Problem
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Factorial of a Number .
Certification: Basic Level
Accuracy: 58.82%
Submissions: 17
Points: 10
Write a C# 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: n = 5
- Output: 120
- Explanation:
- Step 1: Check if n is 0 or 1. If so, return 1 (base case).
- Step 2: For n = 5, recursively calculate 5 × factorial(4).
- Step 3: For factorial(4), recursively calculate 4 × factorial(3).
- Step 4: For factorial(3), recursively calculate 3 × factorial(2).
- Step 5: For factorial(2), recursively calculate 2 × factorial(1).
- Step 6: For factorial(1), return 1 (base case).
- Step 7: Return 5 × 4 × 3 × 2 × 1 = 120.
Example 2
- Input: n = 0
- Output: 1
- Explanation:
- Step 1: Check if n is 0 or 1. Since n = 0, return 1 (base case).
- Step 2: By mathematical definition, factorial of 0 is 1.
Constraints
- 0 ≤ n ≤ 12 (to prevent integer overflow)
- Time Complexity: O(n) (Recursive calls up to n)
- Space Complexity: O(n) (Recursive call stack)
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Solution Hints
- Base case: if n is 0 or 1, return 1
- Recursive case: return n * factorial(n-1)
- Consider using memoization for optimization
- Handle edge case for negative numbers