From 2c4994cb09c6b77c379412e79445283943d49acb Mon Sep 17 00:00:00 2001
From: AasheeshLikePanner <ashishlearningsoftware@gmail.com>
Date: Mon, 2 Oct 2023 22:54:16 +0530
Subject: [PATCH 01/12] Adding doctests and changing file name

---
 ...ntiation_2.py => binary_multiplication.py} | 58 +++++++++++++++++++
 1 file changed, 58 insertions(+)
 rename maths/{binary_exponentiation_2.py => binary_multiplication.py} (51%)

diff --git a/maths/binary_exponentiation_2.py b/maths/binary_multiplication.py
similarity index 51%
rename from maths/binary_exponentiation_2.py
rename to maths/binary_multiplication.py
index af8f776dd266..ee7dd95c3da5 100644
--- a/maths/binary_exponentiation_2.py
+++ b/maths/binary_multiplication.py
@@ -12,6 +12,32 @@
 
 
 def b_expo(a: int, b: int) -> int:
+    """
+        Calculate the result of multiplying 'a' and 'b' using bitwise multiplication.
+
+        Parameters:
+        a (int): The first number.
+        b (int): The second number.
+
+        Returns:
+        int: The result of 'a' multiplied by 'b'.
+
+        Examples:
+        >>> b_expo(2, 3)
+        6
+        >>> b_expo(5, 0)
+        0
+        >>> b_expo(3, 4)
+        12
+        >>> b_expo(10, 5)
+        50
+        >>> b_expo(0, 5)
+        0
+        >>> b_expo(2, 1)
+        2
+        >>> b_expo(1, 10)
+        10
+        """
     res = 0
     while b > 0:
         if b & 1:
@@ -24,6 +50,35 @@ def b_expo(a: int, b: int) -> int:
 
 
 def b_expo_mod(a: int, b: int, c: int) -> int:
+    """
+       Calculate the result of (a * b) % c using binary exponentiation and modular arithmetic.
+
+       Parameters:
+       a (int): The first number.
+       b (int): The second number.
+       c (int): The modulus.
+
+       Returns:
+       int: The result of (a * b) % c.
+
+       Examples:
+       >>> b_expo_mod(2, 3, 5)
+       1
+       >>> b_expo_mod(5, 0, 7)
+       0
+       >>> b_expo_mod(3, 4, 6)
+       0
+       >>> b_expo_mod(10, 5, 13)
+       8
+       >>> b_expo_mod(2, 1, 5)
+       2
+       >>> b_expo_mod(1, 10, 3)
+       1
+       >>> b_expo_mod(7, 3, 4)
+       1
+       >>> b_expo_mod(8, 2, 10)
+       6
+       """
     res = 0
     while b > 0:
         if b & 1:
@@ -34,6 +89,9 @@ def b_expo_mod(a: int, b: int, c: int) -> int:
 
     return res
 
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod()
 
 """
 * Wondering how this method works !

From 90e5eb8cf1d40962ca8c63f1b0cb3c1d80af8317 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Mon, 2 Oct 2023 17:26:40 +0000
Subject: [PATCH 02/12] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/binary_multiplication.py | 108 +++++++++++++++++----------------
 1 file changed, 55 insertions(+), 53 deletions(-)

diff --git a/maths/binary_multiplication.py b/maths/binary_multiplication.py
index ee7dd95c3da5..573ae615de2e 100644
--- a/maths/binary_multiplication.py
+++ b/maths/binary_multiplication.py
@@ -13,31 +13,31 @@
 
