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Performance: 95% faster Project Euler 187 #10580

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db7a134
Add numpy calculate_prime_numbers
ManpreetXSingh Oct 16, 2023
11aac84
Rename old solution to for_solution
ManpreetXSingh Oct 16, 2023
8943088
Add numpy solution
ManpreetXSingh Oct 16, 2023
d56844a
Update benchmarks
ManpreetXSingh Oct 16, 2023
8b6b3a4
Fix 🐛 in benchmarks in prime_numbers.py
ManpreetXSingh Oct 29, 2023
61219b4
Add prime helper fn in prime_sieve_eratosthenes.py
ManpreetXSingh Oct 29, 2023
938c022
Add benchmark fn in prime_sieve_eratosthenes.py
ManpreetXSingh Oct 29, 2023
e6535b1
Sort imports in prime_sieve_eratosthenes.py
ManpreetXSingh Oct 29, 2023
2e28bde
Import prime helper fn
ManpreetXSingh Oct 29, 2023
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6 changes: 3 additions & 3 deletions maths/prime_numbers.py
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Original file line numberDiff line numberDiff line change
Expand Up@@ -97,9 +97,9 @@ def benchmark():
from timeit import timeit

setup = "from __main__ import slow_primes, primes, fast_primes"
print(timeit("slow_primes(1_000_000_000_000)", setup=setup, number=1_000_000))
print(timeit("primes(1_000_000_000_000)", setup=setup, number=1_000_000))
print(timeit("fast_primes(1_000_000_000_000)", setup=setup, number=1_000_000))
print(timeit("list(slow_primes(1_000))", setup=setup, number=1_000))
print(timeit("list(primes(1_000))", setup=setup, number=1_000))
print(timeit("list(fast_primes(1_000))", setup=setup, number=1_000))


if __name__ == "__main__":
Expand Down
49 changes: 48 additions & 1 deletion maths/prime_sieve_eratosthenes.py
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Original file line numberDiff line numberDiff line change
Expand Up@@ -11,6 +11,10 @@
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
"""

from math import isqrt

import numpy as np


def prime_sieve_eratosthenes(num: int) -> list[int]:
"""
Expand DownExpand Up@@ -45,10 +49,53 @@ def prime_sieve_eratosthenes(num: int) -> list[int]:
return [prime for prime in range(2, num + 1) if primes[prime]]


def np_prime_sieve_eratosthenes(max_number: int) -> list[int]:
"""
Returns prime numbers below max_number.
See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

>>> np_prime_sieve_eratosthenes(10)
[2, 3, 5, 7]
>>> np_prime_sieve_eratosthenes(2)
[2]
>>> np_prime_sieve_eratosthenes(1)
[]
"""
if max_number < 2:
return []

# List containing a bool value for every odd number below max_number/2
is_prime = np.ones((max_number + 1) // 2, dtype=bool)

for i in range(3, isqrt(max_number - 1) + 1, 2):
if is_prime[i // 2]:
# Mark all multiple of i as not prime using list slicing
is_prime[i**2 // 2 :: i] = False

primes = np.where(is_prime)[0] * 2 + 1
primes[0] = 2
return primes.tolist()


def benchmark():
"""
Benchmarks
"""
from timeit import timeit

print("Running performance benchmarks...")

functions = ["prime_sieve_eratosthenes", "np_prime_sieve_eratosthenes"]
for func in functions:
print(f"{func} : {timeit(f'{func}(10_000)', globals=globals(), number=10_000)}")


if __name__ == "__main__":
import doctest

doctest.testmod()

user_num = int(input("Enter a positive integer: ").strip())
print(prime_sieve_eratosthenes(user_num))
print(np_prime_sieve_eratosthenes(user_num))

benchmark()
41 changes: 35 additions & 6 deletions project_euler/problem_187/sol1.py
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Open in desktop
Original file line numberDiff line numberDiff line change
Expand Up@@ -13,6 +13,8 @@

from math import isqrt

from maths.prime_sieve_eratosthenes import np_prime_sieve_eratosthenes


def slow_calculate_prime_numbers(max_number: int) -> list[int]:
"""
Expand All@@ -38,15 +40,15 @@ def slow_calculate_prime_numbers(max_number: int) -> list[int]:
return [i for i in range(2, max_number) if is_prime[i]]


def calculate_prime_numbers(max_number: int) -> list[int]:
def py_calculate_prime_numbers(max_number: int) -> list[int]:
"""
Returns prime numbers below max_number.
See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

>>> calculate_prime_numbers(10)
>>> py_calculate_prime_numbers(10)
[2, 3, 5, 7]

>>> calculate_prime_numbers(2)
>>> py_calculate_prime_numbers(2)
[]
"""

Expand DownExpand Up@@ -100,7 +102,7 @@ def while_solution(max_number: int = 10**8) -> int:
10
"""

prime_numbers = calculate_prime_numbers(max_number // 2)
prime_numbers = py_calculate_prime_numbers(max_number // 2)

semiprimes_count = 0
left = 0
Expand All@@ -114,6 +116,31 @@ def while_solution(max_number: int = 10**8) -> int:
return semiprimes_count


def for_solution(max_number: int = 10**8) -> int:
"""
Returns the number of composite integers below max_number have precisely two,
not necessarily distinct, prime factors.

>>> for_solution(30)
10
"""

prime_numbers = py_calculate_prime_numbers(max_number // 2)

semiprimes_count = 0
right = len(prime_numbers) - 1
for left in range(len(prime_numbers)):
if left > right:
break
for r in range(right, left - 2, -1):
if prime_numbers[left] * prime_numbers[r] < max_number:
break
right = r
semiprimes_count += right - left + 1

return semiprimes_count


def solution(max_number: int = 10**8) -> int:
"""
Returns the number of composite integers below max_number have precisely two,
Expand All@@ -123,7 +150,7 @@ def solution(max_number: int = 10**8) -> int:
10
"""

prime_numbers = calculate_prime_numbers(max_number // 2)
prime_numbers = np_prime_sieve_eratosthenes((max_number - 1) // 2)

semiprimes_count = 0
right = len(prime_numbers) - 1
Expand All@@ -146,14 +173,16 @@ def benchmark() -> None:
# Running performance benchmarks...
# slow_solution : 108.50874730000032
# while_sol : 28.09581200000048
# solution : 25.063097400000515
# for_sol : 25.063097400000515
# solution : 5.219610300000568

from timeit import timeit

print("Running performance benchmarks...")

print(f"slow_solution : {timeit('slow_solution()', globals=globals(), number=10)}")
print(f"while_sol : {timeit('while_solution()', globals=globals(), number=10)}")
print(f"for_sol : {timeit('for_solution()', globals=globals(), number=10)}")
print(f"solution : {timeit('solution()', globals=globals(), number=10)}")


Expand Down
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Performance: 95% faster Project Euler 187 by ManpreetXSingh · Pull Request #10580 · TheAlgorithms/Python · GitHub
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Performance: 95% faster Project Euler 187#10580

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wants to merge
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commits into

from

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Performance: 95% faster Project Euler 187
#10580
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db7a134

Add numpy calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
11aac84

Rename old solution to for_solution


ManpreetXSingh Oct 16, 2023
8943088

Add numpy solution


ManpreetXSingh Oct 16, 2023
d56844a

Update benchmarks


ManpreetXSingh Oct 16, 2023
8b6b3a4

Fix 🐛 in benchmarks in prime_numbers.py


ManpreetXSingh Oct 29, 2023
61219b4

Add prime helper fn in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
938c022

