euler/e019.py

"""How many Sundays fell on the first of the month during the twentieth century?

You are given the following information, but you may prefer to do some research for yourself.

    * 1 Jan 1900 was a Monday.
    * Thirty days has September,
      April, June and November.
      All the rest have thirty-one,
      Saving February alone,
      Which has twenty-eight, rain or shine.
      And on leap years, twenty-nine.
    * A leap year occurs on any year evenly divisible by 4, but not on a century unless it is divisible by 400.

How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)?
"""

class Day:
    SUNDAY, MONDAY, TUESDAY, WEDNESDAY, THURSDAY, FRIDAY, SATURDAY = range(7)

def is_leap_year(year):
    return (year % 100 > 0 and year % 4 == 0) or (year % 400 == 0)

def main():
    year = 1900
    # 1/1/1900 was a Monday
    first_day = Day.MONDAY

    total = 0
    while year < 2000:
        year = year + 1
        # Count last year's days to advance the starting weekday
        days = 366 if is_leap_year(year - 1) else 365
        # List the number of days in each month for this year
        months = [
            31,
            29 if is_leap_year(year) else 28,
            31, 30, 31, 30, 31, 31, 30, 31, 30, 31
        ]
        first_day = (first_day + days % 7) % 7
        sundays = 0
        for m in range(len(months)):
            days = sum(months[:m])
            first_sunday = (7 - ((first_day + days % 7) % 7)) % 7 + 1
            if first_sunday == 1:
                total = total + 1

    print 'Total months beginning on Sunday from 1/1/1901 to 12/31/2000: {0}'.format(total)

if __name__ == '__main__':
    main()