Tipovik1_Java

// Типовой расчет №1 по дисциплине "Дискретная математика" (программный уровень)
// Преподователь: Гилев Павел Андреевич
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {

        // input
        Scanner scanner = new Scanner(System.in);
        int countVars = scanner.nextInt(); // n

        // calculating table size
        int valuesCount = (int)Math.pow(2, countVars); // 2^n
        int rowValuesCount = countVars + 1; // n + 1

        int[][] istTable = new int[valuesCount][rowValuesCount]; // (2^n) x (n + 1) table

        // input
        for(int i = 0; i < valuesCount; i++) {
            for (int j = 0; j < rowValuesCount; j++)
            {
                istTable[i][j] = scanner.nextInt();
            }
        }

        // get last column
        int size = valuesCount;
        int[] currentArray = new int[size];
        for (int i = 0; i < size; i++)
        {
            currentArray[i] = istTable[i][rowValuesCount - 1];
        }

        // calculate Zhegalkin's polynomial variables & convert them to a boolean array
        boolean[] zhpolynom = new boolean[size];

        for (int i = 0; size != 0; i++)
        {
            zhpolynom[i] = currentArray[0] == 1; // push every first value to output result
            int[] nextArray = new int[size - 1];
            for (int j = 0; j < size - 1; j++)
            {
                int firstElement = currentArray[j];
                int secondElement = currentArray[j + 1];
                nextArray[j] = (firstElement + secondElement) % 2;
            }

            currentArray = nextArray;
            size--;
        }


        // transform boolean array to output string

        int countPluses = -1;
        for (boolean value : zhpolynom)
        {
            if(value) countPluses++;
        }

        for (int i = 0; i < zhpolynom.length; i++)
        {
            if(zhpolynom[i])
            {
                if (i == 0)
                {
                    System.out.print("1 + ");
                    countPluses--;
                    continue;
                }
                String binaryIndex = String.format("%0" + countVars + "d", Integer.parseInt(Integer.toBinaryString(i)));
                char[] binaryIndexChars = binaryIndex.toCharArray();
                for (int j = 0; j < binaryIndexChars.length; j++)
                {
                    if(binaryIndexChars[j] == '1')
                    {
                        System.out.print((char)(97+j));
                    }
                }
                if (countPluses-- > 0)
                {
                    System.out.print(" + ");
                }
            }
        }
        System.out.println();
    }
}

Тесты:
Тест 1
Пример ввода:
2
0 0 0
0 1 1
1 0 1
1 1 1

Пример вывода:
b + a + ab

Тест 2
Пример ввода:
5
0 0 0 0 0 0
0 0 0 0 1 0
0 0 0 1 0 0
0 0 0 1 1 0
0 0 1 0 0 0
0 0 1 0 1 0
0 0 1 1 0 0
0 0 1 1 1 1
0 1 0 0 0 0
0 1 0 0 1 0
0 1 0 1 0 0
0 1 0 1 1 1
0 1 1 0 0 0
0 1 1 0 1 1
0 1 1 1 0 1
0 1 1 1 1 1
1 0 0 0 0 0
1 0 0 0 1 0
1 0 0 1 0 0
1 0 0 1 1 1
1 0 1 0 0 0
1 0 1 0 1 1
1 0 1 1 0 1
1 0 1 1 1 1
1 1 0 0 0 0
1 1 0 0 1 1
1 1 0 1 0 1
1 1 0 1 1 1
1 1 1 0 0 1
1 1 1 0 1 1
1 1 1 1 0 1
1 1 1 1 1 1

Пример вывода:
cde + bde + bce + bcd + bcde + ade + ace + acd + acde + abe + abd + abde + abc + abce + abcd