K-th Largest Sum Contiguous Subarray in c#

Programming C#
1

To find the K-th largest sum of contiguous subarrays in C#, you can follow these steps:

  1. Generate All Possible Subarray Sums: Iterate through all possible subarrays, compute their sums, and store them in a list.

  2. Sort the Sums: Once you have all the sums, sort them in descending order.

  3. Return the K-th Largest Sum: The K-th largest sum will be the element at index ( K-1 ) in the sorted list.

Here’s a sample implementation in C#:

using System;
using System.Collections.Generic;

public class Program
{
    public static void Main()
    {
        int[] arr = { 1, 2, 3, 4 }; // Example array
        int k = 3; // K-th largest sum to find
        int result = KthLargestSum(arr, k);
        Console.WriteLine($"The {k}-th largest sum is: {result}");
    }

    public static int KthLargestSum(int[] arr, int k)
    {
        HashSet<int> sums = new HashSet<int>();
        
        // Generate all possible subarray sums
        for (int i = 0; i < arr.Length; i++)
        {
            int currentSum = 0;
            for (int j = i; j < arr.Length; j++)
            {
                currentSum += arr[j];
                sums.Add(currentSum);
            }
        }

        // Convert the HashSet to a List and sort it in descending order
        List<int> sortedSums = new List<int>(sums);
        sortedSums.Sort((a, b) => b.CompareTo(a)); // Sort in descending order

        // Return the K-th largest sum
        return sortedSums[k - 1];
    }
}

Explanation:

  1. Input Array: The arr variable holds the input array, and k specifies which largest sum we want.

  2. Generate Subarray Sums:

    • Use two nested loops. The outer loop (i) selects the starting index of the subarray, while the inner loop (j) extends the subarray by adding elements to the current sum (currentSum).
    • Each calculated sum is added to a HashSet<int> to avoid duplicates.

  3. Sorting:

    • Convert the HashSet to a List<int> to sort it. The sorting is done in descending order using a custom comparison that compares the integers.

  4. Finding the K-th Largest:

    • Finally, return the K-th largest sum by accessing the ( K-1 ) index in the sorted list.

Complexity:

  • Time Complexity: ( O(n^2 \log(n^2)) ) due to generating ( O(n^2) ) sums and sorting them. The logarithmic factor comes from sorting.
  • Space Complexity: ( O(n^2) ) in the worst case for storing sums, though a HashSet helps reduce duplicates.

This approach is straightforward and works well for smaller arrays. For larger arrays or performance-sensitive applications, more efficient algorithms (like using a min-heap) might be needed to improve performance.