(*
http://projecteuler.net/index.php?section=problems&id=19
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)?
*)
type weekday = Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday
type date = { month : int; year : int; weekday : weekday }
let epoch = { month = 1; year = 1900; weekday = Monday }
let is_leap_year year =
if year mod 4 = 0 then
if year mod 100 = 0 then
if year mod 400 = 0 then true
else false
else true
else false
let days_in_month date =
match date.month with
4 | 6 | 9 | 11 -> 30
| 2 -> if is_leap_year date.year then 29 else 28
| _ -> 31
let days_in_year year =
if is_leap_year year then 366 else 365
let compare_date (d1 : date) (d2 : date) =
let year = compare d1.year d2.year in
if year = 0 then compare d1.month d2.month
else year
let incr_weekday day =
match day with
Sunday -> Monday
| Monday -> Tuesday
| Tuesday -> Wednesday
| Wednesday -> Thursday
| Thursday -> Friday
| Friday -> Saturday
| Saturday -> Sunday
let add_weekday day n =
let new_day = ref day in
for i = 1 to (n mod 7) do
new_day := incr_weekday !new_day
done;
!new_day
let incr_date date =
let days = days_in_month !date in
date := { month = succ (!date.month mod 12);
year = !date.year + (!date.month / 12);
weekday = add_weekday !date.weekday days }
let add_date date months =
let new_date = ref date in
for i = 1 to months do
incr_date new_date
done;
!new_date
let _ =
let cur_date = ref (add_date epoch 12)
and count = ref 0 in
while compare_date !cur_date { month = 12; year = 2000; weekday = Sunday } <= 0 do
if !cur_date.weekday = Sunday then incr count;
incr_date cur_date
done;
print_int !count; print_newline ()
