datatype suit = Clubs | Diamonds | Hearts | Spades
datatype rank = Jack | Queen | King | Ace | Num of int
type card = suit * rank

datatype color = Red | Black
datatype move = Discard of card | Draw

exception IllegalMove

(* put your solutions for problem 2 here *)
fun card_color (c:suit * rank)=
    case c of
      ( Clubs,_)  => Black
     |( Diamonds,_) => Red
     |( Hearts,_) => Red
     |( Spades,_) => Black
fun card_value (c:card)=
    case c of
       (_,Ace)  =>11
      |(_,Jack) =>10
      |(_,Queen)=>10
      |(_,King) =>10
      |(_,Num x)  =>x
fun remove_card ( cs:card list, c:card, e:exn)=
(*val mytest = (remove_card([], (Clubs, Jack), IllegalMove); false) handle IllegalMove => true;*)
     case cs of
     []=> raise e (* IllegalMove*)
        |x::xs => if c=x then xs
              else if xs=[] then raise e
                       else x::remove_card(xs,c,e)
fun all_same_color ( cs:card list)=
    case cs of
       []=>true
     | x::xs=> case xs of
          []=>true
         |y::ys=> if card_color(x)= card_color(y) then all_same_color (xs)
                           else false
 (* card_color(x)= card_color (all_same_color(xs)) then true
               else false*)
fun sum_cards (cs:card list)=
    let fun aux( cs, acc)=
        case cs of
        []=>acc
          | x::xs=> aux( xs,card_value(x)+acc)
    in aux(cs,0)
    end
fun score (cs: card list, goal: int)= (*int*)
    let fun prescore (cs: card list, num: int)=
        if  all_same_color (cs) then num div 2
            else num
    in
        if goal< sum_cards(cs) then prescore(cs, 3*(sum_cards(cs)-goal))
        else prescore(cs, goal-sum_cards(cs))
    end
fun officiate (cs:card list, moves : move list, goal : int)=  (* -> int*)
    let fun helperf(cH::cT:card list, mH::mT :move list,held_cards:card list,goal:int)=
          if mH::mT=[] orelse sum_cards(held_cards) >goal  then score(held_cards, goal)
          else case mH of
               Discard c=> helperf(cH::cT,mT,remove_card(held_cards,c,IllegalMove),goal)
             | Draw =>if cH::cT=[] then score(held_cards,goal)
                   else helperf(cT,mT,cH::held_cards,goal)
    in helperf(cs,moves,[], goal)
    end
fun count_of_Aces (cs:card list)=
case cs of
    []=>0
   |x::xs=> case x of
        (_,Ace)=> 1+count_of_Aces(xs)
           |(_,_)=> count_of_Aces(xs)
fun score_challenge (cs: card list, goal: int)=
    case cs of
           []=>0
      | x::xs=> case count_of_Aces(cs) of
        0=>score(cs,goal)
          |_=> if sum_cards(cs)-goal>0 andalso (*  Int.min(  count_of_Aces(cs) ,( (sum_cards(cs)-goal) div 10 )  )+1>=0*)
          (* then if*)  all_same_color(cs)
            then (goal-sum_cards(cs)+ 10*(count_of_Aces(cs)-(goal div 11))) div 2
        (*  else (goal-sum_cards(cs)+ 10*(count_of_Aces(cs)-(goal div 11)))*)
(* sum_cards(cs)- 10*Int.min(count_of_Aces(cs) ,((sum_cards(cs)-goal) div 10)+1)*)
           else score(cs,goal)

fun officiate_challenge (cs:card list, moves : move list, goal : int)=  (* -> int*)
    let fun helperf(cH::cT:card list, mH::mT :move list,held_cards:card list,goal:int)=
          if mH::mT=[] orelse sum_cards(held_cards) >goal  then score_challenge(held_cards, goal)
          else case mH of
               Discard c=> helperf(cH::cT,mT,remove_card(held_cards,c,IllegalMove),goal)
             | Draw =>if cH::cT=[] then score_challenge(held_cards,goal)
                   else helperf(cT,mT,cH::held_cards,goal)
    in helperf(cs,moves,[], goal)
    end
fun rev (some_list:move list)=
    let fun aux(some_list:move list, acc:move list)=
        case some_list of
        []=>acc
           |x::xs=>aux(xs,x::acc)
    in aux(some_list,[])
    end

fun careful_player (cl: card list,  goal:int )= (*move list*)
      let fun helper2 (clH::clT:card list, goal:int, held_cardsH::held_cardsT:card list, move_list:move list)=
if score(held_cardsH::held_cardsT, goal)=0 orelse cl=[] then move_list
else
    if score(clH::held_cardsH::held_cardsT, goal)< score(held_cardsH::held_cardsT, goal) andalso goal- sum_cards(held_cardsH::held_cardsT)>10
    then helper2(clT, goal,clH::held_cardsH::held_cardsT,Draw ::move_list)
    else if  score(clH::held_cardsH::held_cardsT, goal)> score(held_cardsH::held_cardsT, goal) andalso goal-sum_cards(held_cardsH::held_cardsT)>0
         then helper2( cl,goal,held_cardsT,(Discard held_cardsH)::move_list)
         else move_list

     in
      rev(helper2(cl,goal,[],[]))
     end

(* fun helper1 (clH::clT:card list,goal:int,held_cards:card list,moves:move list)=
          if sum_cards(held_cards)-goal>=0 then []::held_cards
          else  if goal- sum_card(held_cards)>10
                then if score(clH::held_cards, goal)=0
             then []::held_cards
                     else helper( clT,goal,clH::held_cards)
                else remove_card (held_cardsH::held_cardsT,held_cardsH,IllegalMove)*)