cheryls_birthday.py

#!/usr/bin/python

# Albert and Bernard have just become friends with Cheryl, and they want to know when her birthday is.

# Cheryl gives them a list of 10 possible dates:

# May 15, May 16, May 19
# June 17, June 18
# July 14, July 16
# August 14, August 15, August 17

# Cheryl then tells Albert and Bernard separately the month and day of her birthday respectively.

# Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know it too.
# Bernard: At first I don't know when Cheryl's birthday is, but now I know.
# Albert: Then I also know when Cheryl's birthday is.


from copy import deepcopy


DATES = {
 'May':    ['15', '16', '19'],
 'June':   ['17', '18'],
 'July':   ['14', '16'],
 'August': ['14', '15', '17']
}


def Month(date):
    return date.split(' ')[0]


def Day(date):
    return date.split(' ')[1]


def day_counts(possible_dates=DATES):
    day_counts = {}
    for month, days in possible_dates.items():
        for day in days:
            if day in day_counts:
                day_counts[day] += 1
            else:
                day_counts[day] = 1
    return day_counts


def remove_unique_days(possible_dates):
    possible_dates = deepcopy(possible_dates)
    counts = day_counts(possible_dates)
    for month, days in possible_dates.items():
        for day, count in counts.items():
            if count < 2 and days.count(day) > 0:
                days.remove(day)
    return possible_dates


def remove_single_days(possible_dates):
    possible_dates = deepcopy(possible_dates)
    for month, days in possible_dates.items():
        if len(days) == 1:
            possible_dates[month] = []
    return possible_dates


def initial_dates(possible_dates):
    print('List of possible dates initially given by Cheryl:\n%s\n' % possible_dates)


def alberts_first_statement(possible_dates):
    '''
    Albert: I don't know when Cheryl's birthday is, but I know that Bernard does not know it too.
    '''

    print('Albert must eliminate any date that is a unique day of the month:\n'
          '    If Bernard knows the day, and it is unique to a month, then he knows the month and day.\n'
          '    May 19th and June 18th are eliminated.')
    possible_dates = remove_unique_days(possible_dates)
    print('%s\n' % possible_dates)

    print('Albert must eliminate any months with only one day:\n'
          '    If Albert knows the month and there is only one day, then he knows the day and month.\n'
          '    June 17th is eliminated.')
    possible_dates = remove_single_days(possible_dates)
    print('%s\n' % possible_dates)

    return possible_dates


def bernards_first_statement(possible_dates):
    '''
    Bernard: At first I don't know when Cheryl's birthday is, but now I know.
    '''
    # XXX: How can this function be written?
    #
    #      At this point, the possible_dates looks like:
    #
    #      {'May': ['15', '16'], 'July': ['14', '16'], 'June': [], 'August': ['14', '15', '17']}
    #
    #      We were NOT required to eliminate May in either of the two previous steps required
    #      to satisfy alberts_first_statement above.
    #
    #      So how can we solve for the remaining requirements?

    print('Bernard cannot narrow down the dates any further with the information he has. :(')
    return possible_dates


def alberts_second_statement(possible_dates):
    '''
    Albert: Then I also know when Cheryl's birthday is.
    '''
    # XXX: How can this function be written?

    print('Albert cannot narrow down the dates any further with the information he has. :(')
    return possible_dates


initial_dates(DATES)

possible_dates = alberts_first_statement(DATES)

possible_dates = bernards_first_statement(possible_dates)

possible_dates = alberts_second_statement(possible_dates)

print('\nFinal possible dates of Cheryls birthday are:\n%s\n' % possible_dates)