Performance: 58% faster Project Euler 070#10558

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Performance: 58% faster Project Euler 070 #10558

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5958ffa
Separate common solution
ManpreetXSingh Oct 15, 2023
d6b16c6
Add slicing_get_totients
ManpreetXSingh Oct 15, 2023
fa8f7f9
Add fast get_totients and calculate_prime_numbers
ManpreetXSingh Oct 15, 2023
9bf2655
Add slow_solution and slicing_solution
ManpreetXSingh Oct 15, 2023
8113df9
Add performance benchmark
ManpreetXSingh Oct 15, 2023
4f42182
Fix broken wikipedia link
ManpreetXSingh Oct 15, 2023
3949c1b
Add missing type hints
ManpreetXSingh Oct 16, 2023
bf95078
Add numpy calculate_prime_numbers
ManpreetXSingh Oct 16, 2023
9c9ad26
Add solution using np_calculate_prime_numbers
ManpreetXSingh Oct 16, 2023
89cc321
Update benchmarks
ManpreetXSingh Oct 16, 2023
7e9e827
Merge branch 'TheAlgorithms:master' into performance-project-euler-070
ManpreetXSingh Dec 29, 2023
c2d35e5
Remove py_solution and slicing_solution
ManpreetXSingh Dec 29, 2023
6ff00c7
Remove slow_solution and benchmark
ManpreetXSingh Dec 29, 2023
480cf3e
Move prime generator to maths/prime_sieve_eratosthenes.py
ManpreetXSingh Dec 29, 2023
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32 changes: 31 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 +49,36 @@ 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)
[]
"""
if max_number <= 2:
return []

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


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))
23 changes: 12 additions & 11 deletions project_euler/problem_070/sol1.py
View file
Open in desktop
Original file line numberDiff line numberDiff line change
Expand Up@@ -26,30 +26,31 @@

References:
Finding totients
https://en.wikipedia.org/wiki/Euler's_totient_function#Euler's_product_formula
https://en.wikipedia.org/wiki/Euler%27s_totient_function#Euler%27s_product_formula
"""
from __future__ import annotations

import numpy as np

from maths.prime_sieve_eratosthenes import np_prime_sieve_eratosthenes

def get_totients(max_one: int) -> list[int]:

def np_get_totients(limit) -> list[int]:
"""
Calculates a list of totients from 0 to max_one exclusive, using the
definition of Euler's product formula.

>>> get_totients(5)
>>> np_get_totients(5)
[0, 1, 1, 2, 2]

>>> get_totients(10)
>>> np_get_totients(10)
[0, 1, 1, 2, 2, 4, 2, 6, 4, 6]
"""
totients = np.arange(max_one)
totients = np.arange(limit)
primes = np_prime_sieve_eratosthenes(limit)

for i in range(2, max_one):
if totients[i] == i:
x = np.arange(i, max_one, i) # array of indexes to select
totients[x] -= totients[x] // i
for i in primes:
totients[i::i] -= totients[i::i] // i

return totients.tolist()

Expand DownExpand Up@@ -81,10 +82,10 @@ def solution(max_n: int = 10000000) -> int:
>>> solution(10000)
4435
"""
totients = np_get_totients(max_n + 1)

min_numerator = 1 # i
min_denominator = 0 # φ(i)
totients = get_totients(max_n + 1)

for i in range(2, max_n + 1):
t = totients[i]
Expand All@@ -97,4 +98,4 @@ def solution(max_n: int = 10000000) -> int:


