gistfile1.py

# -*- coding: utf-8 -*-

from fractions import Fraction
import unittest


def fraction_from_repeating(period, base=10):
    """
    Return a fraction equivalent to the given repeating decimal.

    `period` is a list of integers which represents the repeating period.
    When period = [1, 2, 3], it is regarded as 0.123123123...

    `base` is a base of number, aka radix. It is usually 10 (decimal),
    and may be 2 (binary) or any natural number.
    """
    # eg. n = 0.xyzxyzxyz...
    # 1000n - n = xyz
    # n = xyz/999
    num = sum([d * (base ** i) for i, d in enumerate(reversed(period))])
    denom = (base ** len(period)) - 1
    return Fraction("%d/%d" % (num, denom))


class RepeatingTestCase(unittest.TestCase):
    def test_simple1(self):
        """0.33333... = 1/3"""
        self.assertEquals(fraction_from_repeating([3]),
                          Fraction("1/3"))

    def test_simple2(self):
        """0.123123123... = 41/333"""
        self.assertEquals(fraction_from_repeating([1, 2, 3]),
                          Fraction("41/333"))

    def test_complex(self):
        """2.2234234... = 1234/555"""
        self.assertEquals((22 + fraction_from_repeating([2, 3, 4])) / 10,
                          Fraction("1234/555"))

    def test_limit(self):
        """0.999... = 1"""
        self.assertEquals(fraction_from_repeating([9]),
                          Fraction("1"))

    def test_base(self):
        """0.101010...[2] = 2/3"""
        self.assertEquals(fraction_from_repeating([1, 0], 2),
                          Fraction("2/3"))


if __name__ == '__main__':
    unittest.main()