Add benchmark fn in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
e6535b1

Sort imports in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
2e28bde

Import prime helper fn


ManpreetXSingh Oct 29, 2023

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6 changes: 3 additions & 3 deletions
maths/prime_numbers.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -97,9 +97,9 @@ def benchmark():
 from timeit import timeit

 setup = "from __main__ import slow_primes, primes, fast_primes"
 print(timeit("slow_primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("fast_primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("list(slow_primes(1_000))", setup=setup, number=1_000))
 print(timeit("list(primes(1_000))", setup=setup, number=1_000))
 print(timeit("list(fast_primes(1_000))", setup=setup, number=1_000))


if __name__ == "__main__":
Expand Down

49 changes: 48 additions & 1 deletion
maths/prime_sieve_eratosthenes.py

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Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -11,6 +11,10 @@
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
"""

from math import isqrt

import numpy as np


def prime_sieve_eratosthenes(num: int) -> list[int]:
 """
Expand DownExpand Up@@ -45,10 +49,53 @@ def prime_sieve_eratosthenes(num: int) -> list[int]:
 return [prime for prime in range(2, num + 1) if primes[prime]]


def np_prime_sieve_eratosthenes(max_number: int) -> list[int]:
 """
 Returns prime numbers below max_number.
 See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

 >>> np_prime_sieve_eratosthenes(10)
 [2, 3, 5, 7]
 >>> np_prime_sieve_eratosthenes(2)
 [2]
 >>> np_prime_sieve_eratosthenes(1)
 []
 """
 if max_number < 2:
 return []

 # List containing a bool value for every odd number below max_number/2
 is_prime = np.ones((max_number + 1) // 2, dtype=bool)

 for i in range(3, isqrt(max_number - 1) + 1, 2):
 if is_prime[i // 2]:
 # Mark all multiple of i as not prime using list slicing
 is_prime[i**2 // 2 :: i] = False

 primes = np.where(is_prime)[0] * 2 + 1
 primes[0] = 2
 return primes.tolist()


def benchmark():
 """
 Benchmarks
 """
 from timeit import timeit

 print("Running performance benchmarks...")

 functions = ["prime_sieve_eratosthenes", "np_prime_sieve_eratosthenes"]
 for func in functions:
 print(f"{func} : {timeit(f'{func}(10_000)', globals=globals(), number=10_000)}")


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 user_num = int(input("Enter a positive integer: ").strip())
 print(prime_sieve_eratosthenes(user_num))
 print(np_prime_sieve_eratosthenes(user_num))

 benchmark()

41 changes: 35 additions & 6 deletions
project_euler/problem_187/sol1.py

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Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -13,6 +13,8 @@

from math import isqrt

from maths.prime_sieve_eratosthenes import np_prime_sieve_eratosthenes


def slow_calculate_prime_numbers(max_number: int) -> list[int]:
 """
Expand All@@ -38,15 +40,15 @@ def slow_calculate_prime_numbers(max_number: int) -> list[int]:
 return [i for i in range(2, max_number) if is_prime[i]]


def calculate_prime_numbers(max_number: int) -> list[int]:
def py_calculate_prime_numbers(max_number: int) -> list[int]:
 """
 Returns prime numbers below max_number.
 See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

 >>> calculate_prime_numbers(10)
 >>> py_calculate_prime_numbers(10)
 [2, 3, 5, 7]

 >>> calculate_prime_numbers(2)
 >>> py_calculate_prime_numbers(2)
 []
 """

Expand DownExpand Up@@ -100,7 +102,7 @@ def while_solution(max_number: int = 10**8) -> int:
 10
 """

 prime_numbers = calculate_prime_numbers(max_number // 2)
 prime_numbers = py_calculate_prime_numbers(max_number // 2)

 semiprimes_count = 0
 left = 0
Expand All@@ -114,6 +116,31 @@ def while_solution(max_number: int = 10**8) -> int:
 return semiprimes_count


def for_solution(max_number: int = 10**8) -> int:
 """
 Returns the number of composite integers below max_number have precisely two,
 not necessarily distinct, prime factors.

 >>> for_solution(30)
 10
 """

 prime_numbers = py_calculate_prime_numbers(max_number // 2)

 semiprimes_count = 0
 right = len(prime_numbers) - 1
 for left in range(len(prime_numbers)):
 if left > right:
 break
 for r in range(right, left - 2, -1):
 if prime_numbers[left] * prime_numbers[r] < max_number:
 break
 right = r
 semiprimes_count += right - left + 1

 return semiprimes_count


def solution(max_number: int = 10**8) -> int:
 """
 Returns the number of composite integers below max_number have precisely two,
Expand All@@ -123,7 +150,7 @@ def solution(max_number: int = 10**8) -> int:
 10
 """

 prime_numbers = calculate_prime_numbers(max_number // 2)
 prime_numbers = np_prime_sieve_eratosthenes((max_number - 1) // 2)

 semiprimes_count = 0
 right = len(prime_numbers) - 1
Expand All@@ -146,14 +173,16 @@ def benchmark() -> None:
 # Running performance benchmarks...
 # slow_solution : 108.50874730000032
 # while_sol : 28.09581200000048
 # solution : 25.063097400000515
 # for_sol : 25.063097400000515
 # solution : 5.219610300000568

 from timeit import timeit

 print("Running performance benchmarks...")

 print(f"slow_solution : {timeit('slow_solution()', globals=globals(), number=10)}")
 print(f"while_sol : {timeit('while_solution()', globals=globals(), number=10)}")
 print(f"for_sol : {timeit('for_solution()', globals=globals(), number=10)}")
 print(f"solution : {timeit('solution()', globals=globals(), number=10)}")


Expand Down

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Performance: 95% faster Project Euler 187 by ManpreetXSingh · Pull Request #10580 · TheAlgorithms/Python · GitHub
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Performance: 95% faster Project Euler 187#10580

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 Closed

ManpreetXSingh
wants to merge
9
commits into

from

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Performance: 95% faster Project Euler 187
#10580
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db7a134

Add numpy calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
11aac84

Rename old solution to for_solution


ManpreetXSingh Oct 16, 2023
8943088

Add numpy solution


ManpreetXSingh Oct 16, 2023
d56844a

Update benchmarks


ManpreetXSingh Oct 16, 2023
8b6b3a4

Fix 🐛 in benchmarks in prime_numbers.py


ManpreetXSingh Oct 29, 2023
61219b4

Add prime helper fn in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
938c022

Add benchmark fn in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
e6535b1

Sort imports in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
2e28bde

Import prime helper fn


ManpreetXSingh Oct 29, 2023

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6 changes: 3 additions & 3 deletions
maths/prime_numbers.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -97,9 +97,9 @@ def benchmark():
 from timeit import timeit

 setup = "from __main__ import slow_primes, primes, fast_primes"
 print(timeit("slow_primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("fast_primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("list(slow_primes(1_000))", setup=setup, number=1_000))
 print(timeit("list(primes(1_000))", setup=setup, number=1_000))
 print(timeit("list(fast_primes(1_000))", setup=setup, number=1_000))


if __name__ == "__main__":
Expand Down

49 changes: 48 additions & 1 deletion
maths/prime_sieve_eratosthenes.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -11,6 +11,10 @@
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
"""

from math import isqrt

import numpy as np


def prime_sieve_eratosthenes(num: int) -> list[int]:
 """
Expand DownExpand Up@@ -45,10 +49,53 @@ def prime_sieve_eratosthenes(num: int) -> list[int]:
 return [prime for prime in range(2, num + 1) if primes[prime]]


def np_prime_sieve_eratosthenes(max_number: int) -> list[int]:
 """
 Returns prime numbers below max_number.
 See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