if __name__ == "__main__":
print(f"{solution() = }")
print(f"Solution : {solution()}")
, 'i'); if (__m === '*' || __re.test(location.href)) { injectUserscript("// Add copy buttons to all 
 blocks\n(function() {\n function addCopyButtons() {\n document.querySelectorAll('pre code').forEach(function(codeBlock) {\n if (codeBlock.parentElement.hasAttribute('data-copy-added')) return;\n codeBlock.parentElement.setAttribute('data-copy-added', 'true');\n \n var btn = document.createElement('button');\n btn.textContent = 'Copy';\n btn.style.cssText = 'position:absolute;top:4px;right:4px;padding:2px 8px;font-size:11px;background:#4ecdc4;border:none;border-radius:4px;color:#1a1a2e;cursor:pointer;opacity:0.7;transition:opacity 0.2s;';\n btn.onmouseover = function() { this.style.opacity = '1'; };\n btn.onmouseout = function() { this.style.opacity = '0.7'; };\n btn.onclick = function() {\n navigator.clipboard.writeText(codeBlock.textContent).then(function() {\n btn.textContent = 'Copied!';\n setTimeout(function() { btn.textContent = 'Copy'; }, 1500);\n });\n };\n codeBlock.parentElement.style.position = 'relative';\n codeBlock.parentElement.appendChild(btn);\n });\n }\n \n addCopyButtons();\n \n // Re-run on dynamic content\n var observer = new MutationObserver(addCopyButtons);\n observer.observe(document.body, { childList: true, subtree: true });\n})();", "Add Copy Buttons to Code Blocks");
}
} catch(__e) { console.warn('[Userscript:Add Copy Buttons to Code Blocks]', __e); }
})();
(function(){
try {
var __m = "github.com";
var __re = new RegExp('^' + "github\\.com" + '

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Performance: 58% faster Project Euler 070#10558

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Performance: 58% faster Project Euler 070
#10558
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5958ffa

Separate common solution


ManpreetXSingh Oct 15, 2023
d6b16c6

Add slicing_get_totients


ManpreetXSingh Oct 15, 2023
fa8f7f9

Add fast get_totients and calculate_prime_numbers


ManpreetXSingh Oct 15, 2023
9bf2655

Add slow_solution and slicing_solution


ManpreetXSingh Oct 15, 2023
8113df9

Add performance benchmark


ManpreetXSingh Oct 15, 2023
4f42182

Fix broken wikipedia link


ManpreetXSingh Oct 15, 2023
3949c1b

Add missing type hints


ManpreetXSingh Oct 16, 2023
bf95078

Add numpy calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
9c9ad26

Add solution using np_calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
89cc321

Update benchmarks


ManpreetXSingh Oct 16, 2023
7e9e827

Merge branch 'TheAlgorithms:master' into performance-project-euler-070


ManpreetXSingh Dec 29, 2023
c2d35e5

Remove py_solution and slicing_solution


ManpreetXSingh Dec 29, 2023
6ff00c7

Remove slow_solution and benchmark


ManpreetXSingh Dec 29, 2023
480cf3e

Move prime generator to maths/prime_sieve_eratosthenes.py


ManpreetXSingh Dec 29, 2023

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32 changes: 31 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 +49,36 @@ 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)
 []
 """
 if max_number <= 2:
 return []

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


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))

23 changes: 12 additions & 11 deletions
project_euler/problem_070/sol1.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -26,30 +26,31 @@

References:
Finding totients
https://en.wikipedia.org/wiki/Euler's_totient_function#Euler's_product_formula
https://en.wikipedia.org/wiki/Euler%27s_totient_function#Euler%27s_product_formula
"""
from __future__ import annotations

import numpy as np

from maths.prime_sieve_eratosthenes import np_prime_sieve_eratosthenes

def get_totients(max_one: int) -> list[int]:

def np_get_totients(limit) -> list[int]:
 """
 Calculates a list of totients from 0 to max_one exclusive, using the
 definition of Euler's product formula.

 >>> get_totients(5)
 >>> np_get_totients(5)
 [0, 1, 1, 2, 2]

 >>> get_totients(10)
 >>> np_get_totients(10)
 [0, 1, 1, 2, 2, 4, 2, 6, 4, 6]
 """
 totients = np.arange(max_one)
 totients = np.arange(limit)
 primes = np_prime_sieve_eratosthenes(limit)

 for i in range(2, max_one):
 if totients[i] == i:
 x = np.arange(i, max_one, i) # array of indexes to select
 totients[x] -= totients[x] // i
 for i in primes:
 totients[i::i] -= totients[i::i] // i

 return totients.tolist()

Expand DownExpand Up@@ -81,10 +82,10 @@ def solution(max_n: int = 10000000) -> int:
 >>> solution(10000)
 4435
 """
 totients = np_get_totients(max_n + 1)

 min_numerator = 1 # i
 min_denominator = 0 # φ(i)
 totients = get_totients(max_n + 1)

 for i in range(2, max_n + 1):
 t = totients[i]
Expand All@@ -97,4 +98,4 @@ def solution(max_n: int = 10000000) -> int:


if __name__ == "__main__":
 print(f"{solution() = }")
 print(f"Solution : {solution()}")

