Finds low median of 2 sorted arrays

median.py

import unittest


def median(a, b):
    """ finds the low median of 2 sorted arrays, a and b """

    def _median(a, b, index):
        if index == 0:
            if len(a) == 0:
                return b[0]
            elif len(b) == 0:
                return a[0]
            else:
                return min(a[0], b[0])
        elif len(a) == 0:
            return _median(a, b[1:], index - 1)
        elif len(b) == 0:
            return _median(a[1:], b, index - 1)
        elif a[0] < b[0]:
            return _median(a[1:], b, index - 1)
        else:
            return _median(a, b[1:], index - 1)

    n = len(a) + len(b)
    if n == 0:
        return None
    if n % 2 == 0:
        index = n // 2 - 1
    else:
        index = n // 2
    return _median(a, b, index)


class Test(unittest.TestCase):

    def test_median(self):
        assert median([1, 2, 3], [1, 2, 3]) == 2
        assert median([1, 2, 3, 4, 5], []) == 3
        assert median([], [1, 2, 3, 4, 5]) == 3
        assert median([1, 2, 3], [4, 5]) == 3
        assert median([0, 1], [2, 3, 4]) == 2
        assert median([1, 1, 1], [1, 1, 1]) == 1
        assert median([1, 3, 5], [4, 7]) == 4
        assert median([4, 5, 6], [1, 3, 5]) == 4
        assert median([1], [2]) == 1
        assert median([], [2]) == 2
        assert median([], []) is None


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