 def b_expo(a: int, b: int) -> int:
     """
-        Calculate the result of multiplying 'a' and 'b' using bitwise multiplication.
-
-        Parameters:
-        a (int): The first number.
-        b (int): The second number.
-
-        Returns:
-        int: The result of 'a' multiplied by 'b'.
-
-        Examples:
-        >>> b_expo(2, 3)
-        6
-        >>> b_expo(5, 0)
-        0
-        >>> b_expo(3, 4)
-        12
-        >>> b_expo(10, 5)
-        50
-        >>> b_expo(0, 5)
-        0
-        >>> b_expo(2, 1)
-        2
-        >>> b_expo(1, 10)
-        10
-        """
+    Calculate the result of multiplying 'a' and 'b' using bitwise multiplication.
+
+    Parameters:
+    a (int): The first number.
+    b (int): The second number.
+
+    Returns:
+    int: The result of 'a' multiplied by 'b'.
+
+    Examples:
+    >>> b_expo(2, 3)
+    6
+    >>> b_expo(5, 0)
+    0
+    >>> b_expo(3, 4)
+    12
+    >>> b_expo(10, 5)
+    50
+    >>> b_expo(0, 5)
+    0
+    >>> b_expo(2, 1)
+    2
+    >>> b_expo(1, 10)
+    10
+    """
     res = 0
     while b > 0:
         if b & 1:
@@ -51,34 +51,34 @@ def b_expo(a: int, b: int) -> int:
 
 def b_expo_mod(a: int, b: int, c: int) -> int:
     """
-       Calculate the result of (a * b) % c using binary exponentiation and modular arithmetic.
-
-       Parameters:
-       a (int): The first number.
-       b (int): The second number.
-       c (int): The modulus.
-
-       Returns:
-       int: The result of (a * b) % c.
-
-       Examples:
-       >>> b_expo_mod(2, 3, 5)
-       1
-       >>> b_expo_mod(5, 0, 7)
-       0
-       >>> b_expo_mod(3, 4, 6)
-       0
-       >>> b_expo_mod(10, 5, 13)
-       8
-       >>> b_expo_mod(2, 1, 5)
-       2
-       >>> b_expo_mod(1, 10, 3)
-       1
-       >>> b_expo_mod(7, 3, 4)
-       1
-       >>> b_expo_mod(8, 2, 10)
-       6
-       """
+    Calculate the result of (a * b) % c using binary exponentiation and modular arithmetic.
+
+    Parameters:
+    a (int): The first number.
+    b (int): The second number.
+    c (int): The modulus.
+
+    Returns:
+    int: The result of (a * b) % c.
+
+    Examples:
+    >>> b_expo_mod(2, 3, 5)
+    1
+    >>> b_expo_mod(5, 0, 7)
+    0
+    >>> b_expo_mod(3, 4, 6)
+    0
+    >>> b_expo_mod(10, 5, 13)
+    8
+    >>> b_expo_mod(2, 1, 5)
+    2
+    >>> b_expo_mod(1, 10, 3)
+    1
+    >>> b_expo_mod(7, 3, 4)
+    1
+    >>> b_expo_mod(8, 2, 10)
+    6
+    """
     res = 0
     while b > 0:
         if b & 1:
@@ -89,8 +89,10 @@ def b_expo_mod(a: int, b: int, c: int) -> int:
 
     return res
 
+
 if __name__ == "__main__":
     import doctest
+
     doctest.testmod()
 
 """

From 85f2cc1a3e90564c2b8257568acb41830aee4d46 Mon Sep 17 00:00:00 2001
From: Aasheesh <126905285+AasheeshLikePanner@users.noreply.github.com>
Date: Tue, 3 Oct 2023 16:15:08 +0530
Subject: [PATCH 03/12] Update binary_multiplication.py

---
 maths/binary_multiplication.py | 7 +------
 1 file changed, 1 insertion(+), 6 deletions(-)

diff --git a/maths/binary_multiplication.py b/maths/binary_multiplication.py
index 573ae615de2e..8769316f7370 100644
--- a/maths/binary_multiplication.py
+++ b/maths/binary_multiplication.py
@@ -51,7 +51,7 @@ def b_expo(a: int, b: int) -> int:
 
 def b_expo_mod(a: int, b: int, c: int) -> int:
     """
-    Calculate the result of (a * b) % c using binary exponentiation and modular arithmetic.
+    Calculate (a * b) % c using binary exponentiation and modular arithmetic.
 
