To find the K-th largest sum of contiguous subarrays in C#, you can follow these steps:
-
Generate All Possible Subarray Sums: Iterate through all possible subarrays, compute their sums, and store them in a list.
-
Sort the Sums: Once you have all the sums, sort them in descending order.
-
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:
-
Input Array: The
arr
variable holds the input array, andk
specifies which largest sum we want. -
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.
- Use two nested loops. The outer loop (
-
Sorting:
- Convert the
HashSet
to aList<int>
to sort it. The sorting is done in descending order using a custom comparison that compares the integers.
- Convert the
-
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.