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Removed redundant greatest_common_divisor code (#9358)

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* Deleted greatest_common_divisor def from many files and instead imported the method from Maths folder

* Deleted greatest_common_divisor def from many files and instead imported the method from Maths folder, also fixed comments

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* Deleted greatest_common_divisor def from many files and instead imported the method from Maths folder, also fixed comments

* Imports organized

* recursive gcd function implementation rolledback

* more gcd duplicates removed

* more gcd duplicates removed

* Update maths/carmichael_number.py

* updated files

* moved a file to another location

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>
This commit is contained in:
Siddik Patel
2023-10-09 17:49:12 +05:30
committed by GitHub
parent 876087be99
commit 583a614fef
9 changed files with 24 additions and 131 deletions
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32
blockchain/diophantine_equation.py
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@@ -1,11 +1,13 @@
from __future__ import annotations
from maths.greatest_common_divisor import greatest_common_divisor
def diophantine(a: int, b: int, c: int) -> tuple[float, float]:
"""
Diophantine Equation : Given integers a,b,c ( at least one of a and b != 0), the
diophantine equation a*x + b*y = c has a solution (where x and y are integers)
iff gcd(a,b) divides c.
iff greatest_common_divisor(a,b) divides c.
GCD ( Greatest Common Divisor ) or HCF ( Highest Common Factor )
@@ -22,7 +24,7 @@ def diophantine(a: int, b: int, c: int) -> tuple[float, float]:
assert (
c % greatest_common_divisor(a, b) == 0
) # greatest_common_divisor(a,b) function implemented below
) # greatest_common_divisor(a,b) is in maths directory
(d, x, y) = extended_gcd(a, b) # extended_gcd(a,b) function implemented below
r = c / d
return (r * x, r * y)
@@ -69,32 +71,6 @@ def diophantine_all_soln(a: int, b: int, c: int, n: int = 2) -> None:
print(x, y)
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
Note : In number theory, two integers a and b are said to be relatively prime,
mutually prime, or co-prime if the only positive integer (factor) that
divides both of them is 1 i.e., gcd(a,b) = 1.
>>> greatest_common_divisor(121, 11)
11
"""
if a < b:
a, b = b, a
while a % b != 0:
a, b = b, a % b
return b
def extended_gcd(a: int, b: int) -> tuple[int, int, int]:
"""
Extended Euclid's Algorithm : If d divides a and b and d = a*x + b*y for integers