     Parameters:
     a (int): The first number.
@@ -74,10 +74,6 @@ def b_expo_mod(a: int, b: int, c: int) -> int:
     2
     >>> b_expo_mod(1, 10, 3)
     1
-    >>> b_expo_mod(7, 3, 4)
-    1
-    >>> b_expo_mod(8, 2, 10)
-    6
     """
     res = 0
     while b > 0:
@@ -92,7 +88,6 @@ def b_expo_mod(a: int, b: int, c: int) -> int:
 
 if __name__ == "__main__":
     import doctest
-
     doctest.testmod()
 
 """

From dd16da3a74d00af727071b599c04353ae6c82343 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 3 Oct 2023 10:47:13 +0000
Subject: [PATCH 04/12] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/binary_multiplication.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/maths/binary_multiplication.py b/maths/binary_multiplication.py
index 8769316f7370..fda4669ea493 100644
--- a/maths/binary_multiplication.py
+++ b/maths/binary_multiplication.py
@@ -88,6 +88,7 @@ def b_expo_mod(a: int, b: int, c: int) -> int:
 
 if __name__ == "__main__":
     import doctest
+
     doctest.testmod()
 
 """

From ff50144aad5723c877f61a1896c95526f13b9028 Mon Sep 17 00:00:00 2001
From: Aasheesh <126905285+AasheeshLikePanner@users.noreply.github.com>
Date: Tue, 3 Oct 2023 16:20:18 +0530
Subject: [PATCH 05/12] Update binary_multiplication.py

---
 maths/binary_multiplication.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/maths/binary_multiplication.py b/maths/binary_multiplication.py
index fda4669ea493..1be5b93048a2 100644
--- a/maths/binary_multiplication.py
+++ b/maths/binary_multiplication.py
@@ -69,7 +69,7 @@ def b_expo_mod(a: int, b: int, c: int) -> int:
     >>> b_expo_mod(3, 4, 6)
     0
     >>> b_expo_mod(10, 5, 13)
-    8
+    11
     >>> b_expo_mod(2, 1, 5)
     2
     >>> b_expo_mod(1, 10, 3)

From c20642e277ea76de32546b5d1c02fdc79b6f96a4 Mon Sep 17 00:00:00 2001
From: AasheeshLikePanner <ashishlearningsoftware@gmail.com>
Date: Tue, 3 Oct 2023 19:51:46 +0530
Subject: [PATCH 06/12] Changing comment and changing name function

---
 maths/binary_multiplication.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/maths/binary_multiplication.py b/maths/binary_multiplication.py
index ee7dd95c3da5..f58f21a7ddd5 100644
--- a/maths/binary_multiplication.py
+++ b/maths/binary_multiplication.py
@@ -1,5 +1,5 @@
 """
-* Binary Exponentiation with Multiplication
+* Binary Multiplication with Multiplication
 * This is a method to find a*b in a time complexity of O(log b)
 * This is one of the most commonly used methods of finding result of multiplication.
 * Also useful in cases where solution to (a*b)%c is required,
@@ -11,7 +11,7 @@
 """
 
 
-def b_expo(a: int, b: int) -> int:
+def b_multi(a: int, b: int) -> int:
     """
         Calculate the result of multiplying 'a' and 'b' using bitwise multiplication.
 
@@ -49,7 +49,7 @@ def b_expo(a: int, b: int) -> int:
     return res
 
 
-def b_expo_mod(a: int, b: int, c: int) -> int:
+def b_multi_mod(a: int, b: int, c: int) -> int:
     """
        Calculate the result of (a * b) % c using binary exponentiation and modular arithmetic.
 

