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;
	}
}

public static String addBinary(){
 // The two input Strings, containing the binary representation of the two values:
    String input0 = "1010";
    String input1 = "10";

    // Use as radix 2 because it's binary    
    int number0 = Integer.parseInt(input0, 2);
    int number1 = Integer.parseInt(input1, 2);

    int sum = number0 + number1;
    return Integer.toBinaryString(sum); //returns the answer as a binary value;
}

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 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 java.util.*;
 
public class HeapSortMain {
 
   public static void buildheap(int []arr) {
 
    /*
     * As last non leaf node will be at (arr.length-1)/2 
     * so we will start from this location for heapifying the elements
     * */
    for(int i=(arr.length-1)/2; i>=0; i--){
           heapify(arr,i,arr.length-1);
      }
   }
 
   public static void heapify(int[] arr, int i,int size) { 
      int left = 2*i+1;
      int right = 2*i+2;
      int max;
      if(left <= size && arr[left] > arr[i]){
         max=left;
      } else {
         max=i;
      }
 
      if(right <= size && arr[right] > arr[max]) {
         max=right;
      }
      // If max is not current node, exchange it with max of left and right child
      if(max!=i) {
         exchange(arr,i, max);
         heapify(arr, max,size);
      }
   }
 
   public static void exchange(int[] arr,int i, int j) {
        int t = arr[i];
        arr[i] = arr[j];
        arr[j] = t; 
   }
 
   public static int[] heapSort(int[] arr) {
 
      buildheap(arr);
      int sizeOfHeap=arr.length-1;
      for(int i=sizeOfHeap; i>0; i--) {
         exchange(arr,0, i);
         sizeOfHeap=sizeOfHeap-1;
         heapify(arr, 0,sizeOfHeap);
      }
      return arr;
   }
 
   public static void main(String[] args) {
      int[] arr={1,10,16,19,3,5};
      System.out.println("Before Heap Sort : ");
      System.out.println(Arrays.toString(arr));
      arr=heapSort(arr);
      System.out.println("=====================");
      System.out.println("After Heap Sort : ");
      System.out.println(Arrays.toString(arr));
   }
}

//Leif Messinger
//Solves wordle
//Needs a list of wordle words, newline separated and 5 characters each

import java.util.*;
import java.io.File;
import java.io.FileNotFoundException;

class WordleSolver {

	public static void printPointer(int position){
		for(int i = 0; i < position; ++i){
			System.out.print(" ");
		}
		System.out.print("^");
	}

	public static void main(String[] args) throws FileNotFoundException{
		if(args.length < 1) return;
		File dictionary = new File(args[0]);
		Scanner sc = new Scanner(dictionary);
		ArrayList<String> possibleWords = new ArrayList<String>();
		while(sc.hasNextLine()){
			possibleWords.add(sc.nextLine());
		}

		Scanner input = new Scanner(System.in);

		while(possibleWords.size() > 0){
			//Choose a word out of the possible words
			final int randomIndex = (int)(Math.random() * possibleWords.size());
			String chosenWord = possibleWords.get(randomIndex);
			possibleWords.remove(randomIndex);

			System.out.println("Is it correct?");
			for(int i = 0; i < chosenWord.length(); ++i){
				System.out.println(chosenWord);
				printPointer(i);
				System.out.println(" y/n?");
				if(input.nextLine().toLowerCase().contains("y")){
					//Filter by correct character
					for(int possibleWord = possibleWords.size() - 1; possibleWord >= 0; --possibleWord){ //Has to be backwards for removing entries, also has to be int not unsigned
						if(possibleWords.get(possibleWord).charAt(i) != chosenWord.charAt(i)){
							possibleWords.remove(possibleWord);
						}
					}
				}
			}
			System.out.println("Is it misplaced?");
			//Stores a count of every letter misplaced
			short[] misplacedCounts = new short[('z'-'a')+1]; //Praise be the garbage collector
			for(int i = 0; i < chosenWord.length(); ++i){
				System.out.println(chosenWord);
				printPointer(i);
				System.out.println(" y/n?");
				if(input.nextLine().toLowerCase().contains("y")){
					//Filter to make sure there's at least as many letters as needed
					++misplacedCounts[(chosenWord.charAt(i) - 'a') - 1];
					for(int possibleWord = possibleWords.size() - 1; possibleWord >= 0; --possibleWord){	//Has to be backwards for removing entries, also has to be int not unsigned
						int count = 0;
						for(int j = 0; j < possibleWords.get(possibleWord).length(); ++j){
							if(possibleWords.get(possibleWord).charAt(j) == chosenWord.charAt(i))
								++count;
						}
						//If there's not enough of the character that we need, then we remove that from the list of possible characters
						if(count < misplacedCounts[(chosenWord.charAt(i) - 'a') - 1]){
							possibleWords.remove(possibleWord);
						}
					}
					//Also filter out words where that letter doesn't belong there
					for(int possibleWord = possibleWords.size() - 1; possibleWord >= 0; --possibleWord){ //Has to be backwards for removing entries, also has to be int not unsigned
						if(possibleWords.get(possibleWord).charAt(i) == chosenWord.charAt(i)){
							possibleWords.remove(possibleWord);
							continue;	//Breaks the current word and moves on in the loop
						}
					}
				}
			}
		}
	}
}