// https://puzzling.stackexchange.com/questions/89598/generating-roman-numerals-with-dice
// Score checker
// Dmitry Kamenetsky, 28th September 2019

import java.util.*;

public class RomanNumerals
{
    static int NumDigs=2000;        //number of digits we will consider
    static int N=3;     //number of dice

    static String[] Romans;     //Romans[i] is i-th number in Roman numerals
    static Map<String,Integer> Romans2Dec;
    static boolean[] Seen;

    public static void main(String[] args)
    {
        generateRomans();

        score("I  II III IV  IX C","V  X  XV  XCV CX C","XX L  LV  LXX C  CXX");            //160 from Bass
        //score("I,II,III,IV,VI,VII","X,XX,XXX,XL,LX,LXX","V,L,IX,LV,XV,XIX");                      //89 from trolley813
        //score("I,II,III,IV,IX,CLXC","V,X,XX,XXX,XL,XXV","V,L,XC,C,CL,CLX");                           //64 from PuzzleGuest
    }

    public static void generateRomans()
    {
        char[] digits={'I','V','X','L','C','D','M'};
        int[][] id={{},{0},{0,0},{0,0,0},{0,1},{1},{1,0},{1,0,0},{1,0,0,0},{0,2}};

        Romans=new String[NumDigs+1];
        Romans2Dec=new HashMap<String,Integer>();

        for (int i=1; i<=NumDigs; i++)
        {
            String a=""+i;
            String roman="";

            for (int k=0; k<a.length(); k++)
            {
                int digit=(int)(a.charAt(k)-'0');

                for (int q=0; q<id[digit].length; q++)
                    roman+=digits[id[digit][q]+2*(a.length()-1-k)];
            }

            //System.out.println(i+" "+roman);
            Romans[i]=roman;
            Romans2Dec.put(roman,i);
        }
    }

    public static void score(String dice1, String dice2, String dice3)
    {
        Seen=new boolean[NumDigs+1];

        String[][] allDice=new String[N][];
        allDice[0]=dice1.split("[, ]+");
        allDice[1]=dice2.split("[, ]+");
        allDice[2]=dice3.split("[, ]+");

        boolean[] done=new boolean[N];

        go(done,allDice,"");

        for (int i=1; i<=NumDigs; i++)
            if (!Seen[i])
            {
                System.out.println(i+"="+Romans[i]+" cannot be made");
                System.out.println("range covered "+(i-1));
                break;
            }
    }

    public static void go(boolean[] done, String[][] allDice, String cur)
    {
        Integer num=Romans2Dec.get(cur);
        if (num!=null) Seen[num]=true;

        for (int i=0; i<N; i++)
            if (!done[i])
            {
                for (int k=0; k<allDice[i].length; k++)
                {
                    done[i]=true;
                    go(done,allDice,cur+allDice[i][k]);
                    done[i]=false;
                }
            }
    }
}