From 4b6dfbfe37fb48e31ee3aa9df9696f6c49afb539 Mon Sep 17 00:00:00 2001
From: AasheeshLikePanner <ashishlearningsoftware@gmail.com>
Date: Tue, 3 Oct 2023 20:07:44 +0530
Subject: [PATCH 07/12] Changing comment and changing name function

---
 maths/binary_multiplication.py | 27 +++++++++++++--------------
 1 file changed, 13 insertions(+), 14 deletions(-)

diff --git a/maths/binary_multiplication.py b/maths/binary_multiplication.py
index 4a7a06d2e68c..b0d12b8776f0 100644
--- a/maths/binary_multiplication.py
+++ b/maths/binary_multiplication.py
@@ -23,19 +23,19 @@ def b_multi(a: int, b: int) -> int:
     int: The result of 'a' multiplied by 'b'.
 
     Examples:
-    >>> b_expo(2, 3)
+    >>> b_multi(2, 3)
     6
-    >>> b_expo(5, 0)
+    >>> b_multi(5, 0)
     0
-    >>> b_expo(3, 4)
+    >>> b_multi(3, 4)
     12
-    >>> b_expo(10, 5)
+    >>> b_multi(10, 5)
     50
-    >>> b_expo(0, 5)
+    >>> b_multi(0, 5)
     0
-    >>> b_expo(2, 1)
+    >>> b_multi(2, 1)
     2
-    >>> b_expo(1, 10)
+    >>> b_multi(1, 10)
     10
     """
     res = 0
@@ -62,17 +62,17 @@ def b_multi_mod(a: int, b: int, c: int) -> int:
     int: The result of (a * b) % c.
 
     Examples:
-    >>> b_expo_mod(2, 3, 5)
+    >>> b_multi_mod(2, 3, 5)
     1
-    >>> b_expo_mod(5, 0, 7)
+    >>> b_multi_mod(5, 0, 7)
     0
-    >>> b_expo_mod(3, 4, 6)
+    >>> b_multi_mod(3, 4, 6)
     0
-    >>> b_expo_mod(10, 5, 13)
+    >>> b_multi_mod(10, 5, 13)
     11
-    >>> b_expo_mod(2, 1, 5)
+    >>> b_multi_mod(2, 1, 5)
     2
-    >>> b_expo_mod(1, 10, 3)
+    >>> b_multi_mod(1, 10, 3)
     1
     """
     res = 0
@@ -88,7 +88,6 @@ def b_multi_mod(a: int, b: int, c: int) -> int:
 
 if __name__ == "__main__":
     import doctest
-
     doctest.testmod()
 
 """

From 6c0e81faf735c627508ff60c0e669ee92d231151 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 3 Oct 2023 14:38:25 +0000
Subject: [PATCH 08/12] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/binary_multiplication.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/maths/binary_multiplication.py b/maths/binary_multiplication.py
index b0d12b8776f0..3c768b8a5075 100644
--- a/maths/binary_multiplication.py
+++ b/maths/binary_multiplication.py
@@ -88,6 +88,7 @@ def b_multi_mod(a: int, b: int, c: int) -> int:
 
 if __name__ == "__main__":
     import doctest
+
     doctest.testmod()
 
 """

From 629eba0598f14911464bbd927e02c06accc7a1f4 Mon Sep 17 00:00:00 2001
From: Aasheesh <126905285+AasheeshLikePanner@users.noreply.github.com>
Date: Tue, 3 Oct 2023 20:10:38 +0530
Subject: [PATCH 09/12] Update binary_multiplication.py

---
 maths/binary_multiplication.py | 1 -
 1 file changed, 1 deletion(-)

diff --git a/maths/binary_multiplication.py b/maths/binary_multiplication.py
index 3c768b8a5075..b0d12b8776f0 100644
--- a/maths/binary_multiplication.py
+++ b/maths/binary_multiplication.py
@@ -88,7 +88,6 @@ def b_multi_mod(a: int, b: int, c: int) -> int:
 
 if __name__ == "__main__":
     import doctest
-
     doctest.testmod()
 
 """

From 7570ac6318d626b05f125c99df21ca7af298f832 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Tue, 3 Oct 2023 14:41:26 +0000
Subject: [PATCH 10/12] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/binary_multiplication.py | 1 +
 1 file changed, 1 insertion(+)

diff --git a/maths/binary_multiplication.py b/maths/binary_multiplication.py
index b0d12b8776f0..3c768b8a5075 100644
--- a/maths/binary_multiplication.py
+++ b/maths/binary_multiplication.py
@@ -88,6 +88,7 @@ def b_multi_mod(a: int, b: int, c: int) -> int:
 
 if __name__ == "__main__":
     import doctest
+
     doctest.testmod()
 
 """

From caadd29b25fec4accbb23a5a4ab2d26176d06fbe Mon Sep 17 00:00:00 2001
From: Tianyi Zheng <tianyizheng02@gmail.com>
Date: Tue, 3 Oct 2023 11:30:55 -0400
Subject: [PATCH 11/12] Update binary_multiplication.py

---
 maths/binary_multiplication.py | 79 ++++++++++++++++------------------
 1 file changed, 37 insertions(+), 42 deletions(-)

diff --git a/maths/binary_multiplication.py b/maths/binary_multiplication.py
index 3c768b8a5075..73b4894cbe63 100644
--- a/maths/binary_multiplication.py
+++ b/maths/binary_multiplication.py
@@ -1,41 +1,50 @@
 """
-* Binary Multiplication with Multiplication
-* This is a method to find a*b in a time complexity of O(log b)
-* This is one of the most commonly used methods of finding result of multiplication.
-* Also useful in cases where solution to (a*b)%c is required,
-* where a,b,c can be numbers over the computers calculation limits.
-* Done using iteration, can also be done using recursion
-
-* @author chinmoy159
-* @version 1.0 dated 10/08/2017
+Binary Multiplication
+This is a method to find a*b in a time complexity of O(log b)
+This is one of the most commonly used methods of finding result of multiplication.
+Also useful in cases where solution to (a*b)%c is required,
+where a,b,c can be numbers over the computers calculation limits.
+Done using iteration, can also be done using recursion
+
+Let's say you need to calculate a * b
+RULE 1 : a * b = (a+a) * (b/2) ---- example : 4 * 4 = (4+4) * (4/2) = 8 * 2
+RULE 2 : IF b is odd, then ---- a * b = a + (a * (b - 1)), where (b - 1) is even.
+Once b is even, repeat the process to get a * b
+Repeat the process until b = 1 or b = 0, because a*1 = a and a*0 = 0
+
+As far as the modulo is concerned,
+the fact : (a+b) % c = ((a%c) + (b%c)) % c
+Now apply RULE 1 or 2, whichever is required.
+
+@author chinmoy159
 """
 
 
-def b_multi(a: int, b: int) -> int:
+def binary_multiply(a: int, b: int) -> int:
     """
-    Calculate the result of multiplying 'a' and 'b' using bitwise multiplication.
+    Multiply 'a' and 'b' using bitwise multiplication.
 
     Parameters:
     a (int): The first number.
     b (int): The second number.
 
     Returns:
-    int: The result of 'a' multiplied by 'b'.
+    int: a * b
 
     Examples:
-    >>> b_multi(2, 3)
+    >>> binary_multiply(2, 3)
     6
-    >>> b_multi(5, 0)
+    >>> binary_multiply(5, 0)
     0
-    >>> b_multi(3, 4)
+    >>> binary_multiply(3, 4)
     12
-    >>> b_multi(10, 5)
+    >>> binary_multiply(10, 5)
     50
-    >>> b_multi(0, 5)
+    >>> binary_multiply(0, 5)
     0
-    >>> b_multi(2, 1)
+    >>> binary_multiply(2, 1)
     2
-    >>> b_multi(1, 10)
+    >>> binary_multiply(1, 10)
     10
     """
     res = 0
@@ -49,9 +58,9 @@ def b_multi(a: int, b: int) -> int:
     return res
 
 
-def b_multi_mod(a: int, b: int, c: int) -> int:
+def binary_mod_multiply(a: int, b: int, c: int) -> int:
     """
-    Calculate (a * b) % c using binary exponentiation and modular arithmetic.
+    Calculate (a * b) % c using binary multiplication and modular arithmetic.
 
