Add binary exponentiation (#687)

* Add binary exponentiation

* Export power functions

* Fix bug in power_recur function

* Add tests for power functions in power.py

* Fix typo in test

* Add power.py link to README.md

Author: ihebu

README.md

@@ -198,6 +198,7 @@ If you want to uninstall algorithms, it is as simple as:
     - [is_isomorphic](algorithms/map/is_isomorphic.py)
     - [is_anagram](algorithms/map/is_anagram.py)    
 - [maths](algorithms/maths)
+    - [power](algorithms/maths/power.py)
     - [base_conversion](algorithms/maths/base_conversion.py)
     - [combination](algorithms/maths/combination.py)
     - [cosine_similarity](algorithms/maths/cosine_similarity.py)

algorithms/maths/__init__.py

@@ -18,3 +18,4 @@
 from .find_order_simple import *
 from .find_primitive_root_simple import *
 from .diffie_hellman_key_exchange import *
+from .power import *

algorithms/maths/power.py

@@ -0,0 +1,45 @@
+def power(a: int, n: int, r: int = None):
+    """
+    Iterative version of binary exponentiation
+    
+    Calculate a ^ n
+    if r is specified, return the result modulo r
+    
+    Time Complexity :  O(log(n))
+    Space Complexity : O(1)
+    """
+    ans = 1
+    while n:
+        if n & 1:
+            ans = ans * a
+        a = a * a
+        if r:
+            ans %= r
+            a %= r
+        n >>= 1
+    return ans
+
+
+def power_recur(a: int, n: int, r: int = None):
+    """
+    Recursive version of binary exponentiation
+    
+    Calculate a ^ n
+    if r is specified, return the result modulo r
+    
+    Time Complexity :  O(log(n))
+    Space Complexity : O(log(n))
+    """
+    if n == 0:
+        ans = 1
+    elif n == 1:
+        ans = a
+    else:
+        ans = power_recur(a, n // 2, r)
+        ans = ans * ans
+        if n % 2:
+            ans = ans * a
+    if r:
+        ans %= r
+    return ans
+

tests/test_maths.py

@@ -1,4 +1,5 @@
 from algorithms.maths import (
+    power,power_recur,
     int_to_base, base_to_int,
     decimal_to_binary_ip,
     euler_totient,
@@ -25,6 +26,27 @@
 import unittest
 
 
+class TestPower(unittest.TestCase):
+    """
+    Test for the file power.py
+
+    Arguments:
+        unittest {[type]} -- [description]
+    """
+
+    def test_power(self):
+        self.assertEqual(8, power(2, 3))
+        self.assertEqual(1, power(5, 0))
+        self.assertEqual(0, power(10, 3, 5))
+        self.assertEqual(280380, power(2265, 1664,465465))
+
+    def test_power_recur(self):
+        self.assertEqual(8, power_recur(2, 3))
+        self.assertEqual(1, power_recur(5, 0))
+        self.assertEqual(0, power_recur(10, 3, 5))
+        self.assertEqual(280380, power_recur(2265, 1664,465465))
+
+
 class TestBaseConversion(unittest.TestCase):
     """
     Test for the file base_conversion.py