From 7444a1f0693c5e08d6859d549ce5485db5a988b1 Mon Sep 17 00:00:00 2001
From: Ghulam Mohiyuddin <subahani98@gmail.com>
Date: Tue, 22 Oct 2019 14:56:06 +0530
Subject: [PATCH] Another method added for GCD (#1387)

* Another method added for GCD

* Now doctest fulfilled for added method.

* Update greatest_common_divisor.py

* Now unnecessary white spaces removed.

* Cycle_Detection_Undirected_Graph

Cycle_Detection_Undirected_Graph using Disjoint set DataStructure

* Update greatest_common_divisor.py again

* Again Updated cycle_detection_undirected_graph.py

* Delete cycle_detection_undirected_graph.py

* Add doctests and format the code with psf/black

* fixup: Typo

* Update greatest_common_divisor.py

* greatest_common_divisor()
---
 maths/greatest_common_divisor.py | 38 ++++++++++++++++++++++++++------
 1 file changed, 31 insertions(+), 7 deletions(-)

diff --git a/maths/greatest_common_divisor.py b/maths/greatest_common_divisor.py
index ebc08f37f..a1b915bc3 100644
--- a/maths/greatest_common_divisor.py
+++ b/maths/greatest_common_divisor.py
@@ -5,20 +5,44 @@ Wikipedia reference: https://en.wikipedia.org/wiki/Greatest_common_divisor
 """
 
 
-def gcd(a, b):
-    """Calculate Greatest Common Divisor (GCD)."""
-    return b if a == 0 else gcd(b % a, a)
+def greatest_common_divisor(a, b):
+    """
+    Calculate Greatest Common Divisor (GCD).
+    >>> greatest_common_divisor(24, 40)
+    8
+    """
+    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.
+"""
+
+
+def gcd_by_iterative(x, y):
+    """
+    >>> gcd_by_iterative(24, 40)
+    8
+    >>> greatest_common_divisor(24, 40) == gcd_by_iterative(24, 40)
+    True
+    """
+    while y:  # --> when y=0 then loop will terminate and return x as final GCD.
+        x, y = y, x % y
+    return x
 
 
 def main():
-    """Call GCD Function."""
+    """Call Greatest Common Divisor function."""
     try:
-        nums = input("Enter two Integers separated by comma (,): ").split(",")
+        nums = input("Enter two integers separated by comma (,): ").split(",")
         num_1 = int(nums[0])
         num_2 = int(nums[1])
-        print(f"gcd({num_1}, {num_2}) = {gcd(num_1, num_2)}")
+        print(f"greatest_common_divisor({num_1}, {num_2}) = {greatest_common_divisor(num_1, num_2)}")
+        print(f"By iterative gcd({num_1}, {num_2}) = {gcd_by_iterative(num_1, num_2)}")
     except (IndexError, UnboundLocalError, ValueError):
-        print("Wrong Input")
+        print("Wrong input")
 
 
 if __name__ == "__main__":