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_039/sol1.py

@@ -0,0 +1,55 @@
+"""
+Problem 39: https://projecteuler.net/problem=39
+
+If p is the perimeter of a right angle triangle with integral length sides,
+{a,b,c}, there are exactly three solutions for p = 120.
+{20,48,52}, {24,45,51}, {30,40,50}
+
+For which value of p ≤ 1000, is the number of solutions maximised?
+"""
+
+from __future__ import annotations
+
+import typing
+from collections import Counter
+
+
+def pythagorean_triple(max_perimeter: int) -> typing.Counter[int]:
+    """
+    Returns a dictionary with keys as the perimeter of a right angled triangle
+    and value as the number of corresponding triplets.
+    >>> pythagorean_triple(15)
+    Counter({12: 1})
+    >>> pythagorean_triple(40)
+    Counter({12: 1, 30: 1, 24: 1, 40: 1, 36: 1})
+    >>> pythagorean_triple(50)
+    Counter({12: 1, 30: 1, 24: 1, 40: 1, 36: 1, 48: 1})
+    """
+    triplets: typing.Counter[int] = Counter()
+    for base in range(1, max_perimeter + 1):
+        for perpendicular in range(base, max_perimeter + 1):
+            hypotenuse = (base * base + perpendicular * perpendicular) ** 0.5
+            if hypotenuse == int(hypotenuse):
+                perimeter = int(base + perpendicular + hypotenuse)
+                if perimeter > max_perimeter:
+                    continue
+                triplets[perimeter] += 1
+    return triplets
+
+
+def solution(n: int = 1000) -> int:
+    """
+    Returns perimeter with maximum solutions.
+    >>> solution(100)
+    90
+    >>> solution(200)
+    180
+    >>> solution(1000)
+    840
+    """
+    triplets = pythagorean_triple(n)
+    return triplets.most_common(1)[0][0]
+
+
+if __name__ == "__main__":
+    print(f"Perimeter {solution()} has maximum solutions")