 >>> np_prime_sieve_eratosthenes(10)
 [2, 3, 5, 7]
 >>> np_prime_sieve_eratosthenes(2)
 [2]
 >>> np_prime_sieve_eratosthenes(1)
 []
 """
 if max_number < 2:
 return []

 # List containing a bool value for every odd number below max_number/2
 is_prime = np.ones((max_number + 1) // 2, dtype=bool)

 for i in range(3, isqrt(max_number - 1) + 1, 2):
 if is_prime[i // 2]:
 # Mark all multiple of i as not prime using list slicing
 is_prime[i**2 // 2 :: i] = False

 primes = np.where(is_prime)[0] * 2 + 1
 primes[0] = 2
 return primes.tolist()


def benchmark():
 """
 Benchmarks
 """
 from timeit import timeit

 print("Running performance benchmarks...")

 functions = ["prime_sieve_eratosthenes", "np_prime_sieve_eratosthenes"]
 for func in functions:
 print(f"{func} : {timeit(f'{func}(10_000)', globals=globals(), number=10_000)}")


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 user_num = int(input("Enter a positive integer: ").strip())
 print(prime_sieve_eratosthenes(user_num))
 print(np_prime_sieve_eratosthenes(user_num))

 benchmark()

41 changes: 35 additions & 6 deletions
project_euler/problem_187/sol1.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -13,6 +13,8 @@

from math import isqrt

from maths.prime_sieve_eratosthenes import np_prime_sieve_eratosthenes


def slow_calculate_prime_numbers(max_number: int) -> list[int]:
 """
Expand All@@ -38,15 +40,15 @@ def slow_calculate_prime_numbers(max_number: int) -> list[int]:
 return [i for i in range(2, max_number) if is_prime[i]]


def calculate_prime_numbers(max_number: int) -> list[int]:
def py_calculate_prime_numbers(max_number: int) -> list[int]:
 """
 Returns prime numbers below max_number.
 See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

 >>> calculate_prime_numbers(10)
 >>> py_calculate_prime_numbers(10)
 [2, 3, 5, 7]

 >>> calculate_prime_numbers(2)
 >>> py_calculate_prime_numbers(2)
 []
 """

Expand DownExpand Up@@ -100,7 +102,7 @@ def while_solution(max_number: int = 10**8) -> int:
 10
 """

 prime_numbers = calculate_prime_numbers(max_number // 2)
 prime_numbers = py_calculate_prime_numbers(max_number // 2)

 semiprimes_count = 0
 left = 0
Expand All@@ -114,6 +116,31 @@ def while_solution(max_number: int = 10**8) -> int:
 return semiprimes_count


def for_solution(max_number: int = 10**8) -> int:
 """
 Returns the number of composite integers below max_number have precisely two,
 not necessarily distinct, prime factors.

 >>> for_solution(30)
 10
 """

 prime_numbers = py_calculate_prime_numbers(max_number // 2)

 semiprimes_count = 0
 right = len(prime_numbers) - 1
 for left in range(len(prime_numbers)):
 if left > right:
 break
 for r in range(right, left - 2, -1):
 if prime_numbers[left] * prime_numbers[r] < max_number:
 break
 right = r
 semiprimes_count += right - left + 1

 return semiprimes_count


def solution(max_number: int = 10**8) -> int:
 """
 Returns the number of composite integers below max_number have precisely two,
Expand All@@ -123,7 +150,7 @@ def solution(max_number: int = 10**8) -> int:
 10
 """

 prime_numbers = calculate_prime_numbers(max_number // 2)
 prime_numbers = np_prime_sieve_eratosthenes((max_number - 1) // 2)

 semiprimes_count = 0
 right = len(prime_numbers) - 1
Expand All@@ -146,14 +173,16 @@ def benchmark() -> None:
 # Running performance benchmarks...
 # slow_solution : 108.50874730000032
 # while_sol : 28.09581200000048
 # solution : 25.063097400000515
 # for_sol : 25.063097400000515
 # solution : 5.219610300000568

 from timeit import timeit

 print("Running performance benchmarks...")

 print(f"slow_solution : {timeit('slow_solution()', globals=globals(), number=10)}")
 print(f"while_sol : {timeit('while_solution()', globals=globals(), number=10)}")
 print(f"for_sol : {timeit('for_solution()', globals=globals(), number=10)}")
 print(f"solution : {timeit('solution()', globals=globals(), number=10)}")


Expand Down

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Highlight search terms from Google/DuckDuckGo/Bing referrer
(function() {
var ref = document.referrer;
var terms = [];
if (ref.includes('google.com') || ref.includes('duckduckgo.com') || ref.includes('bing.com')) {
var url = new URL(ref);
var q = url.searchParams.get('q') || url.searchParams.get('p');
if (q) {
terms = q.split(/\s+/).filter(function(t) { return t.length > 2; });
}
}
if (terms.length === 0) return;
var style = document.createElement('style');
style.textContent = '.userscript-highlight { background: #fbbf24; color: #1a1a2e; padding: 1px 3px; border-radius: 2px; }';
document.head.appendChild(style);
function highlight(node) {
if (node.nodeType === 3) { // text node
var text = node.textContent;
var found = false;
terms.forEach(function(term) {
var regex = new RegExp('(' + term.replace(/[.*+?^${}()|[\]\\]/g, '\\') + ')', 'gi');
if (regex.test(text)) {
found = true;
var frag = document.createDocumentFragment();
var parts = text.split(regex);
parts.forEach(function(part, i) {
if (i % 2 === 0) {
frag.appendChild(document.createTextNode(part));
} else {
var span = document.createElement('span');
span.className = 'userscript-highlight';
span.textContent = part;
frag.appendChild(span);
}
});
node.parentNode.replaceChild(frag, node);
}
});
} else if (node.nodeType === 1 && node.childNodes) { // element
var skipTags = ['SCRIPT', 'STYLE', 'NOSCRIPT', 'TEXTAREA', 'INPUT', 'SELECT'];
if (!skipTags.includes(node.tagName)) {
Array.from(node.childNodes).forEach(highlight);
}
}
}
highlight(document.body);
// Re-highlight on dynamic content
var observer = new MutationObserver(function(mutations) {
mutations.forEach(function(m) {
m.addedNodes.forEach(function(node) {
if (node.nodeType === 1 || node.nodeType === 3) highlight(node);
});
});
});
observer.observe(document.body, { childList: true, subtree: true });
})();
}
} catch(__e) { console.warn('[Userscript:Highlight Search Terms]', __e); }
})();
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try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '
Performance: 95% faster Project Euler 187 by ManpreetXSingh · Pull Request #10580 · TheAlgorithms/Python · GitHub
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Performance: 95% faster Project Euler 187
#10580
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db7a134

