From f06fa44c26a424e2c5ffb491ecc720bbd89e347a Mon Sep 17 00:00:00 2001
From: Rishabh Kumar <rishabh0098@gmail.com>
Date: Tue, 8 Oct 2019 15:31:17 +0530
Subject: [PATCH 1/3] Create karatsuba.py

Added karatsuba algorithm for multiplication of two numbers
---
 maths/karatsuba.py | 27 +++++++++++++++++++++++++++
 1 file changed, 27 insertions(+)
 create mode 100644 maths/karatsuba.py

diff --git a/maths/karatsuba.py b/maths/karatsuba.py
new file mode 100644
index 000000000000..c61006ad5868
--- /dev/null
+++ b/maths/karatsuba.py
@@ -0,0 +1,27 @@
+""" Multiply two numbers using Karatsuba algorithm """
+
+def karatsuba(a, b):
+    if len(str(a)) == 1 or len(str(b)) == 1:
+        return (a * b)
+    else:
+        m1 = max(len(str(a)), len(str(b)))
+        m2 = m1 // 2
+
+        a1 = a // 10**(m2)
+        a2 = a % 10**(m2)
+        b1 = b // 10**(m2)
+        b2 = b % 10**(m2)
+
+        x = karatsuba(a2, b2)
+        y = karatsuba((a1 + a2), (b1 + b2))
+        z = karatsuba(a1, b1)
+
+        return ((z * 10**(2*m2)) + ((y - z - x) * 10**(m2)) + (x))
+
+
+def main():
+    print(karatsuba(15463, 23489))
+
+
+if __name__ == "__main__":
+    main()

From 458aa9b860d035fd36d1d540b5075140a3221353 Mon Sep 17 00:00:00 2001
From: Rishabh Kumar <rishabh0098@gmail.com>
Date: Tue, 8 Oct 2019 16:22:31 +0530
Subject: [PATCH 2/3] Update karatsuba.py

Added doctests and divmod
---
 maths/karatsuba.py | 11 +++++++----
 1 file changed, 7 insertions(+), 4 deletions(-)

diff --git a/maths/karatsuba.py b/maths/karatsuba.py
index c61006ad5868..4fe4bf8b2fbf 100644
--- a/maths/karatsuba.py
+++ b/maths/karatsuba.py
@@ -1,16 +1,19 @@
 """ Multiply two numbers using Karatsuba algorithm """
 
 def karatsuba(a, b):
+    """
+    >>> karatsuba(15463, 23489) == 15463 * 23489
+    True
+    >>> karatsuba(3, 9) == 3 * 9
+    """
     if len(str(a)) == 1 or len(str(b)) == 1:
         return (a * b)
     else:
         m1 = max(len(str(a)), len(str(b)))
         m2 = m1 // 2
 
-        a1 = a // 10**(m2)
-        a2 = a % 10**(m2)
-        b1 = b // 10**(m2)
-        b2 = b % 10**(m2)
+        a1, a2 = divmod(a, 10**m2)
+        b1, b2 = divmod(b, 10**m2)
 
         x = karatsuba(a2, b2)
         y = karatsuba((a1 + a2), (b1 + b2))

From b4a940c582745244eee60b63b81657116304691d Mon Sep 17 00:00:00 2001
From: Rishabh Kumar <rishabh0098@gmail.com>
Date: Tue, 8 Oct 2019 17:19:37 +0530
Subject: [PATCH 3/3] Update karatsuba.py

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

diff --git a/maths/karatsuba.py b/maths/karatsuba.py
index 4fe4bf8b2fbf..be4630184933 100644
--- a/maths/karatsuba.py
+++ b/maths/karatsuba.py
@@ -5,6 +5,7 @@ def karatsuba(a, b):
     >>> karatsuba(15463, 23489) == 15463 * 23489
     True
     >>> karatsuba(3, 9) == 3 * 9
+    True
     """
     if len(str(a)) == 1 or len(str(b)) == 1:
         return (a * b)