Fix style of the first ten solutions for Project Euler (#3242)

* Fix style of the first ten solutions for Project Euler

- Unify the header docstring, and add reference URLs to wikipedia
  or similar
- Fix docstrings to be properly multilined
- Add newlines where appropriate
- Add doctests where they were missing
- Remove doctests that test for the correct solution
- fix obvious spelling or grammar mistakes in comments and
  exception messages
- Fix line endings to be UNIX. This makes two of the files seem
  to have changed completely
- no functional changes in any of the solutions were done
  (except for the spelling fixes mentioned above)

* Fix docstrings and main function as per Style Guide

project_euler/problem_009/sol1.py

@@ -1,26 +1,35 @@
 """
-Problem 9: https://projecteuler.net/problem=9
+Project Euler Problem 9: https://projecteuler.net/problem=9
+
+Special Pythagorean triplet
 
 A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
+
     a^2 + b^2 = c^2
+
 For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
 
 There exists exactly one Pythagorean triplet for which a + b + c = 1000.
-Find the product abc.
+Find the product a*b*c.
+
+References:
+    - https://en.wikipedia.org/wiki/Pythagorean_triple
 """
 
 
 def solution() -> int:
     """
-     Returns the product of a,b,c which are Pythagorean Triplet that satisfies
-     the following:
-     1. a < b < c
-     2. a**2 + b**2 = c**2
-     3. a + b + c = 1000
+    Returns the product of a,b,c which are Pythagorean Triplet that satisfies
+    the following:
+      1. a < b < c
+      2. a**2 + b**2 = c**2
+      3. a + b + c = 1000
+
     # The code below has been commented due to slow execution affecting Travis.
     # >>> solution()
     # 31875000
     """
+
     for a in range(300):
         for b in range(400):
             for c in range(500):
@@ -32,16 +41,17 @@ def solution() -> int:
 
 def solution_fast() -> int:
     """
-     Returns the product of a,b,c which are Pythagorean Triplet that satisfies
-     the following:
-     1. a < b < c
-     2. a**2 + b**2 = c**2
-     3. a + b + c = 1000
+    Returns the product of a,b,c which are Pythagorean Triplet that satisfies
+    the following:
+      1. a < b < c
+      2. a**2 + b**2 = c**2
+      3. a + b + c = 1000
 
     # The code below has been commented due to slow execution affecting Travis.
     # >>> solution_fast()
     # 31875000
     """
+
     for a in range(300):
         for b in range(400):
             c = 1000 - a - b
@@ -66,4 +76,4 @@ def benchmark() -> None:
 
 
 if __name__ == "__main__":
-    benchmark()
+    print(f"{solution() = }")

project_euler/problem_009/sol2.py

@@ -1,30 +1,40 @@
 """
-Problem 9: https://projecteuler.net/problem=9
+Project Euler Problem 9: https://projecteuler.net/problem=9
+
+Special Pythagorean triplet
 
 A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
+
     a^2 + b^2 = c^2
+
 For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
 
 There exists exactly one Pythagorean triplet for which a + b + c = 1000.
-Find the product abc.
+Find the product a*b*c.
+
+References:
+    - https://en.wikipedia.org/wiki/Pythagorean_triple
 """
 
 
 def solution(n: int = 1000) -> int:
     """
-     Return the product of a,b,c which are Pythagorean Triplet that satisfies
-     the following:
-     1. a < b < c
-     2. a**2 + b**2 = c**2
-     3. a + b + c = n
+    Return the product of a,b,c which are Pythagorean Triplet that satisfies
+    the following:
+      1. a < b < c
+      2. a**2 + b**2 = c**2
+      3. a + b + c = n
 
-    >>> solution(1000)
-    31875000
+    >>> solution(36)
+    1620
+    >>> solution(126)
+    66780
     """
+
     product = -1
     candidate = 0
     for a in range(1, n // 3):
-        """Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c"""
+        # Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
         b = (n * n - 2 * a * n) // (2 * n - 2 * a)
         c = n - a - b
         if c * c == (a * a + b * b):
@@ -35,4 +45,4 @@ def solution(n: int = 1000) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_009/sol3.py

@@ -1,5 +1,7 @@
 """
-Problem 9: https://projecteuler.net/problem=9
+Project Euler Problem 9: https://projecteuler.net/problem=9
+
+Special Pythagorean triplet
 
 A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
 
@@ -8,22 +10,25 @@ A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
 For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
 
 There exists exactly one Pythagorean triplet for which a + b + c = 1000.
-Find the product abc.
+Find the product a*b*c.
+
+References:
+    - https://en.wikipedia.org/wiki/Pythagorean_triple
 """
 
 
 def solution() -> int:
     """
-     Returns the product of a,b,c which are Pythagorean Triplet that satisfies
-     the following:
-
-     1. a**2 + b**2 = c**2
-     2. a + b + c = 1000
+    Returns the product of a,b,c which are Pythagorean Triplet that satisfies
+    the following:
+      1. a**2 + b**2 = c**2
+      2. a + b + c = 1000
 
     # The code below has been commented due to slow execution affecting Travis.
     # >>> solution()
     # 31875000
     """
+
     return [
         a * b * (1000 - a - b)
         for a in range(1, 999)
@@ -33,4 +38,4 @@ def solution() -> int:
 
 
 if __name__ == "__main__":
-    print(solution())
+    print(f"{solution() = }")