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Recursive Function to Compute Factorial

Certification: Intermediate Level Accuracy: 50% Submissions: 2 Points: 10

Write a Python function that calculates the factorial of a given number using recursion. The factorial of a non-negative integer n is the product of all positive integers less than or equal to n.

Example 1
    
  
  • Input: 5
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  • Output: 120
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  • Explanation: 
    
      
      
    • Step 1: Take the input number 5.
      • 
      
    • Step 2: Calculate the factorial: 5 × 4 × 3 × 2 × 1 = 120.
      • 
      
    • Step 3: Return 120 as the result.
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Example 2
    
  
  • Input: 0
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  • Output: 1
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  • Explanation: 
    
      
      
    • Step 1: Take the input number 0.
      • 
      
    • Step 2: The factorial of 0 is defined as 1.
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    • Step 3: Return 1 as the result.
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Constraints
    
  
  • 0 ≤ n ≤ 998 (Python recursion limit may be reached for larger values)
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  • Return the factorial of the input number
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  • Time Complexity: O(n), where n is the input number
    • 
  
  • Space Complexity: O(n) due to the recursion stack
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Hint
Solution

Solution Hints

    
  
  • Base case: if n is 0 or 1, return 1
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  • Recursive case: return n * factorial(n-1)
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  • Consider using memoization for optimization
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  • Handle edge case for negative numbers
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Steps to solve by this approach:

 Step 1: Define the base cases for factorial calculation (0! = 1 and 1! = 1).
 Step 2: Check if n equals 0 or 1, and return 1 if true.
 Step 3: For n > 1, use the recursive formula: n! = n × (n-1)!
 Step 4: Make a recursive call to factorial(n-1).
 Step 5: Multiply n with the result of factorial(n-1).
 Step 6: Return the product as the factorial of n.
 Step 7: Example: factorial(5) = 5 × 4! = 5 × 24 = 120.

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