Add numpy calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
11aac84

Rename old solution to for_solution


ManpreetXSingh Oct 16, 2023
8943088

Add numpy solution


ManpreetXSingh Oct 16, 2023
d56844a

Update benchmarks


ManpreetXSingh Oct 16, 2023
8b6b3a4

Fix 🐛 in benchmarks in prime_numbers.py


ManpreetXSingh Oct 29, 2023
61219b4

Add prime helper fn in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
938c022

Add benchmark fn in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
e6535b1

Sort imports in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
2e28bde

Import prime helper fn


ManpreetXSingh Oct 29, 2023

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6 changes: 3 additions & 3 deletions
maths/prime_numbers.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -97,9 +97,9 @@ def benchmark():
 from timeit import timeit

 setup = "from __main__ import slow_primes, primes, fast_primes"
 print(timeit("slow_primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("fast_primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("list(slow_primes(1_000))", setup=setup, number=1_000))
 print(timeit("list(primes(1_000))", setup=setup, number=1_000))
 print(timeit("list(fast_primes(1_000))", setup=setup, number=1_000))


if __name__ == "__main__":
Expand Down

49 changes: 48 additions & 1 deletion
maths/prime_sieve_eratosthenes.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -11,6 +11,10 @@
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
"""

from math import isqrt

import numpy as np


def prime_sieve_eratosthenes(num: int) -> list[int]:
 """
Expand DownExpand Up@@ -45,10 +49,53 @@ def prime_sieve_eratosthenes(num: int) -> list[int]:
 return [prime for prime in range(2, num + 1) if primes[prime]]


def np_prime_sieve_eratosthenes(max_number: int) -> list[int]:
 """
 Returns prime numbers below max_number.
 See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

 >>> np_prime_sieve_eratosthenes(10)
 [2, 3, 5, 7]
 >>> np_prime_sieve_eratosthenes(2)
 [2]
 >>> np_prime_sieve_eratosthenes(1)
 []
 """
 if max_number < 2:
 return []

 # List containing a bool value for every odd number below max_number/2
 is_prime = np.ones((max_number + 1) // 2, dtype=bool)

 for i in range(3, isqrt(max_number - 1) + 1, 2):
 if is_prime[i // 2]:
 # Mark all multiple of i as not prime using list slicing
 is_prime[i**2 // 2 :: i] = False

 primes = np.where(is_prime)[0] * 2 + 1
 primes[0] = 2
 return primes.tolist()


def benchmark():
 """
 Benchmarks
 """
 from timeit import timeit

 print("Running performance benchmarks...")

 functions = ["prime_sieve_eratosthenes", "np_prime_sieve_eratosthenes"]
 for func in functions:
 print(f"{func} : {timeit(f'{func}(10_000)', globals=globals(), number=10_000)}")


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 user_num = int(input("Enter a positive integer: ").strip())
 print(prime_sieve_eratosthenes(user_num))
 print(np_prime_sieve_eratosthenes(user_num))

 benchmark()

41 changes: 35 additions & 6 deletions
project_euler/problem_187/sol1.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -13,6 +13,8 @@

from math import isqrt

from maths.prime_sieve_eratosthenes import np_prime_sieve_eratosthenes


def slow_calculate_prime_numbers(max_number: int) -> list[int]:
 """
Expand All@@ -38,15 +40,15 @@ def slow_calculate_prime_numbers(max_number: int) -> list[int]:
 return [i for i in range(2, max_number) if is_prime[i]]


def calculate_prime_numbers(max_number: int) -> list[int]:
def py_calculate_prime_numbers(max_number: int) -> list[int]:
 """
 Returns prime numbers below max_number.
 See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

 >>> calculate_prime_numbers(10)
 >>> py_calculate_prime_numbers(10)
 [2, 3, 5, 7]

 >>> calculate_prime_numbers(2)
 >>> py_calculate_prime_numbers(2)
 []
 """

Expand DownExpand Up@@ -100,7 +102,7 @@ def while_solution(max_number: int = 10**8) -> int:
 10
 """

 prime_numbers = calculate_prime_numbers(max_number // 2)
 prime_numbers = py_calculate_prime_numbers(max_number // 2)

 semiprimes_count = 0
 left = 0
Expand All@@ -114,6 +116,31 @@ def while_solution(max_number: int = 10**8) -> int:
 return semiprimes_count


def for_solution(max_number: int = 10**8) -> int:
 """
 Returns the number of composite integers below max_number have precisely two,
 not necessarily distinct, prime factors.

 >>> for_solution(30)
 10
 """

 prime_numbers = py_calculate_prime_numbers(max_number // 2)

 semiprimes_count = 0
 right = len(prime_numbers) - 1
 for left in range(len(prime_numbers)):
 if left > right:
 break
 for r in range(right, left - 2, -1):
 if prime_numbers[left] * prime_numbers[r] < max_number:
 break
 right = r
 semiprimes_count += right - left + 1

 return semiprimes_count


def solution(max_number: int = 10**8) -> int:
 """
 Returns the number of composite integers below max_number have precisely two,
Expand All@@ -123,7 +150,7 @@ def solution(max_number: int = 10**8) -> int:
 10
 """

 prime_numbers = calculate_prime_numbers(max_number // 2)
 prime_numbers = np_prime_sieve_eratosthenes((max_number - 1) // 2)

 semiprimes_count = 0
 right = len(prime_numbers) - 1
Expand All@@ -146,14 +173,16 @@ def benchmark() -> None:
 # Running performance benchmarks...
 # slow_solution : 108.50874730000032
 # while_sol : 28.09581200000048
 # solution : 25.063097400000515
 # for_sol : 25.063097400000515
 # solution : 5.219610300000568

 from timeit import timeit

 print("Running performance benchmarks...")

 print(f"slow_solution : {timeit('slow_solution()', globals=globals(), number=10)}")
 print(f"while_sol : {timeit('while_solution()', globals=globals(), number=10)}")
 print(f"for_sol : {timeit('for_solution()', globals=globals(), number=10)}")
 print(f"solution : {timeit('solution()', globals=globals(), number=10)}")


Expand Down

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Strip utm_, fbclid, gclid, etc. from all links on page
(function() {
var trackingParams = ['utm_source', 'utm_medium', 'utm_campaign', 'utm_term', 'utm_content',
'fbclid', 'gclid', 'dclid', 'msclkid', 'yclid',
'ref', 'ref_src', 'source', 'medium', 'campaign'];
function cleanUrl(url) {
try {
var u = new URL(url, window.location.origin);
var changed = false;
trackingParams.forEach(function(p) {
if (u.searchParams.has(p)) {
u.searchParams.delete(p);
changed = true;
}
});
return changed ? u.toString() : url;
} catch (e) {
return url;
}
}
function cleanLinks() {
document.querySelectorAll('a[href]').forEach(function(a) {
var clean = cleanUrl(a.href);
if (clean !== a.href) a.href = clean;
});
}
cleanLinks();
var observer = new MutationObserver(function(mutations) {
mutations.forEach(function(m) {
m.addedNodes.forEach(function(node) {
if (node.nodeType === 1) {
if (node.tagName === 'A') cleanLinks();
node.querySelectorAll('a[href]').forEach(function(a) {
var clean = cleanUrl(a.href);
if (clean !== a.href) a.href = clean;
});
}
});
});
});
observer.observe(document.body, { childList: true, subtree: true });
})();
}
} catch(__e) { console.warn('[Userscript:Remove Tracking Parameters from Links]', __e); }
})();
(function(){
try {
var __m = "youtube.com";
var __re = new RegExp('^' + "youtube\\.com" + '
Performance: 95% faster Project Euler 187 by ManpreetXSingh · Pull Request #10580 · TheAlgorithms/Python · GitHub
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Performance: 95% faster Project Euler 187#10580

