Project Euler Problem 10: style improvements

project_euler/problem_10/sol1.py

@@ -1,4 +1,6 @@
 """
+https://projecteuler.net/problem=10
+
 Problem Statement:
 The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
 
@@ -7,28 +9,25 @@
 from math import sqrt
 
 
-def is_prime(n):
+def is_prime(n: int) -> bool:
+    """Returns boolean representing primality of given number num.
+    >>> is_prime(2)
+    True
+    >>> is_prime(3)
+    True
+    >>> is_prime(27)
+    False
+    >>> is_prime(2999)
+    True
+    """
     for i in range(2, int(sqrt(n)) + 1):
         if n % i == 0:
             return False
 
     return True
 
 
-def sum_of_primes(n):
-    if n > 2:
-        sumOfPrimes = 2
-    else:
-        return 0
-
-    for i in range(3, n, 2):
-        if is_prime(i):
-            sumOfPrimes += i
-
-    return sumOfPrimes
-
-
-def solution(n):
+def solution(n: int = 2000000) -> int:
     """Returns the sum of all the primes below n.
 
     # The code below has been commented due to slow execution affecting Travis.
@@ -43,7 +42,16 @@ def solution(n):
     >>> solution(7)
     10
     """
-    return sum_of_primes(n)
+    if n > 2:
+        sum_of_primes = 2
+    else:
+        return 0
+
+    for i in range(3, n, 2):
+        if is_prime(i):
+            sum_of_primes += i
+
+    return sum_of_primes
 
 
 if __name__ == "__main__":

project_euler/problem_10/sol2.py

@@ -1,28 +1,41 @@
 """
+https://projecteuler.net/problem=10
+
 Problem Statement:
 The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
 
 Find the sum of all the primes below two million.
 """
 import math
 from itertools import takewhile
-
-
-def primeCheck(number):
+from typing import Iterator
+
+
+def is_prime(number: int) -> bool:
+    """Returns boolean representing primality of given number num.
+    >>> is_prime(2)
+    True
+    >>> is_prime(3)
+    True
+    >>> is_prime(27)
+    False
+    >>> is_prime(2999)
+    True
+    """
     if number % 2 == 0 and number > 2:
         return False
     return all(number % i for i in range(3, int(math.sqrt(number)) + 1, 2))
 
 
-def prime_generator():
+def prime_generator() -> Iterator[int]:
     num = 2
     while True:
-        if primeCheck(num):
+        if is_prime(num):
             yield num
         num += 1
 
 
-def solution(n):
+def solution(n: int = 2000000) -> int:
     """Returns the sum of all the primes below n.
 
     # The code below has been commented due to slow execution affecting Travis.

project_euler/problem_10/sol3.py

@@ -4,55 +4,54 @@
 Problem Statement:
 The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
 
-Find the sum of all the primes below two million using Sieve_of_Eratosthenes:
-
-The sieve of Eratosthenes is one of the most efficient ways to find all primes
-smaller than n when n is smaller than 10 million.  Only for positive numbers.
+Find the sum of all the primes below two million.
 """
 
 
-def prime_sum(n: int) -> int:
-    """Returns the sum of all the primes below n.
+def solution(n: int = 2000000) -> int:
+    """Returns the sum of all the primes below n using Sieve of Eratosthenes:
+
+    https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
+    The sieve of Eratosthenes is one of the most efficient ways to find all primes
+    smaller than n when n is smaller than 10 million.  Only for positive numbers.
 
-    >>> prime_sum(2_000_000)
+    >>> solution(2_000_000)
     142913828922
-    >>> prime_sum(1_000)
+    >>> solution(1_000)
     76127
-    >>> prime_sum(5_000)
+    >>> solution(5_000)
     1548136
-    >>> prime_sum(10_000)
+    >>> solution(10_000)
     5736396
-    >>> prime_sum(7)
+    >>> solution(7)
     10
-    >>> prime_sum(7.1)  # doctest: +ELLIPSIS
+    >>> solution(7.1)  # doctest: +ELLIPSIS
     Traceback (most recent call last):
     ...
     TypeError: 'float' object cannot be interpreted as an integer
-    >>> prime_sum(-7)  # doctest: +ELLIPSIS
+    >>> solution(-7)  # doctest: +ELLIPSIS
     Traceback (most recent call last):
     ...
     IndexError: list assignment index out of range
-    >>> prime_sum("seven")  # doctest: +ELLIPSIS
+    >>> solution("seven")  # doctest: +ELLIPSIS
     Traceback (most recent call last):
     ...
     TypeError: can only concatenate str (not "int") to str
     """
-    list_ = [0 for i in range(n + 1)]
-    list_[0] = 1
-    list_[1] = 1
+    primality_list = [0 for i in range(n + 1)]
+    primality_list[0] = 1
+    primality_list[1] = 1
 
     for i in range(2, int(n ** 0.5) + 1):
-        if list_[i] == 0:
+        if primality_list[i] == 0:
             for j in range(i * i, n + 1, i):
-                list_[j] = 1
-    s = 0
+                primality_list[j] = 1
+    sum_of_primes = 0
     for i in range(n):
-        if list_[i] == 0:
-            s += i
-    return s
+        if primality_list[i] == 0:
+            sum_of_primes += i
+    return sum_of_primes
 
 
 if __name__ == "__main__":
-    # import doctest
-    # doctest.testmod()
-    print(prime_sum(int(input().strip())))
+    print(solution(int(input().strip())))