import java.util.ArrayList;
import java.util.Iterator;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		char[] variables = setVariables(in);
		int[] minTerms = setMinTerms(in);
		String[] binaryMinTerms = decimalToBinary(variables, minTerms);
		
		ArrayList<Group> groups = computeSuccessiveGroups(minTerms, binaryMinTerms);
		
		displayInput(variables, minTerms);
		printPIs(groups, variables);
	}
	
	private static char[] setVariables(Scanner in) {
		System.out.print("Enter the number of variables: ");
		int numVariables = in.nextInt();
		char[] variables = new char[numVariables];
		
		System.out.print("Enter each variable separated by spaces: ");
		for(int i = 0; i < numVariables; i++) {
			variables[i] = in.next().charAt(0);
		}
		return variables;
	}
	
	private static int[] setMinTerms(Scanner in) {
		System.out.print("Enter the number of min terms: ");
		int numMinTerms = in.nextInt();
		int[] minTerms = new int[numMinTerms];
		
		System.out.print("Enter each min term separated by spaces: ");
		for(int i = 0; i < numMinTerms; i++) {
			minTerms[i] = in.nextInt();
		}
		return minTerms;
	}
	
	private static String[] decimalToBinary(char[] variables, int[] minTerms) {
		String[] binaryMinTerms = new String[minTerms.length];
		for(int i = 0; i < minTerms.length; i++) {
			binaryMinTerms[i] = Integer.toBinaryString(minTerms[i]);
			if(binaryMinTerms[i].length() < variables.length) {
				String zeros = "";
				int len = binaryMinTerms[i].length();
				while(len < variables.length) {
					zeros = zeros.concat("0");
					len++;
				}
				binaryMinTerms[i] = zeros + binaryMinTerms[i];
			}
		}
		return binaryMinTerms;
	}
	
	private static void displayInput(char[] variables, int[] minTerms) {
		System.out.print("Function: f(");
		for(int i = 0; i < variables.length; i++) {
			if(i == variables.length-1)
				System.out.print(variables[i]);
			else
				System.out.print(variables[i] + ", ");
		}
		System.out.print(") = SIGMAm(");
		for(int i = 0; i < minTerms.length; i++) {
			if(i == minTerms.length-1)
				System.out.print(minTerms[i]);
			else
				System.out.print(minTerms[i] + ", ");
		}
		System.out.println(")");
	}
	
	private static ArrayList<Group> computeSuccessiveGroups(int[] minTerms, String[] binaryMinTerms) {
		ArrayList<Group> groups = new ArrayList<Group>();
		for(int i = 0; i < minTerms.length; i++)
			groups.add(new Group(Integer.toString(minTerms[i]), binaryMinTerms[i]));
		
		int sizeBeforeRemoval = 0, currentSize;
		while(sizeBeforeRemoval != groups.size()) {
			currentSize = groups.size();
			for(int i = 0; i < currentSize; i++) {
				for(int j = i+1; j < currentSize; j++) {
					if(differences(groups.get(i).binary, groups.get(j).binary) == 1) {
						String combinedBin = combineBinary(groups.get(i).binary, groups.get(j).binary);
						
						groups.get(i).grouped = true;
						groups.get(j).grouped = true;
						
						if(isUniqueBin(groups, combinedBin)) {
							String newTuple = groups.get(i).decimal + "," + groups.get(j).decimal;
							groups.add(new Group(newTuple, combinedBin));
						}
						else break;
					}
				}
			}
			
			sizeBeforeRemoval = groups.size();
			
			Iterator<Group> iter = groups.iterator();
			while(iter.hasNext()) {
				Group next = iter.next();
				if(next.grouped)
					iter.remove();
			}
		}
		return groups;
	}
	
	private static int differences(String a, String b) {
		int diff = 0;
		
		for(int i = 0; i < a.length(); i++)
			if(a.charAt(i) != b.charAt(i))
				diff++;
		
		return diff;
	}
	
	private static String combineBinary(String a, String b) {
		String combined = "";
		for(int i = 0; i < a.length(); i++) {
			if(a.charAt(i) != b.charAt(i))
				combined = combined.concat("-");
			else
				combined = combined.concat(Character.toString(a.charAt(i)));
		}
		return combined;
	}
	
	private static boolean isUniqueBin(ArrayList<Group> groups, String s) {
		for(int i = 0; i < groups.size(); i++)
			if(groups.get(i).binary.equals(s))
				return false;
		