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Performance: 95% faster Project Euler 187
#10580
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db7a134

Add numpy calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
11aac84

Rename old solution to for_solution


ManpreetXSingh Oct 16, 2023
8943088

Add numpy solution


ManpreetXSingh Oct 16, 2023
d56844a

Update benchmarks


ManpreetXSingh Oct 16, 2023
8b6b3a4

Fix 🐛 in benchmarks in prime_numbers.py


ManpreetXSingh Oct 29, 2023
61219b4

Add prime helper fn in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
938c022

Add benchmark fn in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
e6535b1

Sort imports in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
2e28bde

Import prime helper fn


ManpreetXSingh Oct 29, 2023

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6 changes: 3 additions & 3 deletions
maths/prime_numbers.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -97,9 +97,9 @@ def benchmark():
 from timeit import timeit

 setup = "from __main__ import slow_primes, primes, fast_primes"
 print(timeit("slow_primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("fast_primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("list(slow_primes(1_000))", setup=setup, number=1_000))
 print(timeit("list(primes(1_000))", setup=setup, number=1_000))
 print(timeit("list(fast_primes(1_000))", setup=setup, number=1_000))


if __name__ == "__main__":
Expand Down

49 changes: 48 additions & 1 deletion
maths/prime_sieve_eratosthenes.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -11,6 +11,10 @@
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
"""

from math import isqrt

import numpy as np


def prime_sieve_eratosthenes(num: int) -> list[int]:
 """
Expand DownExpand Up@@ -45,10 +49,53 @@ def prime_sieve_eratosthenes(num: int) -> list[int]:
 return [prime for prime in range(2, num + 1) if primes[prime]]


def np_prime_sieve_eratosthenes(max_number: int) -> list[int]:
 """
 Returns prime numbers below max_number.
 See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

 >>> np_prime_sieve_eratosthenes(10)
 [2, 3, 5, 7]
 >>> np_prime_sieve_eratosthenes(2)
 [2]
 >>> np_prime_sieve_eratosthenes(1)
 []
 """
 if max_number < 2:
 return []

 # List containing a bool value for every odd number below max_number/2
 is_prime = np.ones((max_number + 1) // 2, dtype=bool)

 for i in range(3, isqrt(max_number - 1) + 1, 2):
 if is_prime[i // 2]:
 # Mark all multiple of i as not prime using list slicing
 is_prime[i**2 // 2 :: i] = False

 primes = np.where(is_prime)[0] * 2 + 1
 primes[0] = 2
 return primes.tolist()


def benchmark():
 """
 Benchmarks
 """
 from timeit import timeit

 print("Running performance benchmarks...")

 functions = ["prime_sieve_eratosthenes", "np_prime_sieve_eratosthenes"]
 for func in functions:
 print(f"{func} : {timeit(f'{func}(10_000)', globals=globals(), number=10_000)}")


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 user_num = int(input("Enter a positive integer: ").strip())
 print(prime_sieve_eratosthenes(user_num))
 print(np_prime_sieve_eratosthenes(user_num))

 benchmark()

41 changes: 35 additions & 6 deletions
project_euler/problem_187/sol1.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -13,6 +13,8 @@

from math import isqrt

from maths.prime_sieve_eratosthenes import np_prime_sieve_eratosthenes


def slow_calculate_prime_numbers(max_number: int) -> list[int]:
 """
Expand All@@ -38,15 +40,15 @@ def slow_calculate_prime_numbers(max_number: int) -> list[int]:
 return [i for i in range(2, max_number) if is_prime[i]]


def calculate_prime_numbers(max_number: int) -> list[int]:
def py_calculate_prime_numbers(max_number: int) -> list[int]:
 """
 Returns prime numbers below max_number.
 See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

 >>> calculate_prime_numbers(10)
 >>> py_calculate_prime_numbers(10)
 [2, 3, 5, 7]

 >>> calculate_prime_numbers(2)
 >>> py_calculate_prime_numbers(2)
 []
 """

Expand DownExpand Up@@ -100,7 +102,7 @@ def while_solution(max_number: int = 10**8) -> int:
 10
 """

 prime_numbers = calculate_prime_numbers(max_number // 2)
 prime_numbers = py_calculate_prime_numbers(max_number // 2)

 semiprimes_count = 0
 left = 0
Expand All@@ -114,6 +116,31 @@ def while_solution(max_number: int = 10**8) -> int:
 return semiprimes_count


def for_solution(max_number: int = 10**8) -> int:
 """
 Returns the number of composite integers below max_number have precisely two,
 not necessarily distinct, prime factors.

 >>> for_solution(30)
 10
 """

 prime_numbers = py_calculate_prime_numbers(max_number // 2)

 semiprimes_count = 0
 right = len(prime_numbers) - 1
 for left in range(len(prime_numbers)):
 if left > right:
 break
 for r in range(right, left - 2, -1):
 if prime_numbers[left] * prime_numbers[r] < max_number:
 break
 right = r
 semiprimes_count += right - left + 1

 return semiprimes_count


def solution(max_number: int = 10**8) -> int:
 """
 Returns the number of composite integers below max_number have precisely two,
Expand All@@ -123,7 +150,7 @@ def solution(max_number: int = 10**8) -> int:
 10
 """

 prime_numbers = calculate_prime_numbers(max_number // 2)
 prime_numbers = np_prime_sieve_eratosthenes((max_number - 1) // 2)

 semiprimes_count = 0
 right = len(prime_numbers) - 1
Expand All@@ -146,14 +173,16 @@ def benchmark() -> None:
 # Running performance benchmarks...
 # slow_solution : 108.50874730000032
 # while_sol : 28.09581200000048
 # solution : 25.063097400000515
 # for_sol : 25.063097400000515
 # solution : 5.219610300000568

 from timeit import timeit

 print("Running performance benchmarks...")

 print(f"slow_solution : {timeit('slow_solution()', globals=globals(), number=10)}")
 print(f"while_sol : {timeit('while_solution()', globals=globals(), number=10)}")
 print(f"for_sol : {timeit('for_solution()', globals=globals(), number=10)}")
 print(f"solution : {timeit('solution()', globals=globals(), number=10)}")


Expand Down

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Auto-enable theater mode on YouTube
(function() {
function tryTheater() {
var btn = document.querySelector('button[aria-label="Theater mode"], ytd-player #player button[title="Theater mode"]');
if (btn && !btn.classList.contains('activated')) {
btn.click();
}
}
// Try immediately
tryTheater();
// Try after navigation (SPA)
var lastUrl = location.href;
setInterval(function() {
if (location.href !== lastUrl) {
lastUrl = location.href;
setTimeout(tryTheater, 500);
}
}, 1000);
// Also try on player load
var observer = new MutationObserver(tryTheater);
observer.observe(document.body, { childList: true, subtree: true });
})();
}
} catch(__e) { console.warn('[Userscript:YouTube Theater Mode Default]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '
Performance: 95% faster Project Euler 187 by ManpreetXSingh · Pull Request #10580 · TheAlgorithms/Python · GitHub
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Performance: 95% faster Project Euler 187#10580

