reorganize dir

Signed-off-by: Mia Steinkirch <mia.steinkirch@gmail.com>

other_resources/Project-Euler/065-100th-e-numerator.py

@@ -0,0 +1,43 @@
+#!/usr/bin/python
+
+__author__ = "Mari Wahl"
+__email__ = "marina.w4hl@gmail.com"
+
+'''
+e = [2; 1,2,1, 1,4,1, 1,6,1 , ... , 1,2k,1, ...].
+
+The first ten terms in the sequence of convergents for e are:
+
+2, 3, 8/3, 11/4, 19/7, 87/32, 106/39, 193/71, 1264/465, 1457/536, ...
+The sum of digits in the numerator of the 10th convergent is 1+4+5+7=17.
+
+Find the sum of digits in the numerator of the 100th convergent of the continued fraction for e.
+'''
+
+from itertools import islice
+
+def take(iterable, n):
+    #Make an iterator that returns selected elements from the iterable.
+    return list(islice(iterable, n))
+
+def e():
+    yield 2
+    k = 1
+    while True:
+        yield 1
+        yield 2*k
+        yield 1
+        k += 1
+
+def rationalize(frac):
+    if len(frac) == 0:
+        return (1, 0)
+    elif len(frac) == 1:
+        return (frac[0], 1)
+    else:
+        remainder = frac[1:len(frac)]
+        (num, denom) = rationalize(remainder)
+        return (frac[0] * num + denom, num)
+
+numerator = rationalize(take(e(), 100))[0]
+print sum(int(d) for d in str(numerator))