Честно казано, много е трудно да се следва логиката в кода, затова направо пренаписах частта, която анализира inputInt[] и решението мина в Judge:

package demo;

import java.util.Scanner;

public class KaminoFactory {

    public static void main(String[] args) {
        Scanner scanner = new Scanner(System.in);

        int num = Integer.parseInt(scanner.nextLine());

        String input = scanner.nextLine();
        int positionMAx = num - 1;
        int maxSum = 0;
        int lengthMax = 0;
        int[] winInt = new int[num];
        int counter = 0;
        int counterWin = 0;
        while (!(input.equals("Clone them!"))) {
            counter++;
            int[] inputInt = new int[num];
            String[] inputArr = input.split("!+");
            for (int i = 0; i < num; i++) {
                inputInt[i] = Integer.parseInt(inputArr[i]);
            }

            int sum = 0;
            int curStart = -1;
            int curLength = 0;
            int currentPositionMax = -1;
            int currentLengthMax = 0;
            for (int i = 0; i < inputInt.length; i++) {
                if (inputInt[i] == 1) {
                    if (curStart == -1) {
                        curStart = i;
                    }
                    sum++;
                    curLength++;
                }
                if (inputInt[i] == 0 || i == inputInt.length - 1){
                    if(curLength > currentLengthMax) {
                        currentLengthMax = curLength;
                        currentPositionMax = curStart;
                    }
                    curLength = 0;
                    curStart = -1;
                }
            }

            boolean flagWin = false;

            if (currentLengthMax > lengthMax) {
                flagWin = true;
            }
            if (currentLengthMax == lengthMax && currentPositionMax < positionMAx) {
                flagWin = true;
            }
            if (currentLengthMax == lengthMax && currentPositionMax == positionMAx && sum > maxSum) {
                flagWin = true;

            }
            if (flagWin) {
                lengthMax = currentLengthMax;
                positionMAx = currentPositionMax;
                winInt = inputInt;
                maxSum = sum;
                counterWin = counter;
            }
            input = scanner.nextLine();
        }


        System.out.printf("Best DNA sample %d with sum: %d.%n", counterWin, maxSum);
        for (int i = 0; i < num; i++) {

            System.out.print(winInt[i] + " ");
        }
    }
}