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Performance: 95% faster Project Euler 187
#10580
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db7a134

Add numpy calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
11aac84

Rename old solution to for_solution


ManpreetXSingh Oct 16, 2023
8943088

Add numpy solution


ManpreetXSingh Oct 16, 2023
d56844a

Update benchmarks


ManpreetXSingh Oct 16, 2023
8b6b3a4

Fix 🐛 in benchmarks in prime_numbers.py


ManpreetXSingh Oct 29, 2023
61219b4

Add prime helper fn in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
938c022

Add benchmark fn in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
e6535b1

Sort imports in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
2e28bde

Import prime helper fn


ManpreetXSingh Oct 29, 2023

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6 changes: 3 additions & 3 deletions
maths/prime_numbers.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -97,9 +97,9 @@ def benchmark():
 from timeit import timeit

 setup = "from __main__ import slow_primes, primes, fast_primes"
 print(timeit("slow_primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("fast_primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("list(slow_primes(1_000))", setup=setup, number=1_000))
 print(timeit("list(primes(1_000))", setup=setup, number=1_000))
 print(timeit("list(fast_primes(1_000))", setup=setup, number=1_000))


if __name__ == "__main__":
Expand Down

49 changes: 48 additions & 1 deletion
maths/prime_sieve_eratosthenes.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -11,6 +11,10 @@
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
"""

from math import isqrt

import numpy as np


def prime_sieve_eratosthenes(num: int) -> list[int]:
 """
Expand DownExpand Up@@ -45,10 +49,53 @@ def prime_sieve_eratosthenes(num: int) -> list[int]:
 return [prime for prime in range(2, num + 1) if primes[prime]]


def np_prime_sieve_eratosthenes(max_number: int) -> list[int]:
 """
 Returns prime numbers below max_number.
 See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

 >>> np_prime_sieve_eratosthenes(10)
 [2, 3, 5, 7]
 >>> np_prime_sieve_eratosthenes(2)
 [2]
 >>> np_prime_sieve_eratosthenes(1)
 []
 """
 if max_number < 2:
 return []

 # List containing a bool value for every odd number below max_number/2
 is_prime = np.ones((max_number + 1) // 2, dtype=bool)

 for i in range(3, isqrt(max_number - 1) + 1, 2):
 if is_prime[i // 2]:
 # Mark all multiple of i as not prime using list slicing
 is_prime[i**2 // 2 :: i] = False

 primes = np.where(is_prime)[0] * 2 + 1
 primes[0] = 2
 return primes.tolist()


def benchmark():
 """
 Benchmarks
 """
 from timeit import timeit

 print("Running performance benchmarks...")

 functions = ["prime_sieve_eratosthenes", "np_prime_sieve_eratosthenes"]
 for func in functions:
 print(f"{func} : {timeit(f'{func}(10_000)', globals=globals(), number=10_000)}")


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 user_num = int(input("Enter a positive integer: ").strip())
 print(prime_sieve_eratosthenes(user_num))
 print(np_prime_sieve_eratosthenes(user_num))

 benchmark()

41 changes: 35 additions & 6 deletions
project_euler/problem_187/sol1.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -13,6 +13,8 @@

from math import isqrt

from maths.prime_sieve_eratosthenes import np_prime_sieve_eratosthenes


def slow_calculate_prime_numbers(max_number: int) -> list[int]:
 """
Expand All@@ -38,15 +40,15 @@ def slow_calculate_prime_numbers(max_number: int) -> list[int]:
 return [i for i in range(2, max_number) if is_prime[i]]


def calculate_prime_numbers(max_number: int) -> list[int]:
def py_calculate_prime_numbers(max_number: int) -> list[int]:
 """
 Returns prime numbers below max_number.
 See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

 >>> calculate_prime_numbers(10)
 >>> py_calculate_prime_numbers(10)
 [2, 3, 5, 7]

 >>> calculate_prime_numbers(2)
 >>> py_calculate_prime_numbers(2)
 []
 """

Expand DownExpand Up@@ -100,7 +102,7 @@ def while_solution(max_number: int = 10**8) -> int:
 10
 """

 prime_numbers = calculate_prime_numbers(max_number // 2)
 prime_numbers = py_calculate_prime_numbers(max_number // 2)

 semiprimes_count = 0
 left = 0
Expand All@@ -114,6 +116,31 @@ def while_solution(max_number: int = 10**8) -> int:
 return semiprimes_count


def for_solution(max_number: int = 10**8) -> int:
 """
 Returns the number of composite integers below max_number have precisely two,
 not necessarily distinct, prime factors.

 >>> for_solution(30)
 10
 """

 prime_numbers = py_calculate_prime_numbers(max_number // 2)

 semiprimes_count = 0
 right = len(prime_numbers) - 1
 for left in range(len(prime_numbers)):
 if left > right:
 break
 for r in range(right, left - 2, -1):
 if prime_numbers[left] * prime_numbers[r] < max_number:
 break
 right = r
 semiprimes_count += right - left + 1

 return semiprimes_count


def solution(max_number: int = 10**8) -> int:
 """
 Returns the number of composite integers below max_number have precisely two,
Expand All@@ -123,7 +150,7 @@ def solution(max_number: int = 10**8) -> int:
 10
 """

 prime_numbers = calculate_prime_numbers(max_number // 2)
 prime_numbers = np_prime_sieve_eratosthenes((max_number - 1) // 2)

 semiprimes_count = 0
 right = len(prime_numbers) - 1
Expand All@@ -146,14 +173,16 @@ def benchmark() -> None:
 # Running performance benchmarks...
 # slow_solution : 108.50874730000032
 # while_sol : 28.09581200000048
 # solution : 25.063097400000515
 # for_sol : 25.063097400000515
 # solution : 5.219610300000568

 from timeit import timeit

 print("Running performance benchmarks...")

 print(f"slow_solution : {timeit('slow_solution()', globals=globals(), number=10)}")
 print(f"while_sol : {timeit('while_solution()', globals=globals(), number=10)}")
 print(f"for_sol : {timeit('for_solution()', globals=globals(), number=10)}")
 print(f"solution : {timeit('solution()', globals=globals(), number=10)}")


Expand Down

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// Remove or un-stick sticky/fixed headers that block content
(function() {
function unstick() {
document.querySelectorAll('header, nav, [role="banner"], .header, .navbar, .sticky, .fixed-top, [style*="position: fixed"], [style*="position:sticky"]').forEach(function(el) {
if (el.style.position === 'fixed' || el.style.position === 'sticky' || getComputedStyle(el).position === 'fixed' || getComputedStyle(el).position === 'sticky') {
el.style.position = 'static';
el.style.top = 'auto';
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unstick();
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observer.observe(document.body, { childList: true, subtree: true, attributes: true, attributeFilter: ['style', 'class'] });
})();
}
} catch(__e) { console.warn('[Userscript:Kill Sticky Headers]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '
Performance: 95% faster Project Euler 187 by ManpreetXSingh · Pull Request #10580 · TheAlgorithms/Python · GitHub
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Performance: 95% faster Project Euler 187
#10580
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db7a134

