Add simple recursion examples: factorial, fibonacci, sum_of_digits

Author: Toshaksha

other/simple_recursion.py

@@ -0,0 +1,100 @@
+"""
+Simple Recursion Examples.
+
+This module contains a few basic examples of recursion for beginners.
+
+Functions:
+- factorial(n): Calculate factorial of n.
+- fibonacci(n): Calculate nth Fibonacci number.
+- sum_of_digits(n): Calculate sum of digits of n.
+
+Each function has doctests to verify correct behavior.
+"""
+
+def factorial(n: int) -> int:
+    """
+    Calculate the factorial of a non-negative integer n using recursion.
+
+    Args:
+        n (int): Non-negative integer.
+
+    Returns:
+        int: Factorial of n.
+
+    Raises:
+        ValueError: If n is negative.
+
+    Examples:
+    >>> factorial(5)
+    120
+    >>> factorial(0)
+    1
+    >>> factorial(1)
+    1
+    """
+    if n < 0:
+        raise ValueError("Input must be a non-negative integer")
+    if n == 0:
+        return 1
+    return n * factorial(n - 1)
+
+
+def fibonacci(n: int) -> int:
+    """
+    Calculate the nth Fibonacci number using recursion.
+
+    Args:
+        n (int): Non-negative integer index.
+
+    Returns:
+        int: nth Fibonacci number.
+
+    Raises:
+        ValueError: If n is negative.
+
+    Examples:
+    >>> fibonacci(0)
+    0
+    >>> fibonacci(1)
+    1
+    >>> fibonacci(7)
+    13
+    """
+    if n < 0:
+        raise ValueError("Input must be a non-negative integer")
+    if n <= 1:
+        return n
+    return fibonacci(n - 1) + fibonacci(n - 2)
+
+
+def sum_of_digits(n: int) -> int:
+    """
+    Calculate the sum of digits of a non-negative integer n using recursion.
+
+    Args:
+        n (int): Non-negative integer.
+
+    Returns:
+        int: Sum of digits of n.
+
+    Raises:
+        ValueError: If n is negative.
+
+    Examples:
+    >>> sum_of_digits(123)
+    6
+    >>> sum_of_digits(0)
+    0
+    >>> sum_of_digits(999)
+    27
+    """
+    if n < 0:
+        raise ValueError("Input must be a non-negative integer")
+    if n == 0:
+        return 0
+    return n % 10 + sum_of_digits(n // 10)
+
+
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod()