Add Magic Number to maths algorithms (keon#730)

Nanak360 · Nanak Bandyopadhyay · web-flow · commit 422b1d16c1dd · 2020-10-29T12:14:57.000-06:00
* add magic number to maths

* add Magic Number to maths

* Update test_maths.py

* Updated variable names and condition statements

Co-authored-by: Nanak Bandyopadhyay &lt;nanakbandyopadhay@hotmail.com&gt;
diff --git a/README.md b/README.md
@@ -209,6 +209,7 @@ If you want to uninstall algorithms, it is as simple as:
     - [gcd/lcm](algorithms/maths/gcd.py)
     - [generate_strobogrammtic](algorithms/maths/generate_strobogrammtic.py)
     - [is_strobogrammatic](algorithms/maths/is_strobogrammatic.py)
+    - [magic_number](algorithms/maths/magic_number.py)
     - [krishnamurthy_number](algorithms/maths/krishnamurthy_number.py)
     - [modular_exponential](algorithms/maths/modular_exponential.py)
     - [modular_inverse](algorithms/maths/modular_inverse.py)
diff --git a/algorithms/maths/__init__.py b/algorithms/maths/__init__.py
@@ -19,4 +19,5 @@
 from .find_primitive_root_simple import *
 from .diffie_hellman_key_exchange import *
 from .power import *
-from .krishnamurthy_number import *
+from .magic_number import *
+from .krishnamurthy_number import *
diff --git a/algorithms/maths/magic_number.py b/algorithms/maths/magic_number.py
@@ -0,0 +1,36 @@
+"""Magic Number
+A number is said to be a magic number,
+if the sum of its digits are calculated till a single digit recursively
+by adding the sum of the digits after every addition.
+If the single digit comes out to be 1,then the number is a magic number.
+
+Example:
+    Number = 50113 => 5+0+1+1+3=10 => 1+0=1 [This is a Magic Number]
+    Number = 1234 => 1+2+3+4=10 => 1+0=1 [This is a Magic Number]
+    Number = 199 => 1+9+9=19 => 1+9=10 => 1+0=1 [This is a Magic Number]
+    Number = 111 => 1+1+1=3 [This is NOT a Magic Number]
+
+The following function checks for Magic numbers and returns a Boolean accordingly.
+"""
+
+
+def magic_number(n):
+    total_sum = 0
+
+    # will end when n becomes 0
+    # AND
+    # sum becomes single digit.
+    while n > 0 or total_sum > 9:
+        
+        # when n becomes 0 but we have a total_sum,
+        # we update the value of n with the value of the sum digits
+        if n == 0:
+            n = total_sum  # only when sum of digits isn't single digit
+            total_sum = 0
+        total_sum += n % 10
+        n //= 10
+
+    # Return true if sum becomes 1
+    return total_sum == 1
+
+
diff --git a/tests/test_maths.py b/tests/test_maths.py
@@ -1,5 +1,5 @@
 from algorithms.maths import (
-    power,power_recur,
+    power, power_recur,
     int_to_base, base_to_int,
     decimal_to_binary_ip,
     euler_totient,
@@ -19,10 +19,11 @@
     combination, combination_memo,
     hailstone,
     cosine_similarity,
+    magic_number,
     find_order,
     find_primitive_root,
-    alice_private_key, alice_public_key, bob_private_key, bob_public_key, alice_shared_key, bob_shared_key, diffie_hellman_key_exchange,
-    krishnamurthy_number,
+    alice_private_key, alice_public_key, bob_private_key, bob_public_key, alice_shared_key, bob_shared_key,
+    diffie_hellman_key_exchange, krishnamurthy_number
 )
 
 import unittest
@@ -40,13 +41,13 @@ 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))
+        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))
+        self.assertEqual(280380, power_recur(2265, 1664, 465465))
 
 
 class TestBaseConversion(unittest.TestCase):
@@ -136,6 +137,7 @@ def test_gcd_bit(self):
         self.assertEqual(4, gcd_bit(8, 12))
         self.assertEqual(1, gcd(13, 17))
 
+
 class TestGenerateStroboGrammatic(unittest.TestCase):
     """[summary]
     Test for the file generate_strobogrammatic.py
@@ -174,7 +176,7 @@ class TestModularInverse(unittest.TestCase):
 
     Arguments:
         unittest {[type]} -- [description]
-    """    
+    """
 
     def test_modular_inverse(self):
         # checks if x * x_inv == 1 (mod m)
@@ -183,6 +185,7 @@ def test_modular_inverse(self):
         self.assertEqual(1, 2 * modular_inverse.modular_inverse(2, 1000000007) % 1000000007)
         self.assertRaises(ValueError, modular_inverse.modular_inverse, 2, 20)
 
+
 class TestModularExponential(unittest.TestCase):
     """[summary]
     Test for the file modular_Exponential.py
@@ -193,8 +196,8 @@ class TestModularExponential(unittest.TestCase):
 
     def test_modular_exponential(self):
         self.assertEqual(1, modular_exponential(5, 117, 19))
-        self.assertEqual(pow(1243, 65321, 10**9 + 7),
-                         modular_exponential(1243, 65321, 10**9 + 7))
+        self.assertEqual(pow(1243, 65321, 10 ** 9 + 7),
+                         modular_exponential(1243, 65321, 10 ** 9 + 7))
         self.assertEqual(1, modular_exponential(12, 0, 78))
         self.assertRaises(ValueError, modular_exponential, 12, -2, 455)
 
@@ -284,7 +287,6 @@ class TestRSA(unittest.TestCase):
     """
 
     def test_encrypt_decrypt(self):
-
         self.assertEqual(7, decrypt(encrypt(7, 23, 143), 47, 143))
 
     # def test_key_generator(self):  # this test takes a while!
@@ -326,15 +328,15 @@ def test_factorial(self):
         self.assertEqual(1, factorial(0))
         self.assertEqual(120, factorial(5))
         self.assertEqual(3628800, factorial(10))
-        self.assertEqual(637816310, factorial(34521, 10**9 + 7))
+        self.assertEqual(637816310, factorial(34521, 10 ** 9 + 7))
         self.assertRaises(ValueError, factorial, -42)
         self.assertRaises(ValueError, factorial, 42, -1)
 
     def test_factorial_recur(self):
         self.assertEqual(1, factorial_recur(0))
         self.assertEqual(120, factorial_recur(5))
         self.assertEqual(3628800, factorial_recur(10))
-        self.assertEqual(637816310, factorial_recur(34521, 10**9 + 7))
+        self.assertEqual(637816310, factorial_recur(34521, 10 ** 9 + 7))
         self.assertRaises(ValueError, factorial_recur, -42)
         self.assertRaises(ValueError, factorial_recur, 42, -1)
 
@@ -346,6 +348,7 @@ class TestHailstone(unittest.TestCase):
     Arguments:
         unittest {[type]} -- [description]
     """
+
     def test_hailstone(self):
         self.assertEqual([8, 4, 2, 1], hailstone.hailstone(8))
         self.assertEqual([10, 5, 16, 8, 4, 2, 1], hailstone.hailstone(10))
@@ -358,6 +361,7 @@ class TestCosineSimilarity(unittest.TestCase):
     Arguments:
         unittest {[type]} -- [description]
     """
+
     def test_cosine_similarity(self):
         vec_a = [1, 1, 1]
         vec_b = [-1, -1, -1]
@@ -374,12 +378,13 @@ class TestFindPrimitiveRoot(unittest.TestCase):
     Arguments:
         unittest {[type]} -- [description]
     """
+
     def test_find_primitive_root_simple(self):
         self.assertListEqual([0], find_primitive_root(1))
         self.assertListEqual([2, 3], find_primitive_root(5))
         self.assertListEqual([], find_primitive_root(24))
         self.assertListEqual([2, 5, 13, 15, 17, 18, 19, 20, 22, 24, 32, 35], find_primitive_root(37))
-        
+
 
 class TestFindOrder(unittest.TestCase):
     """[summary]
@@ -388,6 +393,7 @@ class TestFindOrder(unittest.TestCase):
     Arguments:
         unittest {[type]} -- [description]
     """
+
     def test_find_order_simple(self):
         self.assertEqual(1, find_order(1, 1))
         self.assertEqual(6, find_order(3, 7))
@@ -410,19 +416,37 @@ def test_krishnamurthy_number(self):
         self.assertTrue(krishnamurthy_number(40585))
 
 
+class TestMagicNumber(unittest.TestCase):
+    """[summary]
+    Test for the file find_order_simple.py
+
+    Arguments:
+        unittest {[type]} -- [description]
+    """
+
+    def test_magic_number(self):
+        self.assertTrue(magic_number(50113))
+        self.assertTrue(magic_number(1234))
+        self.assertTrue(magic_number(100))
+        self.assertTrue(magic_number(199))
+        self.assertFalse(magic_number(2000))
+        self.assertFalse(magic_number(500000))
+
+
 class TestDiffieHellmanKeyExchange(unittest.TestCase):
     """[summary]
     Test for the file diffie_hellman_key_exchange.py
 
     Arguments:
         unittest {[type]} -- [description]
     """
+
     def test_find_order_simple(self):
         self.assertFalse(diffie_hellman_key_exchange(3, 6))
         self.assertTrue(diffie_hellman_key_exchange(3, 353))
         self.assertFalse(diffie_hellman_key_exchange(5, 211))
         self.assertTrue(diffie_hellman_key_exchange(11, 971))
 
+
 if __name__ == "__main__":
     unittest.main()
-
