Fix: improve GCD function with documentation and better test cases

Author: Achintya47

maths/greatest_common_divisor.py

@@ -1,55 +1,171 @@
 """
 Greatest Common Divisor.
-
 Wikipedia reference: https://en.wikipedia.org/wiki/Greatest_common_divisor
-
 gcd(a, b) = gcd(a, -b) = gcd(-a, b) = gcd(-a, -b) by definition of divisibility
 """
 
 
 def greatest_common_divisor(a: int, b: int) -> int:
     """
-    Calculate Greatest Common Divisor (GCD).
-    >>> greatest_common_divisor(24, 40)
-    8
-    >>> greatest_common_divisor(1, 1)
-    1
-    >>> greatest_common_divisor(1, 800)
-    1
-    >>> greatest_common_divisor(11, 37)
-    1
-    >>> greatest_common_divisor(3, 5)
-    1
-    >>> greatest_common_divisor(16, 4)
-    4
-    >>> greatest_common_divisor(-3, 9)
-    3
-    >>> greatest_common_divisor(9, -3)
-    3
-    >>> greatest_common_divisor(3, -9)
-    3
-    >>> greatest_common_divisor(-3, -9)
-    3
+    Calculate Greatest Common Divisor (GCD) using Euclidean algorithm recursively.
+    
+    The GCD of two integers is the largest positive integer that divides both numbers.
+    
+    Args:
+        a: First integer
+        b: Second integer
+    
+    Returns:
+        The greatest common divisor of a and b
+    
+    Examples:
+        Basic cases:
+        >>> greatest_common_divisor(24, 40)
+        8
+        >>> greatest_common_divisor(48, 18)
+        6
+        >>> greatest_common_divisor(100, 25)
+        25
+        >>> greatest_common_divisor(17, 19)
+        1
+        
+        Edge cases with small numbers:
+        >>> greatest_common_divisor(1, 1)
+        1
+        >>> greatest_common_divisor(1, 800)
+        1
+        >>> greatest_common_divisor(11, 37)
+        1
+        >>> greatest_common_divisor(3, 5)
+        1
+        >>> greatest_common_divisor(16, 4)
+        4
+        
+        Cases with zero:
+        >>> greatest_common_divisor(0, 5)
+        5
+        >>> greatest_common_divisor(5, 0)
+        5
+        >>> greatest_common_divisor(0, 0)
+        0
+        
+        Negative numbers:
+        >>> greatest_common_divisor(-3, 9)
+        3
+        >>> greatest_common_divisor(9, -3)
+        3
+        >>> greatest_common_divisor(3, -9)
+        3
+        >>> greatest_common_divisor(-3, -9)
+        3
+        >>> greatest_common_divisor(-24, -40)
+        8
+        >>> greatest_common_divisor(-48, 18)
+        6
+        
+        Large numbers:
+        >>> greatest_common_divisor(1071, 462)
+        21
+        >>> greatest_common_divisor(12345, 54321)
+        3
+        
+        Same numbers:
+        >>> greatest_common_divisor(42, 42)
+        42
+        >>> greatest_common_divisor(-15, -15)
+        15
+        
+        One divides the other:
+        >>> greatest_common_divisor(15, 45)
+        15
+        >>> greatest_common_divisor(7, 49)
+        7
     """
     return abs(b) if a == 0 else greatest_common_divisor(b % a, a)
 
 
 def gcd_by_iterative(x: int, y: int) -> int:
     """
-    Below method is more memory efficient because it does not create additional
-    stack frames for recursive functions calls (as done in the above method).
-    >>> gcd_by_iterative(24, 40)
-    8
-    >>> greatest_common_divisor(24, 40) == gcd_by_iterative(24, 40)
-    True
-    >>> gcd_by_iterative(-3, -9)
-    3
-    >>> gcd_by_iterative(3, -9)
-    3
-    >>> gcd_by_iterative(1, -800)
-    1
-    >>> gcd_by_iterative(11, 37)
-    1
+    Calculate Greatest Common Divisor (GCD) using iterative Euclidean algorithm.
+    
+    This method is more memory efficient because it does not create additional
+    stack frames for recursive function calls.
+    
+    Args:
+        x: First integer
+        y: Second integer
+    
+    Returns:
+        The greatest common divisor of x and y
+    
+    Examples:
+        Basic cases:
+        >>> gcd_by_iterative(24, 40)
+        8
+        >>> gcd_by_iterative(48, 18)
+        6
+        >>> gcd_by_iterative(100, 25)
+        25
+        >>> gcd_by_iterative(17, 19)
+        1
+        
+        Verify equivalence with recursive version:
+        >>> greatest_common_divisor(24, 40) == gcd_by_iterative(24, 40)
+        True
+        >>> greatest_common_divisor(48, 18) == gcd_by_iterative(48, 18)
+        True
+        >>> greatest_common_divisor(100, 25) == gcd_by_iterative(100, 25)
+        True
+        
+        Edge cases with small numbers:
+        >>> gcd_by_iterative(1, 1)
+        1
+        >>> gcd_by_iterative(1, 800)
+        1
+        >>> gcd_by_iterative(11, 37)
+        1
+        >>> gcd_by_iterative(16, 4)
+        4
+        
+        Cases with zero:
+        >>> gcd_by_iterative(0, 5)
+        5
+        >>> gcd_by_iterative(5, 0)
+        5
+        >>> gcd_by_iterative(0, 0)
+        0
+        
+        Negative numbers:
+        >>> gcd_by_iterative(-3, -9)
+        3
+        >>> gcd_by_iterative(3, -9)
+        3
+        >>> gcd_by_iterative(-3, 9)
+        3
+        >>> gcd_by_iterative(1, -800)
+        1
+        >>> gcd_by_iterative(-24, -40)
+        8
+        >>> gcd_by_iterative(-48, 18)
+        6
+        
+        Large numbers:
+        >>> gcd_by_iterative(1071, 462)
+        21
+        >>> gcd_by_iterative(12345, 54321)
+        3
+        
+        Same numbers:
+        >>> gcd_by_iterative(42, 42)
+        42
+        >>> gcd_by_iterative(-15, -15)
+        15
+        
+        One divides the other:
+        >>> gcd_by_iterative(15, 45)
+        15
+        >>> gcd_by_iterative(7, 49)
+        7
     """
     while y:  # --> when y=0 then loop will terminate and return x as final GCD.
         x, y = y, x % y
@@ -58,7 +174,14 @@ def gcd_by_iterative(x: int, y: int) -> int:
 
 def main():
     """
-    Call Greatest Common Divisor function.
+    Call Greatest Common Divisor function with user input.
+    
+    Prompts user for two integers separated by comma and calculates their GCD
+    using both recursive and iterative methods.
+    
+    Examples:
+        This function handles user input, so direct doctests aren't practical.
+        However, it should handle valid input like "24,40" and invalid input gracefully.
     """
     try:
         nums = input("Enter two integers separated by comma (,): ").split(",")
@@ -74,4 +197,4 @@ def main():
 
 
 if __name__ == "__main__":
-    main()
+    main()