1. Introduction

Given a set of numbers, the task is to arrange them in a way that yields the largest value. This problem has significance in various applications, especially in domains like e-commerce, where it can be used to create the maximum price by a specific combination of numbers.

2. Program Steps

1. Convert all numbers to strings to compare them as strings rather than integers.

2. Sort the numbers (in their string form) in a custom order. The idea is to decide, for every two numbers a and b, if ab is greater or ba is greater.

3. After sorting, concatenate all numbers to get the desired largest number.

3. Code Program

import java.util.Arrays;
import java.util.Comparator;

public class LargestNumberPossible {

    public static String largestNumber(int[] nums) {
        if (nums == null || nums.length == 0) {
            return "";
        }

        // Convert integers to strings
        String[] strNums = new String[nums.length];
        for (int i = 0; i < nums.length; i++) {
            strNums[i] = String.valueOf(nums[i]);
        }

        // Sort strings based on custom comparator
        Arrays.sort(strNums, new Comparator<String>() {
            public int compare(String a, String b) {
                String ab = a + b;
                String ba = b + a;
                return ba.compareTo(ab);
            }
        });

        // Handle cases like [0, 0]
        if (strNums[0].charAt(0) == &apos;0&apos;) {
            return "0";
        }

        StringBuilder sb = new StringBuilder();
        for (String str : strNums) {
            sb.append(str);
        }

        return sb.toString();
    }

    public static void main(String[] args) {
        int[] nums = {3, 30, 34, 5, 9};
        System.out.println("Largest Number: " + largestNumber(nums));
    }
}

Output:

Largest Number: 9534330

4. Step By Step Explanation

1. First, every integer in the array is converted to its String representation. This allows us to concatenate two numbers and determine which concatenation would produce a larger number.

2. A custom comparator is used to sort the String representations of numbers. For two strings a and b, we compare ab and ba. The order that produces a larger number is used to sort a and b.

3. After sorting, simply concatenate each number in the sorted array to produce the largest possible number.

4. A special check is added to handle cases where the sorted array starts with '0', such as in [0, 0], as the output in such cases should be '0' and not '00'.