programming language part a 第二周作业

(*Homework1*)
(*2018-3-11*)
(*zhemuwoa*)

(*1*)
fun is_older(da1:int*int*int,da2:int*int*int) = 
    let
    val y1 = #1 da1
    val y2 = #1 da2
    val m1 = #2 da1
    val m2 = #2 da2
    val d1 = #3 da1
    val d2 = #3 da2
    in
    y1 < y2 orelse (y1 = y2 andalso  m1 < m2)
    orelse (y1 = y2 andalso m1 = m2 andalso d1 < d2)
    end

(*2*)
fun number_in_month(dl:(int*int*int) list,mo:int) =
    if null dl
    then 0
    else 
    if #2 (hd dl) = mo
    then 1 + number_in_month(tl dl,mo)
    else number_in_month(tl dl,mo)

(*3*)                    
fun number_in_months(dl:(int * int * int) list , ml : int list) =
    if null ml
    then 0
    else number_in_month(dl,hd ml)+number_in_months(dl,tl ml)

(*4*)
fun dates_in_month(dl:(int * int * int) list , mo : int) =
    if null dl
    then []
    else 
    if #2 (hd dl) = mo
    then hd dl :: dates_in_month(tl dl,mo)
    else dates_in_month(tl dl,mo)

(*5*)
fun dates_in_months(dl:(int * int * int) list,ml : int list) =
    if null ml
    then []
    else dates_in_month(dl,hd ml) @ dates_in_months(dl,tl ml) 

(*6*)
fun get_nth(sl:string list,n:int) =
    if n = 1
    then hd sl
    else
    get_nth(tl sl,n-1)

(*7*)
fun date_to_string(da:(int*int*int)) =
    let
    val mtos=["January","February","March","April","May","June",
           "July","August","September","October","November","December"]
    val year=(#1 da)
    val month=(#2 da)
    val day=(#3 da)
    in
    get_nth(mtos,month)^" "^Int.toString(day)^", "^Int.toString(year)
    end
                
(*9*)                
fun number_before_reaching_sum(sum:int,il:int list) =
    if sum <= 0
    then ~1
    else number_before_reaching_sum(sum-(hd il),tl il)+1

(*10*)
fun what_month(doy:int) = 
    let
    val md=[31,28,31,30,31,30,31,31,30,31,30,31]
    in
    number_before_reaching_sum(doy,md)+1
    end

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

(*11*)
fun oldest(dl:(int*int*int) list) =
    if null dl
    then NONE
    else
    let
        fun oldest_h(dl_x:(int*int*int) list) =
        if null (tl dl_x)
        then hd dl_x
        else
            let
            val ans=oldest_h(tl dl_x)
            in
            if is_older(hd dl_x,ans)
            then hd dl_x
            else ans
            end
    in
      SOME (oldest_h dl)
    end
    
(*12*)
fun rem_dup(xs:int list) = 
    if null xs
    then []
    else 
    let 
        fun is_in(e:int,xl:int list) =
        not (null xl) andalso (e = hd xl orelse is_in(e,tl xl))
        val tl_ans=rem_dup(tl xs)
    in
        if is_in(hd xs,tl_ans)
        then tl_ans
        else hd xs :: tl_ans
    end

fun number_in_months_challenge(da:(int*int*int) list,mo:int list) =
    number_in_months(da,rem_dup mo)

fun dates_in_months_challenge(da:(int*int*int) list,mo:int list) =
    dates_in_months(da,rem_dup mo)

(*13*)
fun reasonable_date(date : int*int*int) =
    let
    val year = #1 date
    val month = #2 date
    val day = #3 date
    val isleap = year mod 400 = 0 orelse 
             (year mod 4 = 0 andalso year mod 100 <> 0)
    val feb= if isleap then 29 else 28
    val mon_l=[31,feb,31,30,31,30,31,31,30,31,30,31]
    fun get_nth(ml:int list,n:int) =
        if n = 1
        then hd ml
        else get_nth(tl ml , n - 1)
    in
    year > 0 andalso month >= 1 andalso month <= 12
    andalso day >= 1 andalso day <= get_nth(mon_l,month)
    end

如何判断闰年在一般情况下只要判断

是否是400 的倍数或者是4的倍数不是100的倍数

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