Performance: 58% faster Project Euler 070

maths/prime_sieve_eratosthenes.py

@@ -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]:
     """
@@ -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))

project_euler/problem_070/sol1.py

@@ -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()
 
@@ -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]
@@ -97,4 +98,4 @@ def solution(max_n: int = 10000000) -> int:
 
 
 if __name__ == "__main__":
-    print(f"{solution() = }")
+    print(f"Solution    : {solution()}")