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Force GitHub README to respect dark mode\n(function() {\n var style = document.createElement('style');\n style.textContent = '\n .markdown-body {\n color-scheme: dark light;\n }\n .markdown-body pre { background: #161b22 !important; }\n .markdown-body code { background: rgba(110, 118, 129, 0.4) !important; }\n .markdown-body table th, .markdown-body table td { border-color: #30363d !important; }\n .markdown-body img { background: #0d1117; }\n .markdown-body blockquote { border-left-color: #8b949e; }\n .markdown-body hr { border-color: #30363d; }\n ';\n document.head.appendChild(style);\n})();", "GitHub Dark Mode README Fix");
}
} catch(__e) { console.warn('[Userscript:GitHub Dark Mode README Fix]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

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Performance: 58% faster Project Euler 070#10558

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 Closed

ManpreetXSingh
wants to merge
14
commits into

from

 Closed


Performance: 58% faster Project Euler 070
#10558
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14 commits


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5958ffa

Separate common solution


ManpreetXSingh Oct 15, 2023
d6b16c6

Add slicing_get_totients


ManpreetXSingh Oct 15, 2023
fa8f7f9

Add fast get_totients and calculate_prime_numbers


ManpreetXSingh Oct 15, 2023
9bf2655

Add slow_solution and slicing_solution


ManpreetXSingh Oct 15, 2023
8113df9

Add performance benchmark


ManpreetXSingh Oct 15, 2023
4f42182

Fix broken wikipedia link


ManpreetXSingh Oct 15, 2023
3949c1b

Add missing type hints


ManpreetXSingh Oct 16, 2023
bf95078

Add numpy calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
9c9ad26

Add solution using np_calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
89cc321

Update benchmarks


ManpreetXSingh Oct 16, 2023
7e9e827

Merge branch 'TheAlgorithms:master' into performance-project-euler-070


ManpreetXSingh Dec 29, 2023
c2d35e5

Remove py_solution and slicing_solution


ManpreetXSingh Dec 29, 2023
6ff00c7

Remove slow_solution and benchmark


ManpreetXSingh Dec 29, 2023
480cf3e

Move prime generator to maths/prime_sieve_eratosthenes.py


ManpreetXSingh Dec 29, 2023

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32 changes: 31 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 +49,36 @@ 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)
 []
 """
 if max_number <= 2:
 return []

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


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))

23 changes: 12 additions & 11 deletions
project_euler/problem_070/sol1.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -26,30 +26,31 @@

References:
Finding totients
https://en.wikipedia.org/wiki/Euler's_totient_function#Euler's_product_formula
https://en.wikipedia.org/wiki/Euler%27s_totient_function#Euler%27s_product_formula
"""
from __future__ import annotations

import numpy as np

from maths.prime_sieve_eratosthenes import np_prime_sieve_eratosthenes

def get_totients(max_one: int) -> list[int]:

def np_get_totients(limit) -> list[int]:
 """
 Calculates a list of totients from 0 to max_one exclusive, using the
 definition of Euler's product formula.

 >>> get_totients(5)
 >>> np_get_totients(5)
 [0, 1, 1, 2, 2]

 >>> get_totients(10)
 >>> np_get_totients(10)
 [0, 1, 1, 2, 2, 4, 2, 6, 4, 6]
 """
 totients = np.arange(max_one)
 totients = np.arange(limit)
 primes = np_prime_sieve_eratosthenes(limit)

 for i in range(2, max_one):
 if totients[i] == i:
 x = np.arange(i, max_one, i) # array of indexes to select
 totients[x] -= totients[x] // i
 for i in primes:
 totients[i::i] -= totients[i::i] // i

 return totients.tolist()

Expand DownExpand Up@@ -81,10 +82,10 @@ def solution(max_n: int = 10000000) -> int:
 >>> solution(10000)
 4435
 """
 totients = np_get_totients(max_n + 1)

 min_numerator = 1 # i
 min_denominator = 0 # φ(i)
 totients = get_totients(max_n + 1)

 for i in range(2, max_n + 1):
 t = totients[i]
Expand All@@ -97,4 +98,4 @@ def solution(max_n: int = 10000000) -> int:


if __name__ == "__main__":
 print(f"{solution() = }")
 print(f"Solution : {solution()}")

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

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Performance: 58% faster Project Euler 070#10558