Add numpy calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
11aac84

Rename old solution to for_solution


ManpreetXSingh Oct 16, 2023
8943088

Add numpy solution


ManpreetXSingh Oct 16, 2023
d56844a

Update benchmarks


ManpreetXSingh Oct 16, 2023
8b6b3a4

Fix 🐛 in benchmarks in prime_numbers.py


ManpreetXSingh Oct 29, 2023
61219b4

Add prime helper fn in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
938c022

Add benchmark fn in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
e6535b1

Sort imports in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
2e28bde

Import prime helper fn


ManpreetXSingh Oct 29, 2023

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6 changes: 3 additions & 3 deletions
maths/prime_numbers.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -97,9 +97,9 @@ def benchmark():
 from timeit import timeit

 setup = "from __main__ import slow_primes, primes, fast_primes"
 print(timeit("slow_primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("fast_primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("list(slow_primes(1_000))", setup=setup, number=1_000))
 print(timeit("list(primes(1_000))", setup=setup, number=1_000))
 print(timeit("list(fast_primes(1_000))", setup=setup, number=1_000))


if __name__ == "__main__":
Expand Down

49 changes: 48 additions & 1 deletion
maths/prime_sieve_eratosthenes.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -11,6 +11,10 @@
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
"""

from math import isqrt

import numpy as np


def prime_sieve_eratosthenes(num: int) -> list[int]:
 """
Expand DownExpand Up@@ -45,10 +49,53 @@ def prime_sieve_eratosthenes(num: int) -> list[int]:
 return [prime for prime in range(2, num + 1) if primes[prime]]


def np_prime_sieve_eratosthenes(max_number: int) -> list[int]:
 """
 Returns prime numbers below max_number.
 See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

 >>> np_prime_sieve_eratosthenes(10)
 [2, 3, 5, 7]
 >>> np_prime_sieve_eratosthenes(2)
 [2]
 >>> np_prime_sieve_eratosthenes(1)
 []
 """
 if max_number < 2:
 return []

 # List containing a bool value for every odd number below max_number/2
 is_prime = np.ones((max_number + 1) // 2, dtype=bool)

 for i in range(3, isqrt(max_number - 1) + 1, 2):
 if is_prime[i // 2]:
 # Mark all multiple of i as not prime using list slicing
 is_prime[i**2 // 2 :: i] = False

 primes = np.where(is_prime)[0] * 2 + 1
 primes[0] = 2
 return primes.tolist()


def benchmark():
 """
 Benchmarks
 """
 from timeit import timeit

 print("Running performance benchmarks...")

 functions = ["prime_sieve_eratosthenes", "np_prime_sieve_eratosthenes"]
 for func in functions:
 print(f"{func} : {timeit(f'{func}(10_000)', globals=globals(), number=10_000)}")


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 user_num = int(input("Enter a positive integer: ").strip())
 print(prime_sieve_eratosthenes(user_num))
 print(np_prime_sieve_eratosthenes(user_num))

 benchmark()

41 changes: 35 additions & 6 deletions
project_euler/problem_187/sol1.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -13,6 +13,8 @@

from math import isqrt

from maths.prime_sieve_eratosthenes import np_prime_sieve_eratosthenes


def slow_calculate_prime_numbers(max_number: int) -> list[int]:
 """
Expand All@@ -38,15 +40,15 @@ def slow_calculate_prime_numbers(max_number: int) -> list[int]:
 return [i for i in range(2, max_number) if is_prime[i]]


def calculate_prime_numbers(max_number: int) -> list[int]:
def py_calculate_prime_numbers(max_number: int) -> list[int]:
 """
 Returns prime numbers below max_number.
 See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

 >>> calculate_prime_numbers(10)
 >>> py_calculate_prime_numbers(10)
 [2, 3, 5, 7]

 >>> calculate_prime_numbers(2)
 >>> py_calculate_prime_numbers(2)
 []
 """

Expand DownExpand Up@@ -100,7 +102,7 @@ def while_solution(max_number: int = 10**8) -> int:
 10
 """

 prime_numbers = calculate_prime_numbers(max_number // 2)
 prime_numbers = py_calculate_prime_numbers(max_number // 2)

 semiprimes_count = 0
 left = 0
Expand All@@ -114,6 +116,31 @@ def while_solution(max_number: int = 10**8) -> int:
 return semiprimes_count


def for_solution(max_number: int = 10**8) -> int:
 """
 Returns the number of composite integers below max_number have precisely two,
 not necessarily distinct, prime factors.

 >>> for_solution(30)
 10
 """

 prime_numbers = py_calculate_prime_numbers(max_number // 2)

 semiprimes_count = 0
 right = len(prime_numbers) - 1
 for left in range(len(prime_numbers)):
 if left > right:
 break
 for r in range(right, left - 2, -1):
 if prime_numbers[left] * prime_numbers[r] < max_number:
 break
 right = r
 semiprimes_count += right - left + 1

 return semiprimes_count


def solution(max_number: int = 10**8) -> int:
 """
 Returns the number of composite integers below max_number have precisely two,
Expand All@@ -123,7 +150,7 @@ def solution(max_number: int = 10**8) -> int:
 10
 """

 prime_numbers = calculate_prime_numbers(max_number // 2)
 prime_numbers = np_prime_sieve_eratosthenes((max_number - 1) // 2)

 semiprimes_count = 0
 right = len(prime_numbers) - 1
Expand All@@ -146,14 +173,16 @@ def benchmark() -> None:
 # Running performance benchmarks...
 # slow_solution : 108.50874730000032
 # while_sol : 28.09581200000048
 # solution : 25.063097400000515
 # for_sol : 25.063097400000515
 # solution : 5.219610300000568

 from timeit import timeit

 print("Running performance benchmarks...")

 print(f"slow_solution : {timeit('slow_solution()', globals=globals(), number=10)}")
 print(f"while_sol : {timeit('while_solution()', globals=globals(), number=10)}")
 print(f"for_sol : {timeit('for_solution()', globals=globals(), number=10)}")
 print(f"solution : {timeit('solution()', globals=globals(), number=10)}")


Expand Down

, 'i');
if (__m === '*' || __re.test(location.href)) {
// Universal Dark Mode - works on any site
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var enabled = true;
function applyDarkMode() {
if (!enabled) return;
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/* Invert everything except media */
html {
filter: invert(1) hue-rotate(180deg) !important;
background: #1a1a2e !important;
}
/* Restore images, videos, iframes, canvas */
img, video, iframe, canvas, svg, picture, [style*="background-image"] {
filter: invert(1) hue-rotate(180deg) !important;
}
/* Preserve specific elements that should not be inverted */
.no-dark-mode, .no-dark-mode *,
[data-theme="light"], [data-theme="light"],
.ace_editor, .ace_editor *,
.CodeMirror, .CodeMirror *,
.monaco-editor, .monaco-editor *,
.markdown-body pre, .markdown-body pre *,
.highlight, .highlight *,
pre code, pre code * {
filter: none !important;
}
/* Fix common UI elements */
.modal, .popup, .dropdown-menu, .tooltip, .popover {
filter: invert(1) hue-rotate(180deg) !important;
background: #2d2d44 !important;
border-color: #444 !important;
}
/* Scrollbars */
::-webkit-scrollbar { background: #1a1a2e !important; }
::-webkit-scrollbar-thumb { background: #444 !important; }
::-webkit-scrollbar-thumb:hover { background: #555 !important; }
/* Selection */
::selection { background: #4ecdc4 !important; color: #1a1a2e !important; }
::-moz-selection { background: #4ecdc4 !important; color: #1a1a2e !important; }
';
}
function removeDarkMode() {
var style = document.getElementById('universal-dark-mode-style');
if (style) style.remove();
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document.addEventListener('keydown', function(e) {
if (e.altKey && e.shiftKey && e.key === 'D') {
e.preventDefault();
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if (enabled) {
applyDarkMode();
console.log('[Universal Dark Mode] Enabled');
} else {
removeDarkMode();
console.log('[Universal Dark Mode] Disabled');
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var observer = new MutationObserver(function(mutations) {
if (enabled && !document.getElementById('universal-dark-mode-style')) {
applyDarkMode();
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Performance: 95% faster Project Euler 187 by ManpreetXSingh · Pull Request #10580 · TheAlgorithms/Python · GitHub
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Performance: 95% faster Project Euler 187#10580

