def levenshtein(a, b, mem={}):
    """ calculates the Levenshtein distance between two strings, a and b.

        PARAMETERS:
        a: str
        b: str

        RETURNS:
        integer distance between two strings

        EXAMPLE:
        > levenshtein('hello world', 'howdy world')
        4
    """
    try:
        assert isinstance(a, str) and isinstance(b, str)
    except AssertionError as e:
        print(e)
        sys.exit(2)

    ij = (len(a), len(b))

    if min(ij) == 0:
        mem[ij] = max(ij)
    elif ij not in mem:
        cost = a[-1] != b[-1]
        mem[ij] = min(levenshtein(a[0:-1], b, mem) + 1,
                      levenshtein(a, b[0:-1], mem) + 1,
                      levenshtein(a[0:-1], b[0:-1], mem) + cost)

    return mem[ij]