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 Closed

ManpreetXSingh
wants to merge
14
commits into

from

 Closed


Performance: 58% faster Project Euler 070
#10558
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5958ffa

Separate common solution


ManpreetXSingh Oct 15, 2023
d6b16c6

Add slicing_get_totients


ManpreetXSingh Oct 15, 2023
fa8f7f9

Add fast get_totients and calculate_prime_numbers


ManpreetXSingh Oct 15, 2023
9bf2655

Add slow_solution and slicing_solution


ManpreetXSingh Oct 15, 2023
8113df9

Add performance benchmark


ManpreetXSingh Oct 15, 2023
4f42182

Fix broken wikipedia link


ManpreetXSingh Oct 15, 2023
3949c1b

Add missing type hints


ManpreetXSingh Oct 16, 2023
bf95078

Add numpy calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
9c9ad26

Add solution using np_calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
89cc321

Update benchmarks


ManpreetXSingh Oct 16, 2023
7e9e827

Merge branch 'TheAlgorithms:master' into performance-project-euler-070


ManpreetXSingh Dec 29, 2023
c2d35e5

Remove py_solution and slicing_solution


ManpreetXSingh Dec 29, 2023
6ff00c7

Remove slow_solution and benchmark


ManpreetXSingh Dec 29, 2023
480cf3e

Move prime generator to maths/prime_sieve_eratosthenes.py


ManpreetXSingh Dec 29, 2023

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32 changes: 31 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 +49,36 @@ 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)
 []
 """
 if max_number <= 2:
 return []

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


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))

23 changes: 12 additions & 11 deletions
project_euler/problem_070/sol1.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -26,30 +26,31 @@

References:
Finding totients
https://en.wikipedia.org/wiki/Euler's_totient_function#Euler's_product_formula
https://en.wikipedia.org/wiki/Euler%27s_totient_function#Euler%27s_product_formula
"""
from __future__ import annotations

import numpy as np

from maths.prime_sieve_eratosthenes import np_prime_sieve_eratosthenes

def get_totients(max_one: int) -> list[int]:

def np_get_totients(limit) -> list[int]:
 """
 Calculates a list of totients from 0 to max_one exclusive, using the
 definition of Euler's product formula.

 >>> get_totients(5)
 >>> np_get_totients(5)
 [0, 1, 1, 2, 2]

 >>> get_totients(10)
 >>> np_get_totients(10)
 [0, 1, 1, 2, 2, 4, 2, 6, 4, 6]
 """
 totients = np.arange(max_one)
 totients = np.arange(limit)
 primes = np_prime_sieve_eratosthenes(limit)

 for i in range(2, max_one):
 if totients[i] == i:
 x = np.arange(i, max_one, i) # array of indexes to select
 totients[x] -= totients[x] // i
 for i in primes:
 totients[i::i] -= totients[i::i] // i

 return totients.tolist()

Expand DownExpand Up@@ -81,10 +82,10 @@ def solution(max_n: int = 10000000) -> int:
 >>> solution(10000)
 4435
 """
 totients = np_get_totients(max_n + 1)

 min_numerator = 1 # i
 min_denominator = 0 # φ(i)
 totients = get_totients(max_n + 1)

 for i in range(2, max_n + 1):
 t = totients[i]
Expand All@@ -97,4 +98,4 @@ def solution(max_n: int = 10000000) -> int:


if __name__ == "__main__":
 print(f"{solution() = }")
 print(f"Solution : {solution()}")

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

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Performance: 58% faster Project Euler 070#10558

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 Closed

ManpreetXSingh
wants to merge
14
commits into

from

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Performance: 58% faster Project Euler 070
#10558
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5958ffa

Separate common solution


ManpreetXSingh Oct 15, 2023
d6b16c6

Add slicing_get_totients


ManpreetXSingh Oct 15, 2023
fa8f7f9

Add fast get_totients and calculate_prime_numbers


ManpreetXSingh Oct 15, 2023
9bf2655

Add slow_solution and slicing_solution


ManpreetXSingh Oct 15, 2023
8113df9

Add performance benchmark


ManpreetXSingh Oct 15, 2023
4f42182

Fix broken wikipedia link


ManpreetXSingh Oct 15, 2023
3949c1b

Add missing type hints


ManpreetXSingh Oct 16, 2023
bf95078

Add numpy calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
9c9ad26

Add solution using np_calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
89cc321

