From 1469a9500d70c171c98549f38aa1cd5bed1a866a Mon Sep 17 00:00:00 2001
From: Joyce <jycyeo@yahoo.com.sg>
Date: Fri, 2 Oct 2020 07:41:16 +0800
Subject: [PATCH 1/6] add type hints to math/gcd

---
 maths/greatest_common_divisor.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/maths/greatest_common_divisor.py b/maths/greatest_common_divisor.py
index 0926ade5dec2..9b7a22574677 100644
--- a/maths/greatest_common_divisor.py
+++ b/maths/greatest_common_divisor.py
@@ -5,7 +5,7 @@
 """
 
 
-def greatest_common_divisor(a, b):
+def greatest_common_divisor(a: int, b: int) -> int:
     """
     Calculate Greatest Common Divisor (GCD).
     >>> greatest_common_divisor(24, 40)
@@ -31,7 +31,7 @@ def greatest_common_divisor(a, b):
 """
 
 
-def gcd_by_iterative(x, y):
+def gcd_by_iterative(x: int, y: int) -> int:
     """
     >>> gcd_by_iterative(24, 40)
     8

From bda4aa3be70de20d5e3bfa4429cb290b8d8f090c Mon Sep 17 00:00:00 2001
From: Joyce <jycyeo@yahoo.com.sg>
Date: Fri, 2 Oct 2020 07:43:41 +0800
Subject: [PATCH 2/6] add doctest

---
 maths/greatest_common_divisor.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/maths/greatest_common_divisor.py b/maths/greatest_common_divisor.py
index 9b7a22574677..97c0da12e7ee 100644
--- a/maths/greatest_common_divisor.py
+++ b/maths/greatest_common_divisor.py
@@ -59,4 +59,6 @@ def main():
 
 
 if __name__ == "__main__":
+    import doctest
+    doctest.testmod()
     main()

From 4f7c9eb518acef004782e716ac7e10ae588a81d4 Mon Sep 17 00:00:00 2001
From: Joyce <jycyeo@yahoo.com.sg>
Date: Fri, 2 Oct 2020 07:51:06 +0800
Subject: [PATCH 3/6] math/gcd - run black formatter

---
 maths/greatest_common_divisor.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/maths/greatest_common_divisor.py b/maths/greatest_common_divisor.py
index 97c0da12e7ee..0c341deb39cf 100644
--- a/maths/greatest_common_divisor.py
+++ b/maths/greatest_common_divisor.py
@@ -60,5 +60,6 @@ def main():
 
 if __name__ == "__main__":
     import doctest
+
     doctest.testmod()
     main()

From 83b57dd439efe351b749aef319cf96762de30a20 Mon Sep 17 00:00:00 2001
From: Joyce <jycyeo@yahoo.com.sg>
Date: Fri, 2 Oct 2020 08:12:43 +0800
Subject: [PATCH 4/6] math/gcd: remove manual doctest

---
 maths/greatest_common_divisor.py | 3 ---
 1 file changed, 3 deletions(-)

diff --git a/maths/greatest_common_divisor.py b/maths/greatest_common_divisor.py
index 0c341deb39cf..9b7a22574677 100644
--- a/maths/greatest_common_divisor.py
+++ b/maths/greatest_common_divisor.py
@@ -59,7 +59,4 @@ def main():
 
 
 if __name__ == "__main__":
-    import doctest
-
-    doctest.testmod()
     main()

From de154b2faed4b056396683dd2203b3018a3d2937 Mon Sep 17 00:00:00 2001
From: Joyce <jycyeo@yahoo.com.sg>
Date: Fri, 2 Oct 2020 13:41:30 +0800
Subject: [PATCH 5/6] add correction to gcd of negative numbers

---
 maths/greatest_common_divisor.py | 31 +++++++++++++++++++++----------
 1 file changed, 21 insertions(+), 10 deletions(-)

diff --git a/maths/greatest_common_divisor.py b/maths/greatest_common_divisor.py
index 9b7a22574677..121869cb2be2 100644
--- a/maths/greatest_common_divisor.py
+++ b/maths/greatest_common_divisor.py
@@ -2,6 +2,8 @@
 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
 """
 
 
@@ -20,31 +22,40 @@ def greatest_common_divisor(a: int, b: int) -> int:
     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
     """
-    return b if a == 0 else greatest_common_divisor(b % a, a)
-
-
-"""
-Below method is more memory efficient because it does not use the stack (chunk of
-memory).  While above method is good, uses more memory for huge numbers because of the
-recursive calls required to calculate the greatest common divisor.
-"""
+    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
     """
     while y:  # --> when y=0 then loop will terminate and return x as final GCD.
         x, y = y, x % y
-    return x
+    return abs(x)
 
 
 def main():
-    """Call Greatest Common Divisor function."""
+    """
+    Call Greatest Common Divisor function.
+    """
     try:
         nums = input("Enter two integers separated by comma (,): ").split(",")
         num_1 = int(nums[0])

From cd0f1c4c03b61eacbcf2a126d41d1c28532735fc Mon Sep 17 00:00:00 2001
From: Joyce <jycyeo@yahoo.com.sg>
Date: Fri, 2 Oct 2020 14:19:10 +0800
Subject: [PATCH 6/6] add more doctest in iterative gcd

---
 maths/greatest_common_divisor.py | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/maths/greatest_common_divisor.py b/maths/greatest_common_divisor.py
index 121869cb2be2..a2174a8eb74a 100644
--- a/maths/greatest_common_divisor.py
+++ b/maths/greatest_common_divisor.py
@@ -46,6 +46,10 @@ def gcd_by_iterative(x: int, y: int) -> int:
     3
     >>> gcd_by_iterative(3, -9)
     3
+    >>> gcd_by_iterative(1, -800)
+    1
+    >>> gcd_by_iterative(11, 37)
+    1
     """
     while y:  # --> when y=0 then loop will terminate and return x as final GCD.
         x, y = y, x % y