From f7c58e4c4b66750cbb3afd9ad29e9c246b2480ab Mon Sep 17 00:00:00 2001
From: Nikos Giachoudis <ngiachou@gmail.com>
Date: Mon, 11 Jul 2022 10:36:57 -0400
Subject: [PATCH] Unify primality checking (#6228)
* renames prime functions and occurances in comments
* changes implementation of primality testing to be uniform
* adds static typing as per conventions
* updating DIRECTORY.md
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
---
DIRECTORY.md | 1 -
data_structures/hashing/double_hash.py | 4 +-
.../hashing/number_theory/prime_numbers.py | 52 ++++++++++++----
maths/prime_check.py | 61 ++++++++++---------
maths/primelib.py | 22 +++----
5 files changed, 87 insertions(+), 53 deletions(-)
diff --git a/DIRECTORY.md b/DIRECTORY.md
index c8f03658c..2e9c03cbc 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -444,7 +444,6 @@
* [Scoring Functions](machine_learning/scoring_functions.py)
* [Sequential Minimum Optimization](machine_learning/sequential_minimum_optimization.py)
* [Similarity Search](machine_learning/similarity_search.py)
- * [Support Vector Machines](machine_learning/support_vector_machines.py)
* [Word Frequency Functions](machine_learning/word_frequency_functions.py)
## Maths
diff --git a/data_structures/hashing/double_hash.py b/data_structures/hashing/double_hash.py
index 57b1ffff4..bd1355fca 100644
--- a/data_structures/hashing/double_hash.py
+++ b/data_structures/hashing/double_hash.py
@@ -1,6 +1,6 @@
#!/usr/bin/env python3
from .hash_table import HashTable
-from .number_theory.prime_numbers import check_prime, next_prime
+from .number_theory.prime_numbers import is_prime, next_prime
class DoubleHash(HashTable):
@@ -15,7 +15,7 @@ class DoubleHash(HashTable):
next_prime_gt = (
next_prime(value % self.size_table)
- if not check_prime(value % self.size_table)
+ if not is_prime(value % self.size_table)
else value % self.size_table
) # gt = bigger than
return next_prime_gt - (data % next_prime_gt)
diff --git a/data_structures/hashing/number_theory/prime_numbers.py b/data_structures/hashing/number_theory/prime_numbers.py
index bf614e7d4..b88ab76ec 100644
--- a/data_structures/hashing/number_theory/prime_numbers.py
+++ b/data_structures/hashing/number_theory/prime_numbers.py
@@ -3,25 +3,55 @@
module to operations with prime numbers
"""
+import math
-def check_prime(number):
- """
- it's not the best solution
- """
- special_non_primes = [0, 1, 2]
- if number in special_non_primes[:2]:
- return 2
- elif number == special_non_primes[-1]:
- return 3
- return all(number % i for i in range(2, number))
+def is_prime(number: int) -> bool:
+ """Checks to see if a number is a prime in O(sqrt(n)).
+
+ A number is prime if it has exactly two factors: 1 and itself.
+
+ >>> is_prime(0)
+ False
+ >>> is_prime(1)
+ False
+ >>> is_prime(2)
+ True
+ >>> is_prime(3)
+ True
+ >>> is_prime(27)
+ False
+ >>> is_prime(87)
+ False
+ >>> is_prime(563)
+ True
+ >>> is_prime(2999)
+ True
+ >>> is_prime(67483)
+ False
+ """
+
+ # precondition
+ assert isinstance(number, int) and (
+ number >= 0
+ ), "'number' must been an int and positive"
+
+ if 1 < number < 4:
+ # 2 and 3 are primes
+ return True
+ elif number < 2 or not number % 2:
+ # Negatives, 0, 1 and all even numbers are not primes
+ return False
+
+ odd_numbers = range(3, int(math.sqrt(number) + 1), 2)
+ return not any(not number % i for i in odd_numbers)
def next_prime(value, factor=1, **kwargs):
value = factor * value
first_value_val = value
- while not check_prime(value):
+ while not is_prime(value):
value += 1 if not ("desc" in kwargs.keys() and kwargs["desc"] is True) else -1
if value == first_value_val:
diff --git a/maths/prime_check.py b/maths/prime_check.py
index 92d31cfee..315492054 100644
--- a/maths/prime_check.py
+++ b/maths/prime_check.py
@@ -4,31 +4,36 @@ import math
import unittest
-def prime_check(number: int) -> bool:
+def is_prime(number: int) -> bool:
"""Checks to see if a number is a prime in O(sqrt(n)).
A number is prime if it has exactly two factors: 1 and itself.
