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def iter_window(g, window_size):
    """
    interate over 'g' bit-by-bit and yield a window with the given 'window_size' width.

    >>> for v in iter_window([1,2,3,4], window_size=2): v
    [1, 2]
    [2, 3]
    [3, 4]
    >>> for v in iter_window([1,2,3,4,5], window_size=3): v
    [1, 2, 3]
    [2, 3, 4]
    [3, 4, 5]

    >>> for v in iter_window([1,2,3,4], window_size=2):
    ...    v
    ...    v.append(True)
    [1, 2]
    [2, 3]
    [3, 4]
    """
    values = collections.deque(maxlen=window_size)
    for value in g:
        values.append(value)
        if len(values) == window_size:
            yield list(values)


def iter_pare_sum(data):
    """
    >>> def g(data):
    ...     for i in data: yield i
    >>> list(iter_pare_sum(g([5,5,10,10,4,4,10,10,5,5])))
    [20, 8, 20, 10]

    >>> list(iter_pare_sum([5,10,10,4,4,10,10,5,5,10]))
    [20, 8, 20, 10]

    >>> list(iter_pare_sum([5,4,10,11,5,4,21,22,2,1]))
    [21, 9, 43, 3]

    >>> list(iter_pare_sum([
    ... 5,5,10,10,5,5,
    ... 5,                # <- resync 1
    ... 8,8,5,5,10,10,
    ... 10,               # <- resync 2
    ... 7,7,5,5,10,10,2,2,3,3
    ... ]))
    [20, 10, 10, 16, 10, 20, 14, 10, 20, 4, 6]

    resync      ^           ^
    """
    skip = True
    for previous, current, next_value in iter_window(data, window_size=3):
        if skip:
            skip = False
            continue
        skip = True
        diff1 = abs(previous - current)
        diff2 = abs(current - next_value)
        if diff1 < diff2:
            yield previous + current
        else:
            yield current + next_value


if __name__ == "__main__":
    import doctest
    print doctest.testmod()

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def iter_pare_sum(data):
    for previous, current, next_value in itertools.islice(iter_window(data, window_size=3), 1):
        diff1 = abs(previous - current)
        diff2 = abs(current - next_value)

        if diff1 < diff2:
            yield previous + current
        else:
            yield current + next_value

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...
    for previous, current, next_value in itertools.islice(iter_window(data, window_size=3), 1, None, 2):
...

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def compose(f, *gs):
    def composed(x):
        x = f(x)
        for g in gs:
            x = g(x)
        return x
    return composed

def pairwise(iterable):
    a, b = tee(iterable)
    next(b, None)
    return izip(a, b)

def paired(iterable):
    iterable = iter(iterable)
    return izip(iterable, iterable)

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paired_pairwise = compose(paired, pairwise)

def sum_nearest_neighbor(iterable):
    """
    >>> def g(data):
    ...     for i in data: yield i
    >>> list(sum_nearest_neighbor(g([5,5,10,10,4,4,10,10,5,5])))
    [20, 8, 20, 10]

    >>> list(sum_nearest_neighbor([5,10,10,4,4,10,10,5,5,10]))
    [20, 8, 20, 10]

    >>> list(sum_nearest_neighbor([5,4,10,11,5,4,21,22,2,1]))
    [21, 9, 43, 3]

    >>> list(sum_nearest_neighbor([
    ... 5,5,10,10,5,5,
    ... 5,                # <- resync 1
    ... 8,8,5,5,10,10,
    ... 10,               # <- resync 2
    ... 7,7,5,5,10,10,2,2,3,3
    ... ]))
    [20, 10, 10, 16, 10, 20, 14, 10, 20, 4, 6]

    resync      ^           ^
    """
    for (a, b), (c, d) in paired_pairwise(iterable):
        if abs(b - c) < abs(c - d):
            yield b + c
        else:
            yield c + d

if __name__ == "__main__":
    import doctest
    print doctest.testmod()

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def sum_nearest_neighbor(iterable):
    """..."""
    first_pair_selected = False
    for (a, b), (c, d) in paired_pairwise(iterable):
        first_pair_selected = abs(a - b) < abs(b - c)
        if first_pair_selected:
            yield a + b
        else:
            yield b + c
    if first_pair_selected:
        yield c + d

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[10, 20, 8, 20, 10]
[9, 21, 9, 43, 3]
[10, 20, 10, 16, 10, 20, 20, 14, 10, 20, 4, 6]