Add style improvements to Project Euler problem 9 (TheAlgorithms#3046)

Author: archaengel

Diff for: project_euler/problem_09/sol1.py

@@ -1,5 +1,6 @@
 """
-Problem Statement:
+Problem 9: https://projecteuler.net/problem=9
+
 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.
@@ -9,7 +10,7 @@
 """
 
 
-def solution():
+def solution() -> int:
     """
      Returns the product of a,b,c which are Pythagorean Triplet that satisfies
      the following:
@@ -29,7 +30,7 @@ def solution():
                             return a * b * c
 
 
-def solution_fast():
+def solution_fast() -> int:
     """
      Returns the product of a,b,c which are Pythagorean Triplet that satisfies
      the following:

Diff for: project_euler/problem_09/sol2.py

@@ -1,5 +1,6 @@
 """
-Problem Statement:
+Problem 9: https://projecteuler.net/problem=9
+
 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.
@@ -9,27 +10,27 @@
 """
 
 
-def solution(n):
+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 = 1000
+     3. a + b + c = n
 
     >>> solution(1000)
     31875000
     """
     product = -1
-    d = 0
+    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"""
         b = (n * n - 2 * a * n) // (2 * n - 2 * a)
         c = n - a - b
         if c * c == (a * a + b * b):
-            d = a * b * c
-            if d >= product:
-                product = d
+            candidate = a * b * c
+            if candidate >= product:
+                product = candidate
     return product
 
 

Diff for: project_euler/problem_09/sol3.py

@@ -1,5 +1,5 @@
 """
-Problem Statement:
+Problem 9: https://projecteuler.net/problem=9
 
 A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
 
@@ -12,7 +12,7 @@
 """
 
 
-def solution():
+def solution() -> int:
     """
      Returns the product of a,b,c which are Pythagorean Triplet that satisfies
      the following: