Rename Project Euler directories and other dependent changes (#3300)

* Rename all Project Euler directories:

Reason:
The change was done to maintain consistency throughout the directory
and to keep all directories in sorted order.

Due to the above change, some config files had to be modified:
'problem_22` -> `problem_022`

* Update scripts to pad zeroes in PE directories

project_euler/problem_006/sol1.py

@@ -0,0 +1,45 @@
+"""
+Problem 6: https://projecteuler.net/problem=6
+
+The sum of the squares of the first ten natural numbers is,
+            1^2 + 2^2 + ... + 10^2 = 385
+
+The square of the sum of the first ten natural numbers is,
+            (1 + 2 + ... + 10)^2 = 552 = 3025
+
+Hence the difference between the sum of the squares of the first ten natural
+numbers and the square of the sum is 3025 − 385 = 2640.
+
+Find the difference between the sum of the squares of the first N natural
+numbers and the square of the sum.
+"""
+
+
+def solution(n: int = 100) -> int:
+    """Returns the difference between the sum of the squares of the first n
+    natural numbers and the square of the sum.
+
+    >>> solution(10)
+    2640
+    >>> solution(15)
+    13160
+    >>> solution(20)
+    41230
+    >>> solution(50)
+    1582700
+    >>> solution()
+    25164150
+    """
+    sum_of_squares = 0
+    sum_of_ints = 0
+    for i in range(1, n + 1):
+        sum_of_squares += i ** 2
+        sum_of_ints += i
+    return sum_of_ints ** 2 - sum_of_squares
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    print(solution(int(input().strip())))

project_euler/problem_006/sol2.py

@@ -0,0 +1,42 @@
+"""
+Problem 6: https://projecteuler.net/problem=6
+
+The sum of the squares of the first ten natural numbers is,
+            1^2 + 2^2 + ... + 10^2 = 385
+
+The square of the sum of the first ten natural numbers is,
+            (1 + 2 + ... + 10)^2 = 552 = 3025
+
+Hence the difference between the sum of the squares of the first ten natural
+numbers and the square of the sum is 3025 − 385 = 2640.
+
+Find the difference between the sum of the squares of the first N natural
+numbers and the square of the sum.
+"""
+
+
+def solution(n: int = 100) -> int:
+    """Returns the difference between the sum of the squares of the first n
+    natural numbers and the square of the sum.
+
+    >>> solution(10)
+    2640
+    >>> solution(15)
+    13160
+    >>> solution(20)
+    41230
+    >>> solution(50)
+    1582700
+    >>> solution()
+    25164150
+    """
+    sum_cubes = (n * (n + 1) // 2) ** 2
+    sum_squares = n * (n + 1) * (2 * n + 1) // 6
+    return sum_cubes - sum_squares
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    print(solution(int(input().strip())))

project_euler/problem_006/sol3.py

@@ -0,0 +1,43 @@
+"""
+Problem 6: https://projecteuler.net/problem=6
+
+The sum of the squares of the first ten natural numbers is,
+            1^2 + 2^2 + ... + 10^2 = 385
+
+The square of the sum of the first ten natural numbers is,
+            (1 + 2 + ... + 10)^2 = 552 = 3025
+
+Hence the difference between the sum of the squares of the first ten natural
+numbers and the square of the sum is 3025 − 385 = 2640.
+
+Find the difference between the sum of the squares of the first N natural
+numbers and the square of the sum.
+"""
+import math
+
+
+def solution(n: int = 100) -> int:
+    """Returns the difference between the sum of the squares of the first n
+    natural numbers and the square of the sum.
+
+    >>> solution(10)
+    2640
+    >>> solution(15)
+    13160
+    >>> solution(20)
+    41230
+    >>> solution(50)
+    1582700
+    >>> solution()
+    25164150
+    """
+    sum_of_squares = sum([i * i for i in range(1, n + 1)])
+    square_of_sum = int(math.pow(sum(range(1, n + 1)), 2))
+    return square_of_sum - sum_of_squares
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    print(solution(int(input().strip())))

project_euler/problem_006/sol4.py

@@ -0,0 +1,42 @@
+"""
+Problem 6: https://projecteuler.net/problem=6
+
+The sum of the squares of the first ten natural numbers is,
+            1^2 + 2^2 + ... + 10^2 = 385
+
+The square of the sum of the first ten natural numbers is,
+            (1 + 2 + ... + 10)^2 = 552 = 3025
+
+Hence the difference between the sum of the squares of the first ten natural
+numbers and the square of the sum is 3025 − 385 = 2640.
+
+Find the difference between the sum of the squares of the first N natural
+numbers and the square of the sum.
+"""
+
+
+def solution(n: int = 100) -> int:
+    """Returns the difference between the sum of the squares of the first n
+    natural numbers and the square of the sum.
+
+    >>> solution(10)
+    2640
+    >>> solution(15)
+    13160
+    >>> solution(20)
+    41230
+    >>> solution(50)
+    1582700
+    >>> solution()
+    25164150
+    """
+    sum_of_squares = n * (n + 1) * (2 * n + 1) / 6
+    square_of_sum = (n * (n + 1) / 2) ** 2
+    return int(square_of_sum - sum_of_squares)
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    print(solution(int(input("Enter a number: ").strip())))