Fix mypy in #3149 (#3988)

* Fix mypy in #3149 
* Fix pre-commit

blockchain/modular_division.py

@@ -1,21 +1,23 @@
-# Modular Division :
-# An efficient algorithm for dividing b by a modulo n.
-
-# GCD ( Greatest Common Divisor ) or HCF ( Highest Common Factor )
-
-# Given three integers a, b, and n, such that gcd(a,n)=1 and n>1, the algorithm should
-# return an integer x such that 0≤x≤n−1, and  b/a=x(modn) (that is, b=ax(modn)).
-
-# Theorem:
-# a has a multiplicative inverse modulo n iff gcd(a,n) = 1
-
-
-# This find x = b*a^(-1) mod n
-# Uses ExtendedEuclid to find the inverse of a
+from typing import Tuple
 
 
 def modular_division(a: int, b: int, n: int) -> int:
     """
+    Modular Division :
+    An efficient algorithm for dividing b by a modulo n.
+
+    GCD ( Greatest Common Divisor ) or HCF ( Highest Common Factor )
+
+    Given three integers a, b, and n, such that gcd(a,n)=1 and n>1, the algorithm should
+    return an integer x such that 0≤x≤n−1, and  b/a=x(modn) (that is, b=ax(modn)).
+
+    Theorem:
+    a has a multiplicative inverse modulo n iff gcd(a,n) = 1
+
+
+    This find x = b*a^(-1) mod n
+    Uses ExtendedEuclid to find the inverse of a
+
     >>> modular_division(4,8,5)
     2
 
@@ -32,9 +34,10 @@ def modular_division(a: int, b: int, n: int) -> int:
     return x
 
 
-# This function find the inverses of a i.e., a^(-1)
 def invert_modulo(a: int, n: int) -> int:
     """
+    This function find the inverses of a i.e., a^(-1)
+
     >>> invert_modulo(2, 5)
     3
 
@@ -50,9 +53,11 @@ def invert_modulo(a: int, n: int) -> int:
 
 # ------------------ Finding Modular division using invert_modulo -------------------
 
-# This function used the above inversion of a to find x = (b*a^(-1))mod n
+
 def modular_division2(a: int, b: int, n: int) -> int:
     """
+    This function used the above inversion of a to find x = (b*a^(-1))mod n
+
     >>> modular_division2(4,8,5)
     2
 
@@ -68,17 +73,15 @@ def modular_division2(a: int, b: int, n: int) -> int:
     return x
 
 
-# Extended Euclid's Algorithm : If d divides a and b and d = a*x + b*y for integers x
-# and y, then d = gcd(a,b)
-
-
-def extended_gcd(a: int, b: int) -> (int, int, int):
+def extended_gcd(a: int, b: int) -> Tuple[int, int, int]:
     """
-     >>> extended_gcd(10, 6)
-     (2, -1, 2)
+    Extended Euclid's Algorithm : If d divides a and b and d = a*x + b*y for integers x
+    and y, then d = gcd(a,b)
+    >>> extended_gcd(10, 6)
+    (2, -1, 2)
 
-     >>> extended_gcd(7, 5)
-     (1, -2, 3)
+    >>> extended_gcd(7, 5)
+    (1, -2, 3)
 
     ** extended_gcd function is used when d = gcd(a,b) is required in output
 
@@ -98,9 +101,9 @@ def extended_gcd(a: int, b: int) -> (int, int, int):
     return (d, x, y)
 
 
-# Extended Euclid
-def extended_euclid(a: int, b: int) -> (int, int):
+def extended_euclid(a: int, b: int) -> Tuple[int, int]:
     """
+    Extended Euclid
     >>> extended_euclid(10, 6)
     (-1, 2)
 
@@ -115,12 +118,11 @@ def extended_euclid(a: int, b: int) -> (int, int):
     return (y, x - k * y)
 
 
-# Euclid's Lemma :  d divides a and b, if and only if d divides a-b and b
-# Euclid's Algorithm
-
-
 def greatest_common_divisor(a: int, b: int) -> int:
     """
+    Euclid's Lemma :  d divides a and b, if and only if d divides a-b and b
+    Euclid's Algorithm
+
     >>> greatest_common_divisor(7,5)
     1