		return true;
	}
	
	private static void printPIs(ArrayList<Group> groups, char[] variables) {
		System.out.println("Prime Implicants: ");
		for(int i = 0; i < groups.size(); i++)
			System.out.println(groups.get(i).decimal + " | " + binaryToMinTerm(variables, groups.get(i).binary));
	}
	
	private static String binaryToMinTerm(char[] variables, String s) {
		String minTerm = "";
		
		for(int i = 0; i < s.length(); i++) {
			if(s.charAt(i) != '-') {
				if(s.charAt(i) == '0')
					minTerm = minTerm.concat(Character.toString(variables[i]) + "'");
				else
					minTerm = minTerm.concat(Character.toString(variables[i]));
			}
		}
		
		return minTerm;
	}
}

//sample code to write 100 random ints to a file, 1 per line

import java.io.PrintStream;
import java.io.IOException;
import java.io.File;

import java.util.Random;

public class WriteToFile {
    public static void main(String[] args) {
        try {
            PrintStream writer = new PrintStream(new File("randInts.txt"));
            Random r = new Random();
            final int LIMIT = 100;

            for (int i = 0; i < LIMIT; i++) {
                writer.println(r.nextInt());
            }
            writer.close();
        } catch (IOException e) {
            System.out.println("An error occured while trying to write to the file");
        }
    }
}

public class Factorial
{
	public static void main(String[] args)
	{	final int NUM_FACTS = 100;
		for(int i = 0; i < NUM_FACTS; i++)
			System.out.println( i + "! is " + factorial(i));
	}
	
	public static int factorial(int n)
	{	int result = 1;
		for(int i = 2; i <= n; i++)
			result *= i;
		return result;
	}
}

public class Solution {
    public ListNode mergeTwoLists(ListNode l1, ListNode l2) {
        ListNode head = new ListNode(0);
        ListNode handler = head;
        while(l1 != null && l2 != null) {
            if (l1.val <= l2.val) {
                handler.next = l1;
                l1 = l1.next;
            } else {
                handler.next = l2;
                l2 = l2.next;
            }
            handler = handler.next;
        }
        
        if (l1 != null) {
            handler.next = l1;
        } else if (l2 != null) {
            handler.next = l2;
        }
        
        return head.next;
    }
}

public class UserService {

  private UserRepository userRepository;

  public UserService(UserRepository userRepository) {
    this.userRepository = userRepository;
  }

  public User getUserById(long id) {
    try {
      return userRepository.getUserById(id);
    } catch (Exception e) {
      // Log the exception here
      System.out.println("An error occurred while fetching the user: " + e.getMessage());
      return null;
    }
  }
}

public class UserRepository {

  public User getUserById(long id) throws Exception {
    // Database query to fetch the user
    if (id < 0) {
      throw new Exception("Invalid user id");
    }
    // Return the user object
    return new User(id, "John Doe");
  }
}

public class User {

  private long id;
  private String name;

  public User(long id, String name) {
    this.id = id;
    this.name = name;
  }

  public long getId() {
    return id;
  }

  public String getName() {
    return name;
  }
}

import static java.lang.System.*;
import java.util.Arrays;        

public class MergeSort{

private static int passCount;

public static void mergeSort(int[] list)
{
    passCount=0;
    mergeSort(list, 0, list.length);
}

private static void mergeSort(int[] list, int front, int back)  //O( Log N )
{
    int mid = (front+back)/2;
    if(mid==front) return;
    mergeSort(list, front, mid);
    mergeSort(list, mid, back);
    merge(list, front, back);

}

private static void merge(int[] list, int front, int back)  //O(N)
{
   int dif = back-front;
   int[] temp = new int[dif];
   int beg = front, mid = (front+back)/2;
   int saveMid = mid;
   int spot = 0;

   while(beg < saveMid && mid < back) {
      if(list[beg] < list[mid]) {
         temp[spot++] = list[beg++];
      } else {
         temp[spot++] = list[mid++];
      }
   }
   while(beg < saveMid)
      temp[spot++] = list[beg++];
   while(mid < back)
      temp[spot++] = list[mid++];
   for(int i = 0; i < back-front; i++) {
      list[front+i] = temp[i];
   }
    System.out.println("pass " + passCount++ + " " + Arrays.toString(list) + "\n");
  }
  
  
    public static void main(String args[])
    {
        mergeSort(new Comparable[]{ 9, 5, 3, 2 });
        System.out.println("\n");
        
        mergeSort(new Comparable[]{ 19, 52, 3, 2, 7, 21 });
        System.out.println("\n");
        
        mergeSort(new Comparable[]{ 68, 66, 11, 2, 42, 31});
        System.out.println("\n");
    }
  
 }