#!/usr/bin/python3

def accumulate(iterable):
    '''Return running totals
    accumulate([1, 2, 3, 4, 5]) --> 1 3 6 10 15
    accumulate() is the inverse function of decumulate()
    accumulate(decumulate(x)) == decumulate(accumulate(x)) == x'''
    items = iter(iterable)
    total = next(items)
    yield total
    for item in items:
        total += item
        yield total

def decumulate(iterable):
    '''Return running differences
    decumulate([1, 3, 6, 10, 15]) --> 1 2 3 4 5
    decumulate() is the inverse function of accumulate()
    decumulate(accumulate(x)) == accumulate(decumulate(x)) == x'''
    items = iter(iterable)
    previous = next(items)
    yield previous
    for item in items:
        yield item - previous
        previous = item

if __name__ == '__main__':
    print(list(accumulate(range(10, 20))))
    print(list(decumulate(range(10, 20))))
    print(list(accumulate(decumulate(range(10, 20)))))
    print(list(decumulate(accumulate(range(10, 20)))))

##    [10, 21, 33, 46, 60, 75, 91, 108, 126, 145]
##    [10, 1, 1, 1, 1, 1, 1, 1, 1, 1]
##    [10, 11, 12, 13, 14, 15, 16, 17, 18, 19]
##    [10, 11, 12, 13, 14, 15, 16, 17, 18, 19]