Update benchmarks


ManpreetXSingh Oct 16, 2023
7e9e827

Merge branch 'TheAlgorithms:master' into performance-project-euler-070


ManpreetXSingh Dec 29, 2023
c2d35e5

Remove py_solution and slicing_solution


ManpreetXSingh Dec 29, 2023
6ff00c7

Remove slow_solution and benchmark


ManpreetXSingh Dec 29, 2023
480cf3e

Move prime generator to maths/prime_sieve_eratosthenes.py


ManpreetXSingh Dec 29, 2023

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32 changes: 31 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 +49,36 @@ 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)
 []
 """
 if max_number <= 2:
 return []

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


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))

23 changes: 12 additions & 11 deletions
project_euler/problem_070/sol1.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -26,30 +26,31 @@

References:
Finding totients
https://en.wikipedia.org/wiki/Euler's_totient_function#Euler's_product_formula
https://en.wikipedia.org/wiki/Euler%27s_totient_function#Euler%27s_product_formula
"""
from __future__ import annotations

import numpy as np

from maths.prime_sieve_eratosthenes import np_prime_sieve_eratosthenes

def get_totients(max_one: int) -> list[int]:

def np_get_totients(limit) -> list[int]:
 """
 Calculates a list of totients from 0 to max_one exclusive, using the
 definition of Euler's product formula.

 >>> get_totients(5)
 >>> np_get_totients(5)
 [0, 1, 1, 2, 2]

 >>> get_totients(10)
 >>> np_get_totients(10)
 [0, 1, 1, 2, 2, 4, 2, 6, 4, 6]
 """
 totients = np.arange(max_one)
 totients = np.arange(limit)
 primes = np_prime_sieve_eratosthenes(limit)

 for i in range(2, max_one):
 if totients[i] == i:
 x = np.arange(i, max_one, i) # array of indexes to select
 totients[x] -= totients[x] // i
 for i in primes:
 totients[i::i] -= totients[i::i] // i

 return totients.tolist()

Expand DownExpand Up@@ -81,10 +82,10 @@ def solution(max_n: int = 10000000) -> int:
 >>> solution(10000)
 4435
 """
 totients = np_get_totients(max_n + 1)

 min_numerator = 1 # i
 min_denominator = 0 # φ(i)
 totients = get_totients(max_n + 1)

 for i in range(2, max_n + 1):
 t = totients[i]
Expand All@@ -97,4 +98,4 @@ def solution(max_n: int = 10000000) -> int:


if __name__ == "__main__":
 print(f"{solution() = }")
 print(f"Solution : {solution()}")

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

Skip to content
Performance: 58% faster Project Euler 070#10558

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 Closed

ManpreetXSingh
wants to merge
14
commits into

from

 Closed


Performance: 58% faster Project Euler 070
#10558
Show file tree
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14 commits


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Hold shift + click to select a range
5958ffa

Separate common solution


ManpreetXSingh Oct 15, 2023
d6b16c6

Add slicing_get_totients


ManpreetXSingh Oct 15, 2023
fa8f7f9

Add fast get_totients and calculate_prime_numbers


ManpreetXSingh Oct 15, 2023
9bf2655

Add slow_solution and slicing_solution


ManpreetXSingh Oct 15, 2023
8113df9

Add performance benchmark


ManpreetXSingh Oct 15, 2023
4f42182

Fix broken wikipedia link


ManpreetXSingh Oct 15, 2023
3949c1b

Add missing type hints


ManpreetXSingh Oct 16, 2023
bf95078

Add numpy calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
9c9ad26

Add solution using np_calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
89cc321

Update benchmarks


ManpreetXSingh Oct 16, 2023
7e9e827

Merge branch 'TheAlgorithms:master' into performance-project-euler-070


ManpreetXSingh Dec 29, 2023
c2d35e5

Remove py_solution and slicing_solution


ManpreetXSingh Dec 29, 2023
6ff00c7

Remove slow_solution and benchmark


ManpreetXSingh Dec 29, 2023
480cf3e

Move prime generator to maths/prime_sieve_eratosthenes.py


ManpreetXSingh Dec 29, 2023

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32 changes: 31 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 +49,36 @@ 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)
 []
 """
 if max_number <= 2:
 return []

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


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))

23 changes: 12 additions & 11 deletions
project_euler/problem_070/sol1.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -26,30 +26,31 @@

References:
Finding totients
https://en.wikipedia.org/wiki/Euler's_totient_function#Euler's_product_formula
https://en.wikipedia.org/wiki/Euler%27s_totient_function#Euler%27s_product_formula
"""
from __future__ import annotations

import numpy as np

from maths.prime_sieve_eratosthenes import np_prime_sieve_eratosthenes

def get_totients(max_one: int) -> list[int]:

def np_get_totients(limit) -> list[int]:
 """
 Calculates a list of totients from 0 to max_one exclusive, using the
 definition of Euler's product formula.

