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_025/sol1.py

@@ -0,0 +1,101 @@
+"""
+The Fibonacci sequence is defined by the recurrence relation:
+
+    Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.
+
+Hence the first 12 terms will be:
+
+    F1 = 1
+    F2 = 1
+    F3 = 2
+    F4 = 3
+    F5 = 5
+    F6 = 8
+    F7 = 13
+    F8 = 21
+    F9 = 34
+    F10 = 55
+    F11 = 89
+    F12 = 144
+
+The 12th term, F12, is the first term to contain three digits.
+
+What is the index of the first term in the Fibonacci sequence to contain 1000
+digits?
+"""
+
+
+def fibonacci(n: int) -> int:
+    """
+    Computes the Fibonacci number for input n by iterating through n numbers
+    and creating an array of ints using the Fibonacci formula.
+    Returns the nth element of the array.
+
+    >>> fibonacci(2)
+    1
+    >>> fibonacci(3)
+    2
+    >>> fibonacci(5)
+    5
+    >>> fibonacci(10)
+    55
+    >>> fibonacci(12)
+    144
+
+    """
+    if n == 1 or type(n) is not int:
+        return 0
+    elif n == 2:
+        return 1
+    else:
+        sequence = [0, 1]
+        for i in range(2, n + 1):
+            sequence.append(sequence[i - 1] + sequence[i - 2])
+
+        return sequence[n]
+
+
+def fibonacci_digits_index(n: int) -> int:
+    """
+    Computes incrementing Fibonacci numbers starting from 3 until the length
+    of the resulting Fibonacci result is the input value n. Returns the term
+    of the Fibonacci sequence where this occurs.
+
+    >>> fibonacci_digits_index(1000)
+    4782
+    >>> fibonacci_digits_index(100)
+    476
+    >>> fibonacci_digits_index(50)
+    237
+    >>> fibonacci_digits_index(3)
+    12
+    """
+    digits = 0
+    index = 2
+
+    while digits < n:
+        index += 1
+        digits = len(str(fibonacci(index)))
+
+    return index
+
+
+def solution(n: int = 1000) -> int:
+    """
+    Returns the index of the first term in the Fibonacci sequence to contain
+    n digits.
+
+    >>> solution(1000)
+    4782
+    >>> solution(100)
+    476
+    >>> solution(50)
+    237
+    >>> solution(3)
+    12
+    """
+    return fibonacci_digits_index(n)
+
+
+if __name__ == "__main__":
+    print(solution(int(str(input()).strip())))

project_euler/problem_025/sol2.py

@@ -0,0 +1,71 @@
+"""
+The Fibonacci sequence is defined by the recurrence relation:
+
+    Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.
+
+Hence the first 12 terms will be:
+
+    F1 = 1
+    F2 = 1
+    F3 = 2
+    F4 = 3
+    F5 = 5
+    F6 = 8
+    F7 = 13
+    F8 = 21
+    F9 = 34
+    F10 = 55
+    F11 = 89
+    F12 = 144
+
+The 12th term, F12, is the first term to contain three digits.
+
+What is the index of the first term in the Fibonacci sequence to contain 1000
+digits?
+"""
+
+
+def fibonacci_generator() -> int:
+    """
+    A generator that produces numbers in the Fibonacci sequence
+
+    >>> generator = fibonacci_generator()
+    >>> next(generator)
+    1
+    >>> next(generator)
+    2
+    >>> next(generator)
+    3
+    >>> next(generator)
+    5
+    >>> next(generator)
+    8
+    """
+    a, b = 0, 1
+    while True:
+        a, b = b, a + b
+        yield b
+
+
+def solution(n: int = 1000) -> int:
+    """Returns the index of the first term in the Fibonacci sequence to contain
+    n digits.
+
+    >>> solution(1000)
+    4782
+    >>> solution(100)
+    476
+    >>> solution(50)
+    237
+    >>> solution(3)
+    12
+    """
+    answer = 1
+    gen = fibonacci_generator()
+    while len(str(next(gen))) < n:
+        answer += 1
+    return answer + 1
+
+
+if __name__ == "__main__":
+    print(solution(int(str(input()).strip())))

project_euler/problem_025/sol3.py

@@ -0,0 +1,56 @@
+"""
+The Fibonacci sequence is defined by the recurrence relation:
+
+    Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.
+
+Hence the first 12 terms will be:
+
+    F1 = 1
+    F2 = 1
+    F3 = 2
+    F4 = 3
+    F5 = 5
+    F6 = 8
+    F7 = 13
+    F8 = 21
+    F9 = 34
+    F10 = 55
+    F11 = 89
+    F12 = 144
+
+The 12th term, F12, is the first term to contain three digits.
+
+What is the index of the first term in the Fibonacci sequence to contain 1000
+digits?
+"""
+
+
+def solution(n: int = 1000) -> int:
+    """Returns the index of the first term in the Fibonacci sequence to contain
+    n digits.
+
+    >>> solution(1000)
+    4782
+    >>> solution(100)
+    476
+    >>> solution(50)
+    237
+    >>> solution(3)
+    12
+    """
+    f1, f2 = 1, 1
+    index = 2
+    while True:
+        i = 0
+        f = f1 + f2
+        f1, f2 = f2, f
+        index += 1
+        for j in str(f):
+            i += 1
+        if i == n:
+            break
+    return index
+
+
+if __name__ == "__main__":
+    print(solution(int(str(input()).strip())))