pair_encode.py

'''
encodes a pair of +ive ints to an int and complementary method
src: http://mathforum.org/library/drmath/view/56036.html
'''


def encode_pair(a: int, b: int) -> int:
    '''
    implements
        [(a + b)^2 + 3a + b]/2
    a - positive int
    b - positive int
    '''
    try:
        a, b = int(a), int(b)
    except TypeError:
        raise
    else:
        if a <= 0 or b <= 0:
            raise ValueError('invalid input. Numbers to encode should be positive integers')

        return int(((a + b)**2 + (3 * a) + b) / 2)


def decode_pair(N: int) -> (int, int):
    '''
    implements
      c = int[[sqrt(8N + 1) - 1]/2]
      a = N - c(c + 1)/2
      b = c(c + 3)/2 - N
    N - +ive int > 3
    return (a - +int, b: +int)
    '''
    try:
        N = int(N)
    except TypeError:
        raise
    else:
        if N < 4:
            raise ValueError('Number to decode should be less than 4')

        c = int(((8 * N + 1)**0.5 - 1) / 2)
        a = N - c * (c + 1) / 2
        b = c * (c + 3) / 2 - N
        return int(a), int(b)