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_002/sol4.py

@@ -0,0 +1,65 @@
+"""
+Problem:
+Each new term in the Fibonacci sequence is generated by adding the previous two
+terms. By starting with 1 and 2, the first 10 terms will be:
+
+    1,2,3,5,8,13,21,34,55,89,..
+
+By considering the terms in the Fibonacci sequence whose values do not exceed
+n, find the sum of the even-valued terms. e.g. for n=10, we have {2,8}, sum is
+10.
+"""
+import math
+from decimal import Decimal, getcontext
+
+
+def solution(n: int = 4000000) -> int:
+    """Returns the sum of all fibonacci sequence even elements that are lower
+    or equals to n.
+
+    >>> solution(10)
+    10
+    >>> solution(15)
+    10
+    >>> solution(2)
+    2
+    >>> solution(1)
+    0
+    >>> solution(34)
+    44
+    >>> solution(3.4)
+    2
+    >>> solution(0)
+    Traceback (most recent call last):
+        ...
+    ValueError: Parameter n must be greater or equal to one.
+    >>> solution(-17)
+    Traceback (most recent call last):
+        ...
+    ValueError: Parameter n must be greater or equal to one.
+    >>> solution([])
+    Traceback (most recent call last):
+        ...
+    TypeError: Parameter n must be int or passive of cast to int.
+    >>> solution("asd")
+    Traceback (most recent call last):
+        ...
+    TypeError: Parameter n must be int or passive of cast to int.
+    """
+    try:
+        n = int(n)
+    except (TypeError, ValueError):
+        raise TypeError("Parameter n must be int or passive of cast to int.")
+    if n <= 0:
+        raise ValueError("Parameter n must be greater or equal to one.")
+    getcontext().prec = 100
+    phi = (Decimal(5) ** Decimal(0.5) + 1) / Decimal(2)
+
+    index = (math.floor(math.log(n * (phi + 2), phi) - 1) // 3) * 3 + 2
+    num = Decimal(round(phi ** Decimal(index + 1))) / (phi + 2)
+    total = num // 2
+    return int(total)
+
+
+if __name__ == "__main__":
+    print(solution(int(input().strip())))