C# Coding Test Course, Maximizing Value by Grouping Numbers

In this lecture, we will cover a problem that frequently appears in coding tests, the ‘Make the Maximum Number by Grouping Numbers’ problem. This problem involves combining given numbers to create the largest possible number. Additionally, I will explain how to solve this using the C# language step by step.

Problem Description

Given several positive integers, write a function that returns the largest number that can be formed by combining these numbers. For example, if the given numbers are [3, 30, 34, 5, 9], the largest number that can be formed by appropriately combining them is 9534330.

Input Format

An integer array numbers will be provided. The size of the array is between 0 and 100, and the length of each number is between 1 and 10.

Output Format

Return the largest number formed by combining all the numbers as a string.

Problem Approach

To solve this problem, several approaches are necessary.

• Sorting: We need to sort the given numbers to create the largest number. The sorting criteria are important, and we need to create rules based on treating each number as a string.
• String Comparison: When comparing two numbers, we need to determine which combination (where one number comes first or second) results in a larger number.

Code Implementation

Let’s write a code in C# to solve the problem based on the above approaches.

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    public static string Solution(int[] numbers)
    {
        // Convert numbers to strings.
        string[] strNumbers = numbers.Select(n => n.ToString()).ToArray();
        
        // Sort the string array.
        Array.Sort(strNumbers, (x, y) => (y + x).CompareTo(x + y));
        
        // Combine the sorted array into a single string.
        string result = string.Join("", strNumbers);
        
        // If the result starts with "0", return only "0".
        return result[0] == '0' ? "0" : result;
    }

    static void Main(string[] args)
    {
        int[] numbers = { 3, 30, 34, 5, 9 };
        string answer = Solution(numbers);
        Console.WriteLine(answer);  // 9534330
    }
}
    

Code Explanation

Let’s take a closer look at the code above.

1. String Conversion: First, convert each number to a string and store it in an array called strNumbers. This is necessary for rearranging the numbers in string form.
2. Sorting: Use the Array.Sort method to sort the strNumbers array. The sorting criterion combines two numbers x and y to sort them in descending order. By comparing (y + x) and (x + y), we determine which combination is larger.
3. Result Combination: Use string.Join to combine the sorted numbers into a single string.
4. Final Check: If the first character of the result string is ‘0’, it indicates that all numbers are 0, so return only ‘0’.

Complexity Analysis

The time complexity of this algorithm is O(N log N). This is the time spent sorting the given number array. N represents the number of digits. The space complexity is O(N) since it requires an array to store the string conversions of each number.

Conclusion

In this lecture, we examined how to solve the ‘Make the Maximum Number by Grouping Numbers’ problem using C#. It is important to understand the problem well and to select appropriate data structures and algorithms to solve algorithmic problems. Practice with various problems!

Additional Practice Problems

I recommend further practicing the following problems:

• Combine the given numbers to generate all possible combinations and find the maximum value among them.
• Write an algorithm to create the maximum number when both positive and negative numbers are mixed.
• Explore methods to prevent performance degradation when the input array size becomes very large.

Reference Materials

There are several reference materials that can help in solving algorithm problems like this. Please check the following links:

• GeeksforGeeks
• LeetCode
• HackerRank