Create karatsuba.py (#1309)

* Create karatsuba.py

Added karatsuba algorithm for multiplication of two numbers

* Update karatsuba.py

Added doctests and divmod

* Update karatsuba.py

maths/karatsuba.py

@@ -0,0 +1,31 @@
+""" Multiply two numbers using Karatsuba algorithm """
+
+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)
+    else:
+        m1 = max(len(str(a)), len(str(b)))
+        m2 = m1 // 2
+
+        a1, a2 = divmod(a, 10**m2)
+        b1, b2 = divmod(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()