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commits into

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Performance: 95% faster Project Euler 187
#10580
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db7a134

Add numpy calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
11aac84

Rename old solution to for_solution


ManpreetXSingh Oct 16, 2023
8943088

Add numpy solution


ManpreetXSingh Oct 16, 2023
d56844a

Update benchmarks


ManpreetXSingh Oct 16, 2023
8b6b3a4

Fix 🐛 in benchmarks in prime_numbers.py


ManpreetXSingh Oct 29, 2023
61219b4

Add prime helper fn in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
938c022

Add benchmark fn in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
e6535b1

Sort imports in prime_sieve_eratosthenes.py


ManpreetXSingh Oct 29, 2023
2e28bde

Import prime helper fn


ManpreetXSingh Oct 29, 2023

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6 changes: 3 additions & 3 deletions
maths/prime_numbers.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -97,9 +97,9 @@ def benchmark():
 from timeit import timeit

 setup = "from __main__ import slow_primes, primes, fast_primes"
 print(timeit("slow_primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("fast_primes(1_000_000_000_000)", setup=setup, number=1_000_000))
 print(timeit("list(slow_primes(1_000))", setup=setup, number=1_000))
 print(timeit("list(primes(1_000))", setup=setup, number=1_000))
 print(timeit("list(fast_primes(1_000))", setup=setup, number=1_000))


if __name__ == "__main__":
Expand Down

49 changes: 48 additions & 1 deletion
maths/prime_sieve_eratosthenes.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -11,6 +11,10 @@
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
"""

from math import isqrt

import numpy as np


def prime_sieve_eratosthenes(num: int) -> list[int]:
 """
Expand DownExpand Up@@ -45,10 +49,53 @@ def prime_sieve_eratosthenes(num: int) -> list[int]:
 return [prime for prime in range(2, num + 1) if primes[prime]]


def np_prime_sieve_eratosthenes(max_number: int) -> list[int]:
 """
 Returns prime numbers below max_number.
 See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

 >>> np_prime_sieve_eratosthenes(10)
 [2, 3, 5, 7]
 >>> np_prime_sieve_eratosthenes(2)
 [2]
 >>> np_prime_sieve_eratosthenes(1)
 []
 """
 if max_number < 2:
 return []

 # List containing a bool value for every odd number below max_number/2
 is_prime = np.ones((max_number + 1) // 2, dtype=bool)

 for i in range(3, isqrt(max_number - 1) + 1, 2):
 if is_prime[i // 2]:
 # Mark all multiple of i as not prime using list slicing
 is_prime[i**2 // 2 :: i] = False

 primes = np.where(is_prime)[0] * 2 + 1
 primes[0] = 2
 return primes.tolist()


def benchmark():
 """
 Benchmarks
 """
 from timeit import timeit

 print("Running performance benchmarks...")

 functions = ["prime_sieve_eratosthenes", "np_prime_sieve_eratosthenes"]
 for func in functions:
 print(f"{func} : {timeit(f'{func}(10_000)', globals=globals(), number=10_000)}")


if __name__ == "__main__":
 import doctest

 doctest.testmod()

 user_num = int(input("Enter a positive integer: ").strip())
 print(prime_sieve_eratosthenes(user_num))
 print(np_prime_sieve_eratosthenes(user_num))

 benchmark()

41 changes: 35 additions & 6 deletions
project_euler/problem_187/sol1.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -13,6 +13,8 @@

from math import isqrt

from maths.prime_sieve_eratosthenes import np_prime_sieve_eratosthenes


def slow_calculate_prime_numbers(max_number: int) -> list[int]:
 """
Expand All@@ -38,15 +40,15 @@ def slow_calculate_prime_numbers(max_number: int) -> list[int]:
 return [i for i in range(2, max_number) if is_prime[i]]


def calculate_prime_numbers(max_number: int) -> list[int]:
def py_calculate_prime_numbers(max_number: int) -> list[int]:
 """
 Returns prime numbers below max_number.
 See: https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes

 >>> calculate_prime_numbers(10)
 >>> py_calculate_prime_numbers(10)
 [2, 3, 5, 7]

 >>> calculate_prime_numbers(2)
 >>> py_calculate_prime_numbers(2)
 []
 """

Expand DownExpand Up@@ -100,7 +102,7 @@ def while_solution(max_number: int = 10**8) -> int:
 10
 """

 prime_numbers = calculate_prime_numbers(max_number // 2)
 prime_numbers = py_calculate_prime_numbers(max_number // 2)

 semiprimes_count = 0
 left = 0
Expand All@@ -114,6 +116,31 @@ def while_solution(max_number: int = 10**8) -> int:
 return semiprimes_count


def for_solution(max_number: int = 10**8) -> int:
 """
 Returns the number of composite integers below max_number have precisely two,
 not necessarily distinct, prime factors.

 >>> for_solution(30)
 10
 """

 prime_numbers = py_calculate_prime_numbers(max_number // 2)

 semiprimes_count = 0
 right = len(prime_numbers) - 1
 for left in range(len(prime_numbers)):
 if left > right:
 break
 for r in range(right, left - 2, -1):
 if prime_numbers[left] * prime_numbers[r] < max_number:
 break
 right = r
 semiprimes_count += right - left + 1

 return semiprimes_count


def solution(max_number: int = 10**8) -> int:
 """
 Returns the number of composite integers below max_number have precisely two,
Expand All@@ -123,7 +150,7 @@ def solution(max_number: int = 10**8) -> int:
 10
 """

 prime_numbers = calculate_prime_numbers(max_number // 2)
 prime_numbers = np_prime_sieve_eratosthenes((max_number - 1) // 2)

 semiprimes_count = 0
 right = len(prime_numbers) - 1
Expand All@@ -146,14 +173,16 @@ def benchmark() -> None:
 # Running performance benchmarks...
 # slow_solution : 108.50874730000032
 # while_sol : 28.09581200000048
 # solution : 25.063097400000515
 # for_sol : 25.063097400000515
 # solution : 5.219610300000568

 from timeit import timeit

 print("Running performance benchmarks...")

 print(f"slow_solution : {timeit('slow_solution()', globals=globals(), number=10)}")
 print(f"while_sol : {timeit('while_solution()', globals=globals(), number=10)}")
 print(f"for_sol : {timeit('for_solution()', globals=globals(), number=10)}")
 print(f"solution : {timeit('solution()', globals=globals(), number=10)}")


Expand Down