def cache(func):
    cached = {}

    def inner_func(*args, **kwargs):
        if args not in cached:
           cached[args] = func(*args)
        return cached[args]
    return inner_func


##return the value, vcont, of the location n... does it need to be n,m? identify a value at a single square
##TODO n equals the total number of samples, h = the nummber of positive values from the total sample set
@cache
def values(total, n, h, reward, cost, continue_val=0):
    if out_of_range(total, n, h):
        raise Exception('Out of range, {} and {} must be less than or equal to {} and greater than equal to 0'.format(n,h,total))
    phit = h / (h + (n - h))
    u = max(phit, 1 - phit) * reward
    vstop = u - (n * cost)
    if is_base_case(total, n):
        ##TODO what is the formuala for the value of the outer edge, in relation to n and h
        #return (vstop, ((phit * continue_val) + ((1 - phit) *  continue_val) - n * cost))
        return (vstop, reward - (total * cost))
    ##TODO vstop vs vcont, what are we returning? return a tuple for the value of stoping and the
    # value of continuing at each point in the grid?
    # the value of stoping seems to have nothing to do with the value of continuing? should we group them together?
    # worth putting this in ab obj? or return a tuple for each location? maybe return an object for each location?
    # object {x, y, vstop, vcont}??
    print('n={}, h={}, phit={}, qhit={}, u={} phit_u={}, EV={}'.format(n,h,phit,1-phit,u,phit*u,phit*u-n*cost))
    return (vstop, ((phit * values(total,  n + 1, h + 1, reward, cost, continue_val)[1])
                    + ((1 - phit) *  values(total,  n + 1, h, reward, cost, continue_val)[1])
                    - cost))


def out_of_range(total, n, h):
    """
    Identifies if the params passed through are out of range
    :param total:
    :param n:
    :param h:
    :return:
    """
    return n > total or h > total or n <= 0 or h < 0 or n < h


def is_base_case(total, n):
    """
    Identifies if the locations are on the outer edge of the graph
    :param total:
    :param n:
    :return:
    """
    return n == total

def main():
    print(values(25, 20, 7, 5, .1))
    pass


if __name__ == '__main__':
    main()