Worksapp3

package jp.co.worksap.global;

import java.util.ArrayList;
import java.util.HashMap;
import java.util.List;
import java.util.Scanner;


public class CharacterRecognition {

    private static int[][][] characters = null;
    private static HashMap<List<Integer>,Integer> dp = new HashMap<>();

    public static void main( String[] args ){

        Scanner in = new Scanner( System.in );

        int n = in.nextInt();
        int m = in.nextInt();
        int c = in.nextInt();
        in.nextLine();

        //This will hold the character pixels.
        characters = new int[c][n][m];

        for( int i = 0; i < c; i++ ){

            in.nextLine();
            for( int j = 0; j<n; j++ ){

                String line = in.nextLine();

                for( int k = 0; k<m; k++ ){

                    characters[i][j][k] = (int)( line.charAt(k) - '0' );
                }
            }
        }

        List<Integer> chars = new ArrayList<>();

        for( int i = 0; i<c; i++ ) chars.add( i );

        System.out.println( getMinPixel( chars,n,m ) );
    }

    private static int getMinPixel( List<Integer> chars, int n, int m ) {

        //If only one character, no pixel needed to check
        if( chars.size() == 1 ){
            return 0;
        }

        //If already solve for this character set, return previously calculated result
        if( dp.containsKey( chars ) )
            return dp.get( chars );

        //In worst case, we have to check all the pixels.
        int min = n*m;

        for( int i = 0; i<n; i++ ){
            for( int j = 0; j<m; j++ ){

                //List to hold characters, which has zero in position i,j
                List<Integer> charHavingzero = new ArrayList<>();

                //List to hold characters, which has one in position i,j
                List<Integer> charHavingOne = new ArrayList<>();

                for( int k = 0; k<chars.size(); k++ ){

                    if( characters[ chars.get(k) ][i][j] == 1 ){
                        charHavingOne.add( k );
                    }
                    else{
                        charHavingzero.add( k );
                    }
                }

                int max = 0;

                //if one of them has zero element, pixel at i,j can't distinguish them.
                //So continue
                if( charHavingOne.isEmpty() || charHavingzero.isEmpty() )
                    continue;

                max = Math.max( getMinPixel( charHavingzero, n, m ), getMinPixel( charHavingOne, n, m ) );

                //Adjust min variable
                min = Math.min( min, max+1 );
            }
        }

        dp.put( chars, min );

        return min;
    }
}