import math

intensity = 0.1 # a parameter modeling the intensity of consumer traffic
scale = 200.0   # a parameter in the consumer price model
shape = 3       # a parameter in the consumer price model

def arrivalProb(time):
    '''Return the probability a potential customer will arrive within an hour.

    argument: time -- the number of hours remaining before sales must end

    assumption: the probability is small, so we can neglect the case that
    two or more potential customers arrive within the same hour'''

    return intensity  # simple version: customer arrival independent of time

def purchaseProb(time,price):
    '''Return the probability an arriving potential customer will buy.

    arguments:
      time -- the number of hours remaining before sales must end
      price -- the price being offered to the potential customer'''

    return math.exp(-((price/scale)**shape)) # simple version: independent of time

def saleProb(time,price):
    '''Return the probability that a sale will occur within an hour.

    arguments:
      time -- the number of hours remaining before sales must end
      price -- the price being offered to any potential customer'''

    # for a sale to occur, a potential customer must arrive and buy
    return arrivalProb(time) * purchaseProb(time,price)
    
import two_d

def revenue(t,s):
    '''Return the expected revenue, choosing an optimal price in each situation.

    arguments:
      t -- the number of hours remaining before sales must end
      s -- the number of seats remaining to sell'''

    table = two_d.make_table(t+1,s+1)

    for time in range(t+1):
        for seats in range(s+1):

            if seats == 0:
                table[time][seats] = 0
            elif time == 0:
                table[time][seats] = 0
            else:
                price = consult_an_oracle()
                sp = saleProb(time,price)  # the probability we sell a ticket this hour
                # if we sell a ticket this hour, we earn "price" worth of revenue this hour,
                # and then we expect to earn some more revenue in future hours, namely
                afterSale = table[time-1][seats-1]
                revenueWithSale = price + afterSale
                # if we don't sell a ticket this hour, he earn no money this hour,
                # and then we expect to earn some more revenue in future hours, namely
                afterNoSale = table[time-1][seats]
                revenueWithNoSale = 0 + afterNoSale
                table[time][seats] = sp*revenueWithSale + (1-sp)*revenueWithNoSale

    return table[t][s]