 >>> get_totients(5)
 >>> np_get_totients(5)
 [0, 1, 1, 2, 2]

 >>> get_totients(10)
 >>> np_get_totients(10)
 [0, 1, 1, 2, 2, 4, 2, 6, 4, 6]
 """
 totients = np.arange(max_one)
 totients = np.arange(limit)
 primes = np_prime_sieve_eratosthenes(limit)

 for i in range(2, max_one):
 if totients[i] == i:
 x = np.arange(i, max_one, i) # array of indexes to select
 totients[x] -= totients[x] // i
 for i in primes:
 totients[i::i] -= totients[i::i] // i

 return totients.tolist()

Expand DownExpand Up@@ -81,10 +82,10 @@ def solution(max_n: int = 10000000) -> int:
 >>> solution(10000)
 4435
 """
 totients = np_get_totients(max_n + 1)

 min_numerator = 1 # i
 min_denominator = 0 # φ(i)
 totients = get_totients(max_n + 1)

 for i in range(2, max_n + 1):
 t = totients[i]
Expand All@@ -97,4 +98,4 @@ def solution(max_n: int = 10000000) -> int:


if __name__ == "__main__":
 print(f"{solution() = }")
 print(f"Solution : {solution()}")

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Remove or un-stick sticky/fixed headers that block content\n(function() {\n function unstick() {\n document.querySelectorAll('header, nav, [role=\"banner\"], .header, .navbar, .sticky, .fixed-top, [style*=\"position: fixed\"], [style*=\"position:sticky\"]').forEach(function(el) {\n if (el.style.position === 'fixed' || el.style.position === 'sticky' || \n getComputedStyle(el).position === 'fixed' || getComputedStyle(el).position === 'sticky') {\n el.style.position = 'static';\n el.style.top = 'auto';\n el.style.zIndex = 'auto';\n }\n });\n }\n \n unstick();\n \n var observer = new MutationObserver(unstick);\n observer.observe(document.body, { childList: true, subtree: true, attributes: true, attributeFilter: ['style', 'class'] });\n})();", "Kill Sticky Headers");
}
} catch(__e) { console.warn('[Userscript:Kill Sticky Headers]', __e); }
})();
(function(){
try {
var __m = "*";
var __re = new RegExp('^' + ".*" + '

Skip to content
Performance: 58% faster Project Euler 070#10558

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 Closed

ManpreetXSingh
wants to merge
14
commits into

from

 Closed


Performance: 58% faster Project Euler 070
#10558
Show file tree
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 Changes from all commits
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14 commits


Select commit
Hold shift + click to select a range
5958ffa

Separate common solution


ManpreetXSingh Oct 15, 2023
d6b16c6

Add slicing_get_totients


ManpreetXSingh Oct 15, 2023
fa8f7f9

Add fast get_totients and calculate_prime_numbers


ManpreetXSingh Oct 15, 2023
9bf2655

Add slow_solution and slicing_solution


ManpreetXSingh Oct 15, 2023
8113df9

Add performance benchmark


ManpreetXSingh Oct 15, 2023
4f42182

Fix broken wikipedia link


ManpreetXSingh Oct 15, 2023
3949c1b

Add missing type hints


ManpreetXSingh Oct 16, 2023
bf95078

Add numpy calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
9c9ad26

Add solution using np_calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
89cc321

Update benchmarks


ManpreetXSingh Oct 16, 2023
7e9e827

Merge branch 'TheAlgorithms:master' into performance-project-euler-070


ManpreetXSingh Dec 29, 2023
c2d35e5

Remove py_solution and slicing_solution


ManpreetXSingh Dec 29, 2023
6ff00c7

Remove slow_solution and benchmark


ManpreetXSingh Dec 29, 2023
480cf3e

Move prime generator to maths/prime_sieve_eratosthenes.py


ManpreetXSingh Dec 29, 2023

File filter

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32 changes: 31 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 +49,36 @@ 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)
 []
 """
 if max_number <= 2:
 return []

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


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))

23 changes: 12 additions & 11 deletions
project_euler/problem_070/sol1.py

View file


Open in desktop

Original file line numberDiff line numberDiff line change
Expand Up@@ -26,30 +26,31 @@

References:
Finding totients
https://en.wikipedia.org/wiki/Euler's_totient_function#Euler's_product_formula
https://en.wikipedia.org/wiki/Euler%27s_totient_function#Euler%27s_product_formula
"""
from __future__ import annotations

import numpy as np

from maths.prime_sieve_eratosthenes import np_prime_sieve_eratosthenes

def get_totients(max_one: int) -> list[int]:

def np_get_totients(limit) -> list[int]:
 """
 Calculates a list of totients from 0 to max_one exclusive, using the
 definition of Euler's product formula.

 >>> get_totients(5)
 >>> np_get_totients(5)
 [0, 1, 1, 2, 2]

 >>> get_totients(10)
 >>> np_get_totients(10)
 [0, 1, 1, 2, 2, 4, 2, 6, 4, 6]
 """
 totients = np.arange(max_one)
 totients = np.arange(limit)
 primes = np_prime_sieve_eratosthenes(limit)

 for i in range(2, max_one):
 if totients[i] == i:
 x = np.arange(i, max_one, i) # array of indexes to select
 totients[x] -= totients[x] // i
 for i in primes:
 totients[i::i] -= totients[i::i] // i

 return totients.tolist()

Expand DownExpand Up@@ -81,10 +82,10 @@ def solution(max_n: int = 10000000) -> int:
 >>> solution(10000)
 4435
 """
 totients = np_get_totients(max_n + 1)

 min_numerator = 1 # i
 min_denominator = 0 # φ(i)
 totients = get_totients(max_n + 1)

 for i in range(2, max_n + 1):
 t = totients[i]
Expand All@@ -97,4 +98,4 @@ def solution(max_n: int = 10000000) -> int:


if __name__ == "__main__":
 print(f"{solution() = }")
 print(f"Solution : {solution()}")

, 'i');
if (__m === '*' || __re.test(location.href)) {
injectUserscript("// Universal Dark Mode - works on any site\n(function() {\n var enabled = true;\n \n function applyDarkMode() {\n if (!enabled) return;\n \n // Create style element if it doesn't exist\n var style = document.getElementById('universal-dark-mode-style');\n if (!style) {\n style = document.createElement('style');\n style.id = 'universal-dark-mode-style';\n document.head.appendChild(style);\n }\n \n // Dark mode CSS - inverts colors but preserves images/video\n style.textContent = '\n /* Invert everything except media */\n html {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #1a1a2e !important;\n }\n \n /* Restore images, videos, iframes, canvas */\n img, video, iframe, canvas, svg, picture, [style*=\"background-image\"] {\n filter: invert(1) hue-rotate(180deg) !important;\n }\n \n /* Preserve specific elements that should not be inverted */\n .no-dark-mode, .no-dark-mode *,\n [data-theme=\"light\"], [data-theme=\"light\"],\n .ace_editor, .ace_editor *,\n .CodeMirror, .CodeMirror *,\n .monaco-editor, .monaco-editor *,\n .markdown-body pre, .markdown-body pre *,\n .highlight, .highlight *,\n pre code, pre code * {\n filter: none !important;\n }\n \n /* Fix common UI elements */\n .modal, .popup, .dropdown-menu, .tooltip, .popover {\n filter: invert(1) hue-rotate(180deg) !important;\n background: #2d2d44 !important;\n border-color: #444 !important;\n }\n \n /* Scrollbars */\n ::-webkit-scrollbar { background: #1a1a2e !important; }\n ::-webkit-scrollbar-thumb { background: #444 !important; }\n ::-webkit-scrollbar-thumb:hover { background: #555 !important; }\n \n /* Selection */\n ::selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ::-moz-selection { background: #4ecdc4 !important; color: #1a1a2e !important; }\n ';\n }\n \n function removeDarkMode() {\n var style = document.getElementById('universal-dark-mode-style');\n if (style) style.remove();\n }\n \n // Toggle with Alt+Shift+D\n document.addEventListener('keydown', function(e) {\n if (e.altKey && e.shiftKey && e.key === 'D') {\n e.preventDefault();\n enabled = !enabled;\n if (enabled) {\n applyDarkMode();\n console.log('[Universal Dark Mode] Enabled');\n } else {\n removeDarkMode();\n console.log('[Universal Dark Mode] Disabled');\n }\n }\n });\n \n // Apply on load\n applyDarkMode();\n \n // Re-apply on dynamic content\n var observer = new MutationObserver(function(mutations) {\n if (enabled && !document.getElementById('universal-dark-mode-style')) {\n applyDarkMode();\n }\n });\n observer.observe(document.head, { childList: true });\n \n console.log('[Universal Dark Mode] Loaded - Press Alt+Shift+D to toggle');\n})();", "Universal Dark Mode");
}
} catch(__e) { console.warn('[Userscript:Universal Dark Mode]', __e); }
})();
})();

