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(* Note that a date_A is older than date_B, refers that date_A comes before date_B *)
fun is_older(one_date : int * int * int, other_date: int * int * int) =
let
val one_year = #1 one_date;
val other_year = #1 other_date;
val one_month = #2 one_date;
val other_month = #2 other_date;
val one_day = #3 one_date;
val other_day = #3 other_date;
in
if one_year <> other_year
then
one_year < other_year
else
if one_month <> other_month
then
one_month < other_month
else
one_day < other_day
end
;

fun number_in_month(dates : (int * int * int) list, month : int) =
if null dates
then
0
else
let
val date = hd(dates)
val a_month = #2 date
in
if a_month = month
then
1 + number_in_month(tl(dates), month)
else
number_in_month(tl(dates), month)
end
;

fun number_in_months(dates : (int * int * int) list, months : (int) list) =
if null months
then
0
else
let
val month = hd(months)
in
number_in_month(dates, month) + number_in_months(dates, tl(months))
end
;

fun dates_in_month(dates : (int * int * int) list, month : int) =
if null dates
then
[]
else
let
val date = hd(dates)
val a_month = #2 date
in
if a_month = month
then
date :: dates_in_month(tl(dates), month)
else
dates_in_month(tl(dates), month)
end
;

fun dates_in_months(dates : (int * int * int) list, months : (int) list) =
if null months
then
[]
else
let
val month = hd(months)
in
dates_in_month(dates, month) @ dates_in_months(dates, tl(months))
end
;

fun get_nth(strings : string list, n : int) =
if n = 1
then
hd(strings)
else
get_nth(tl(strings), n - 1)
;
fun date_to_string(date : (int * int * int)) =
let
val months = ["January", "February", "March", "April", "May", "June", "July", "August", "September", "October", "November", "December"]
val year = Int.toString(#1 date)
val month = get_nth(months, #2 date)
val day = Int.toString(#3 date)
in
month ^ " " ^ day ^ ", " ^ year
end
;

fun number_before_reaching_sum(sum : int, numbers : (int) list) =
let
val num = hd(numbers)
in
if sum > num
then
number_before_reaching_sum(sum - num, tl(numbers)) + 1
else
0
end
;

fun what_month(sum : int) =
let
val days = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]
in
1 + number_before_reaching_sum(sum, days)
end
;

fun month_range(day1: int, day2: int) =
if day1 > day2
then
[]
else
what_month(day1) :: month_range(day1 + 1, day2)
;

fun oldest(dates : (int * int * int) list) =
if null dates
then
NONE
else
let
fun oldest_nonempty(dates : (int * int * int) list) =
if null (tl(dates)) (* Note that 'null tl date' or 'null tl(dates)' is wrong, it should be 'null (tl(dates))' or 'null (tl dates)' *)
then
hd(dates)
else
let
val hd_date = hd(dates);
val tl_date = oldest_nonempty(tl(dates))
in
if is_older(hd_date, tl_date)
then
hd_date
else
tl_date
end
in
SOME(oldest_nonempty(dates))
end
;

fun number_in_months_challenge(dates: (int * int * int) list, months: int list) =
let
(* To check if <code>{{EJS0}}</code> contains <code>{{EJS1}}</code>  *)
fun exists(arr : int list, a: int) =
if null arr
then
false
else
if hd(arr) = a
then
true
else
exists(tl(arr), a);
(* Remove duplicates, then use previous work. *)
fun remove_duplicates(months: int list) =
if null months
then
[]
else
if null (tl(months))
then
hd(months) :: []
else
let
val hd_months = hd(months)
val tl_months = tl(months)
in
if exists(tl_months, hd_months)
then
remove_duplicates(tl_months)
else
hd_months :: remove_duplicates(tl_months)
end
in
number_in_months(dates, remove_duplicates(months))
end
;

fun dates_in_months_challenge(dates: (int * int * int) list, months: int list) =
let
(* To check if <code>{{EJS2}}</code> contains <code>{{EJS3}}</code>  *)
fun exists(arr : int list, a: int) =
if null arr
then
false
else
if hd(arr) = a
then
true
else
exists(tl(arr), a);
(* Remove duplicates, then use previous work. *)
fun remove_duplicates(months: int list) =
if null months
then
[]
else
if null (tl(months))
then
hd(months) :: []
else
let
val hd_months = hd(months)
val tl_months = tl(months)
in
if exists(tl_months, hd_months)
then
remove_duplicates(tl_months)
else
hd_months :: remove_duplicates(tl_months)
end
in
dates_in_months(dates, remove_duplicates(months))
end
;

fun reasonable_date(date: (int * int * int)) =
let
val year = #1 date;
val month = #2 date;
val day = #3 date;
val month_days = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31];
val month_days_leap = [31, 29, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31];
fun is_leap(year : int) =
(year mod 400 = 0) orelse (year mod 4 = 0 andalso year mod 100 <> 0)
;
fun get_month_day(month_days: int list, month : int) =
if month = 1
then
hd(month_days)
else
get_month_day(tl(month_days), month - 1)
in
if year <= 0
then
false
else
if month < 1 orelse month > 12
then
false
else
let
val leap = is_leap(year);
in
if leap
then
day > 0 andalso day <= get_month_day(month_days_leap, month)
else
day > 0 andalso day <= get_month_day(month_days, month)
end
end
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