PyPE solution to PE problem 31

    ProjectEuler.net problem 31
    ===========================

    In England the currency is made up of pound, L, and pence, p, and there
    are eight coins in general circulation:

        1p, 2p, 5p, 10p, 20p, 50p, L1 (100p) and L2 (200p).

    It is possible to make L2 in the following way:

        1*L1 + 1*50p + 2*20p + 1*5p + 1*2p + 3*1p

    How many different ways can L2 be made using any number of coins?

    Solution
    --------

    There are two solutions presented here: the first is a hard-coded solution
    for the specific problem given, which is much faster (~5ms); the second is
    a general solution that solves any problem where we are given a list of
    values and we wish to know how many combinations of those values will add
    up to some desired value.

    The first solution simply iterates over all possible combinations, with a
    few optimizations. First, we don't iterate over the number of 1p pieces we
    use, as there will only ever be exactly one valid candidate given the
    number of other coins. Second, we only iterate each given coin in the
    possible range at each step.

    The second solution is a recursive algorithm that removes the largest value
    from the list of values, and iterates over all possible multiples of that
    value, adding the number of combinations of the remaining problem. The stop
    conditions of the recursion are when the desired value is 0 or the list of
    available values is empty.

    The recursive algorithm is significantly slower (~50x).

    Answer
    ------

    73682