- >>> prime_check(0)
+ >>> is_prime(0)
False
- >>> prime_check(1)
+ >>> is_prime(1)
False
- >>> prime_check(2)
+ >>> is_prime(2)
True
- >>> prime_check(3)
+ >>> is_prime(3)
True
- >>> prime_check(27)
+ >>> is_prime(27)
False
- >>> prime_check(87)
+ >>> is_prime(87)
False
- >>> prime_check(563)
+ >>> is_prime(563)
True
- >>> prime_check(2999)
+ >>> is_prime(2999)
True
- >>> prime_check(67483)
+ >>> is_prime(67483)
False
"""
+ # precondition
+ assert isinstance(number, int) and (
+ number >= 0
+ ), "'number' must been an int and positive"
+
if 1 < number < 4:
# 2 and 3 are primes
return True
@@ -42,35 +47,35 @@ def prime_check(number: int) -> bool:
class Test(unittest.TestCase):
def test_primes(self):
- self.assertTrue(prime_check(2))
- self.assertTrue(prime_check(3))
- self.assertTrue(prime_check(5))
- self.assertTrue(prime_check(7))
- self.assertTrue(prime_check(11))
- self.assertTrue(prime_check(13))
- self.assertTrue(prime_check(17))
- self.assertTrue(prime_check(19))
- self.assertTrue(prime_check(23))
- self.assertTrue(prime_check(29))
+ self.assertTrue(is_prime(2))
+ self.assertTrue(is_prime(3))
+ self.assertTrue(is_prime(5))
+ self.assertTrue(is_prime(7))
+ self.assertTrue(is_prime(11))
+ self.assertTrue(is_prime(13))
+ self.assertTrue(is_prime(17))
+ self.assertTrue(is_prime(19))
+ self.assertTrue(is_prime(23))
+ self.assertTrue(is_prime(29))
def test_not_primes(self):
self.assertFalse(
- prime_check(-19),
+ is_prime(-19),
"Negative numbers are excluded by definition of prime numbers.",
)
self.assertFalse(
- prime_check(0),
+ is_prime(0),
"Zero doesn't have any positive factors, primes must have exactly two.",
)
self.assertFalse(
- prime_check(1),
+ is_prime(1),
"One only has 1 positive factor, primes must have exactly two.",
)
- self.assertFalse(prime_check(2 * 2))
- self.assertFalse(prime_check(2 * 3))
- self.assertFalse(prime_check(3 * 3))
- self.assertFalse(prime_check(3 * 5))
- self.assertFalse(prime_check(3 * 5 * 7))
+ self.assertFalse(is_prime(2 * 2))
+ self.assertFalse(is_prime(2 * 3))
+ self.assertFalse(is_prime(3 * 3))
+ self.assertFalse(is_prime(3 * 5))
+ self.assertFalse(is_prime(3 * 5 * 7))
if __name__ == "__main__":
diff --git a/maths/primelib.py b/maths/primelib.py
index 37883d9cf..3da9c56f6 100644
--- a/maths/primelib.py
+++ b/maths/primelib.py
@@ -41,7 +41,7 @@ goldbach(number) // Goldbach's assumption
from math import sqrt
-def isPrime(number):
+def is_prime(number: int) -> bool:
"""
input: positive integer 'number'
returns true if 'number' is prime otherwise false.
@@ -129,7 +129,7 @@ def getPrimeNumbers(N):
# if a number is prime then appends to list 'ans'
for number in range(2, N + 1):
- if isPrime(number):
+ if is_prime(number):
ans.append(number)
@@ -164,11 +164,11 @@ def primeFactorization(number):
ans.append(number)
# if 'number' not prime then builds the prime factorization of 'number'
- elif not isPrime(number):
+ elif not is_prime(number):
while quotient != 1:
- if isPrime(factor) and (quotient % factor == 0):
+ if is_prime(factor) and (quotient % factor == 0):
ans.append(factor)
quotient /= factor
else:
@@ -317,8 +317,8 @@ def goldbach(number):
isinstance(ans, list)
and (len(ans) == 2)
and (ans[0] + ans[1] == number)
- and isPrime(ans[0])
- and isPrime(ans[1])
+ and is_prime(ans[0])
+ and is_prime(ans[1])
), "'ans' must contains two primes. And sum of elements must been eq 'number'"
return ans
@@ -462,11 +462,11 @@ def getPrime(n):
# if ans not prime then
# runs to the next prime number.
- while not isPrime(ans):
+ while not is_prime(ans):
ans += 1
# precondition
- assert isinstance(ans, int) and isPrime(
+ assert isinstance(ans, int) and is_prime(
ans
), "'ans' must been a prime number and from type int"
@@ -486,7 +486,7 @@ def getPrimesBetween(pNumber1, pNumber2):
# precondition
assert (
- isPrime(pNumber1) and isPrime(pNumber2) and (pNumber1 < pNumber2)
+ is_prime(pNumber1) and is_prime(pNumber2) and (pNumber1 < pNumber2)
), "The arguments must been prime numbers and 'pNumber1' < 'pNumber2'"
number = pNumber1 + 1 # jump to the next number
@@ -495,7 +495,7 @@ def getPrimesBetween(pNumber1, pNumber2):
# if number is not prime then
# fetch the next prime number.
- while not isPrime(number):
+ while not is_prime(number):
number += 1
while number < pNumber2:
@@ -505,7 +505,7 @@ def getPrimesBetween(pNumber1, pNumber2):
number += 1
# fetch the next prime number.
- while not isPrime(number):
+ while not is_prime(number):
number += 1
# precondition