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Performance: 58% faster Project Euler 070#10558

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Performance: 58% faster Project Euler 070
#10558
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5958ffa

Separate common solution


ManpreetXSingh Oct 15, 2023
d6b16c6

Add slicing_get_totients


ManpreetXSingh Oct 15, 2023
fa8f7f9

Add fast get_totients and calculate_prime_numbers


ManpreetXSingh Oct 15, 2023
9bf2655

Add slow_solution and slicing_solution


ManpreetXSingh Oct 15, 2023
8113df9

Add performance benchmark


ManpreetXSingh Oct 15, 2023
4f42182

Fix broken wikipedia link


ManpreetXSingh Oct 15, 2023
3949c1b

Add missing type hints


ManpreetXSingh Oct 16, 2023
bf95078

Add numpy calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
9c9ad26

Add solution using np_calculate_prime_numbers


ManpreetXSingh Oct 16, 2023
89cc321

Update benchmarks


ManpreetXSingh Oct 16, 2023
7e9e827

Merge branch 'TheAlgorithms:master' into performance-project-euler-070


ManpreetXSingh Dec 29, 2023
c2d35e5

Remove py_solution and slicing_solution


ManpreetXSingh Dec 29, 2023
6ff00c7

Remove slow_solution and benchmark


ManpreetXSingh Dec 29, 2023
480cf3e

Move prime generator to maths/prime_sieve_eratosthenes.py


ManpreetXSingh Dec 29, 2023

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32 changes: 31 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 +49,36 @@ 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)
 []
 """
 if max_number <= 2:
 return []

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


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))

23 changes: 12 additions & 11 deletions
project_euler/problem_070/sol1.py

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Original file line numberDiff line numberDiff line change
Expand Up@@ -26,30 +26,31 @@

References:
Finding totients
https://en.wikipedia.org/wiki/Euler's_totient_function#Euler's_product_formula
https://en.wikipedia.org/wiki/Euler%27s_totient_function#Euler%27s_product_formula
"""
from __future__ import annotations

import numpy as np

from maths.prime_sieve_eratosthenes import np_prime_sieve_eratosthenes

def get_totients(max_one: int) -> list[int]:

def np_get_totients(limit) -> list[int]:
 """
 Calculates a list of totients from 0 to max_one exclusive, using the
 definition of Euler's product formula.

 >>> get_totients(5)
 >>> np_get_totients(5)
 [0, 1, 1, 2, 2]

 >>> get_totients(10)
 >>> np_get_totients(10)
 [0, 1, 1, 2, 2, 4, 2, 6, 4, 6]
 """
 totients = np.arange(max_one)
 totients = np.arange(limit)
 primes = np_prime_sieve_eratosthenes(limit)

 for i in range(2, max_one):
 if totients[i] == i:
 x = np.arange(i, max_one, i) # array of indexes to select
 totients[x] -= totients[x] // i
 for i in primes:
 totients[i::i] -= totients[i::i] // i

 return totients.tolist()

Expand DownExpand Up@@ -81,10 +82,10 @@ def solution(max_n: int = 10000000) -> int:
 >>> solution(10000)
 4435
 """
 totients = np_get_totients(max_n + 1)

 min_numerator = 1 # i
 min_denominator = 0 # φ(i)
 totients = get_totients(max_n + 1)

 for i in range(2, max_n + 1):
 t = totients[i]
Expand All@@ -97,4 +98,4 @@ def solution(max_n: int = 10000000) -> int:


if __name__ == "__main__":
 print(f"{solution() = }")
 print(f"Solution : {solution()}")