module _19

open common

//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.

type day =
    Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday

let dayNum d =
    match d with
    | Sunday -> 0
    | Monday -> 1
    | Tuesday -> 2
    | Wednesday -> 3
    | Thursday -> 4
    | Friday -> 5
    | Saturday -> 6

let numDay n =
    match n with
    | 0 -> Sunday
    | 1 -> Monday
    | 2 -> Tuesday
    | 3 -> Wednesday
    | 4 -> Thursday
    | 5 -> Friday
    | 6 -> Saturday
    | _ -> raise(System.ArgumentException("No!"))

type date =
    { Year : int;
      Month : int }

let isLeapYear y =
    y % 4 = 0 && (y % 100 <> 0 || y % 400 = 0)

let getDaysInMonth d =
    let thirtyMonths = [|9;4;6;11|];
    match d with
    | date when date.Month = 2 && isLeapYear date.Year -> 29
    | date when date.Month = 2 -> 28
    | date when Array.exists ((=) date.Month) thirtyMonths  -> 30
    | _ -> 31

let getNextFirstDay d daysInMonth =
    (daysInMonth + (dayNum d)) % 7 |> numDay

let firstSaturdays =
    //getNextFirstDay Thursday 30
    crossMapList [1900..1999] [1..12]
    |> Seq.map (fun (y, m) -> { Year = y; Month = m })
    |> Seq.scan (fun (day:day) ym -> getNextFirstDay day (getDaysInMonth ym)) Monday
    |> Seq.filter ((=) Sunday)
    |> Seq.length