added solution 3 for problem_25

project_euler/problem_25/sol3.py

@@ -0,0 +1,57 @@
+# -*- coding: utf-8 -*-
+"""
+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):
+    """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())))