Factorial Using Recursion in DSA Typescript - Build from Scratch

Factorial Using Recursion

📖 Scenario: Imagine you are helping a friend who wants to calculate the factorial of a number. Factorial means multiplying a number by all the numbers below it down to 1. For example, 4 factorial is 4 x 3 x 2 x 1 = 24.

🎯 Goal: You will write a small program in TypeScript that uses a function calling itself (recursion) to find the factorial of a number.

📋 What You'll Learn

Create a variable called num with the value 5

Create a function called factorial that uses recursion to calculate factorial

Call the factorial function with num and store the result in result

Print the value of result

💡 Why This Matters

🌍 Real World

Calculating factorials is useful in math problems, probability, and computer science algorithms.

💼 Career

Understanding recursion helps in solving complex problems and is a common topic in programming interviews.

1

Create the number variable

Create a variable called num and set it to the number 5.

DSA Typescript

# Your code here

Hint

Use const num = 5; to create the number variable.

2

Write the recursive factorial function

Create a function called factorial that takes a parameter n. Use recursion: if n is 1, return 1; otherwise return n * factorial(n - 1).

DSA Typescript

const num = 5;
// Your code here

Hint

Remember, the function calls itself with n - 1 until it reaches 1.

3

Calculate factorial and store result

Call the factorial function with num and store the result in a variable called result.

DSA Typescript

const num = 5;

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

// Your code here

Hint

Use const result = factorial(num); to store the factorial.

4

Print the factorial result

Print the value of result using console.log.

DSA Typescript

const num = 5;

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

const result = factorial(num);

// Your code here

Hint

Use console.log(result); to print the factorial.

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