factorial
• Returning 0 for even inputs
• Ignoring base case for 0