Create sol5.py for project_eular/problem_025

project_euler/problem_025/sol5.py

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+"""
+Project Euler Problem 25: https://projecteuler.net/problem=25
+1000-digit Fibonacci Number
+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(first_digit_occurrence: 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
+    """
+
+    if first_digit_occurrence < 1:
+        raise ValueError("Parameter search_limit must be greater than or equal to one.")
+
+    last_number, new_number = 0, 1
+
+    last_two_numbers, sequenced_numbers = [last_number, new_number], [1]
+
+    while len(str(last_two_numbers[last_number])) <= first_digit_occurrence:
+        output = last_two_numbers[last_number] + last_two_numbers[new_number]
+
+        if len(str(output)) == first_digit_occurrence:
+            break
+
+        last_two_numbers[last_number], last_two_numbers[new_number] = (
+            last_two_numbers[new_number],
+            output,
+        )
+
+        sequenced_numbers.append(output)
+
+    return len(sequenced_numbers) + 1
+
+
+if __name__ == "__main__":
+    print(f"{solution() = }")