Add simple recursion examples: factorial, fibonacci, sum_of_digits

other/simple_recursion.py

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+"""
+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()