import math

arrivalRate = 0.1 # a parameter modeling the rate 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 arrivalRate  # 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)
    
def priceAndRevenue(t,s):
    '''Return whatever fixed price is best paired with the expected revenue.

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

    price = 0
    bestRevenue = -1 # this surely will be beat
    bestPrice = None # the price at which the bestRevenue is achieved
    while True:
        table = make_table(t+1,s+1)
        for time in range(t+1):
            for seats in range(s+1):
                if time == 0:
                    table[time][seats] = 0
                elif seats == 0:
                    table[time][seats] = 0
                else:
                    # let sp be the probability we sell a ticket the first hour
                    sp = saleProb(time,price)
                    # scenario 1: we sell a ticket this hour
                    # two sources of revenue: (1) this hour, (2) all future hours
                    revenueThisHourIfSale = price
                    revenueFutureIfSale = table[time-1][seats-1]
                    revenueIfSale = revenueThisHourIfSale + revenueFutureIfSale
                    # scenario 2: we don't sell a ticket this hour
                    revenueThisHourNoSale = 0
                    revenueFutureNoSale = table[time-1][seats]
                    revenueNoSale = revenueThisHourNoSale + revenueFutureNoSale
                    # putting them together to get our expected revenue:
                    table[time][seats] = sp * revenueIfSale + (1-sp) * revenueNoSale
        revenue = table[t][s]
        if revenue < bestRevenue:
            break
        bestRevenue = revenue
        bestPrice = price
        price = price + 1
    return bestPrice, bestRevenue
        
def make_table(n,m):
    return [[None]*m for i in range(n)]