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)?
First we'll need to code up a function that tells us whether a year is a leap year based on the logic from the problem description:
function is_leap_year(year)
return (year % 4 == 0 && year % 100 != 0) || (year % 400 == 0)
end
Then we need a function to give us the number of days in a certain month (which will depend on the year!):
function days_in_month(month, year)
if month == 2 # February
return is_leap_year(year) ? 29 : 28
elseif month in [4, 6, 9, 11] # April, June, September, November
return 30
else
return 31
end
end
Let's label Sunday as 0, Monday as 1, etc. Now we can start from January 1st, 1901 with day_of_week = 1. We'll go through every month between start_year and end_year and keep incrementing day_of_week with the number of days in each month. Each time day_of_week == 0 that means the first of the month is a Sunday!
function count_sundays_on_first(start_year, end_year)
# 0 = Sunday, 1 = Monday, ..., 6 = Saturday
day_of_week = 1
sunday_count = 0
for year in 1900:end_year
for month in 1:12
if day_of_week == 0 && year >= start_year
sunday_count += 1
end
days = days_in_month(month, year)
day_of_week = (day_of_week + days) % 7
end
end
return sunday_count
end
Calling count_sundays_on_first(1901, 2000) compute the solution in 2.641 μs.
Going further, calling count_sundays_on_first(2000, 10000) computes 13761 Sundays falling on the first of the month between the years 2000 and 10000 in 211.658 μs.