使用者:Bluedeck/etc/sandbox/box1515419128442

PCS Probabilistic Compile Suite （PCS直譯器） - v 3.0.1.3314

def best_value_vs_optimal_opponent(start=0, end=len(test_vector)-1):

    # memoization
    try:

        return memory[tag(start, end)]

    except KeyError:

        # base case: we have only 2 coins to choose from
        if end - start == 1:
            # return the coin with greater value
            memory[tag(start, end)] = test_vector[start] if test_vector[start] \
                > test_vector[end] else test_vector[end]
            return memory[tag(start, end)]

        # recursive case: figure out the best value if we picked left and right, then get largest value
        elif end - start > 1:
            # if we pick left, then we get the coin we picked.
            # then the rest of the coins are subject to being picked by our opponent.
            # since our algorithm is optimal, the opponent use it too.
            # so the opponent will use it to figure out what's the best he/she can get out of the rest of the coins.
            # after he/she figures that out, we obviously will get the rest of the coins. thus sum() - best_value().
            if_pick_left = test_vector[start] + sum(start+1, end) - best_value_vs_optimal_opponent(start+1, end)
            # vice versa.
            if_pick_right = test_vector[end] + sum(start, end-1) - best_value_vs_optimal_opponent(start, end-1)
            # since this is the value we get versus an optimal opponent, it is what we can guarantee to get.
            memory[tag(start, end)] = if_pick_left if if_pick_left > if_pick_right else if_pick_right
            return memory[tag(start, end)]

    return

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