p019.py

# Steve Beal
# Project Euler problem 19 solution
# 2/15/14

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

# 1 Jan 1900 was a Monday.
# Thirty days have 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)?

reg_month_days = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
leap_month_days = [31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]


def is_leap_year(year):

    if year % 400 == 0:
        return True
    elif year % 4 == 0 and year % 100 != 0:
        return True
    else:
        return False

def num_twentieth_century_first_sundays():

    # first sunday date (month indexed from 0, day indexed from 1)
    day = 6
    month = 0
    year = 1901

    first_sundays = 0

    # gets the first sunday in 1901
    while year < 2001:
        # check if we're in feb of a leap year
        if month == 1 and is_leap_year(year):
            month_days = leap_month_days
        else:
            month_days = reg_month_days

        # get the next sunday
        day += 7

        # advance the month
        if day > month_days[month]:
            day %= month_days[month]
            month += 1

        # advance the year
        if month > 11:
            month %= 12
            year += 1

        # count the sundays that are the first of the month 
        if day == 1:
            first_sundays += 1

    return first_sundays

print(num_twentieth_century_first_sundays())