     Parameters:
     a (int): The first number.
@@ -59,20 +68,20 @@ def b_multi_mod(a: int, b: int, c: int) -> int:
     c (int): The modulus.
 
     Returns:
-    int: The result of (a * b) % c.
+    int: (a * b) % c.
 
     Examples:
-    >>> b_multi_mod(2, 3, 5)
+    >>> binary_mod_multiply(2, 3, 5)
     1
-    >>> b_multi_mod(5, 0, 7)
+    >>> binary_mod_multiply(5, 0, 7)
     0
-    >>> b_multi_mod(3, 4, 6)
+    >>> binary_mod_multiply(3, 4, 6)
     0
-    >>> b_multi_mod(10, 5, 13)
+    >>> binary_mod_multiply(10, 5, 13)
     11
-    >>> b_multi_mod(2, 1, 5)
+    >>> binary_mod_multiply(2, 1, 5)
     2
-    >>> b_multi_mod(1, 10, 3)
+    >>> binary_mod_multiply(1, 10, 3)
     1
     """
     res = 0
@@ -90,17 +99,3 @@ def b_multi_mod(a: int, b: int, c: int) -> int:
     import doctest
 
     doctest.testmod()
-
-"""
-* Wondering how this method works !
-* It's pretty simple.
-* Let's say you need to calculate a ^ b
-* RULE 1 : a * b = (a+a) * (b/2) ---- example : 4 * 4 = (4+4) * (4/2) = 8 * 2
-* RULE 2 : IF b is ODD, then ---- a * b = a + (a * (b - 1)) :: where (b - 1) is even.
-* Once b is even, repeat the process to get a * b
-* Repeat the process till b = 1 OR b = 0, because a*1 = a AND a*0 = 0
-*
-* As far as the modulo is concerned,
-* the fact : (a+b) % c = ((a%c) + (b%c)) % c
-* Now apply RULE 1 OR 2, whichever is required.
-"""

From be6c8b18d71870829dd16c5401db1264e90d934e Mon Sep 17 00:00:00 2001
From: Tianyi Zheng <tianyizheng02@gmail.com>
Date: Tue, 3 Oct 2023 11:35:36 -0400
Subject: [PATCH 12/12] Update binary_multiplication.py

---
 maths/binary_multiplication.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/maths/binary_multiplication.py b/maths/binary_multiplication.py
index 73b4894cbe63..0cc5a575f445 100644
--- a/maths/binary_multiplication.py
+++ b/maths/binary_multiplication.py
@@ -58,17 +58,17 @@ def binary_multiply(a: int, b: int) -> int:
     return res
 
 
-def binary_mod_multiply(a: int, b: int, c: int) -> int:
+def binary_mod_multiply(a: int, b: int, modulus: int) -> int:
     """
     Calculate (a * b) % c using binary multiplication and modular arithmetic.
 
     Parameters:
     a (int): The first number.
     b (int): The second number.
-    c (int): The modulus.
+    modulus (int): The modulus.
 
     Returns:
-    int: (a * b) % c.
+    int: (a * b) % modulus.
 
     Examples:
     >>> binary_mod_multiply(2, 3, 5)
@@ -87,7 +87,7 @@ def binary_mod_multiply(a: int, b: int, c: int) -> int:
     res = 0
     while b > 0:
         if b & 1:
-            res = ((res % c) + (a % c)) % c
+            res = ((res % modulus) + (a % modulus)) % modulus
 
         a += a
         b >>= 1