! Copyright (c) 2007 Samuel Tardieu, Aaron Schaefer.
! See http://factorcode.org/license.txt for BSD license.
USING: calendar combinators kernel math math.ranges namespaces sequences
    math.order project-euler.common ;
IN: project-euler.019

! http://projecteuler.net/index.php?section=problems&id=19

! DESCRIPTION
! -----------

! 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)?


! SOLUTION
! --------

! Use Zeller congruence, which is implemented in the "calendar" module
! already, as "zeller-congruence ( year month day -- n )" where n is
! the day of the week (Sunday is 0).

: euler019 ( -- answer )
    1901 2000 [a,b] [
        12 [1,b] [ 1 zeller-congruence ] with map
    ] map concat [ 0 = ] count ;

! [ euler019 ] 100 ave-time
! 1 ms ave run time - 0.51 SD (100 trials)


! ALTERNATE SOLUTIONS
! -------------------

<PRIVATE

: start-date ( -- timestamp )
    1901 1 1 <date> ;

: end-date ( -- timestamp )
    2000 12 31 <date> ;

: first-days ( end-date start-date -- days )
    [ 2dup after=? ]
    [ dup 1 months time+ swap day-of-week ]
    produce 2nip ;

PRIVATE>

: euler019a ( -- answer )
    end-date start-date first-days [ 0 = ] count ;

! [ euler019a ] 100 ave-time
! 17 ms ave run time - 2.13 SD (100 trials)

SOLUTION: euler019