Smallest subarray with sum greater than a given value in C#

Programming C#
1

To find the smallest subarray with a sum greater than a given value in C#, you can use the sliding window technique. This approach allows you to efficiently find the required subarray in O(n) time complexity. Here’s how it works and a sample implementation.

Explanation of the Sliding Window Technique:

  1. Initialize Variables: Start with pointers for the window (start and end), a variable to keep track of the current sum, and a variable to store the minimum length of the subarray.

  2. Expand the Window: Use the end pointer to expand the window by adding elements to the current sum until it exceeds the target sum.

  3. Shrink the Window: Once the current sum is greater than the target, try to minimize the window by moving the start pointer to the right. After moving the start, update the current sum and check if the window still satisfies the condition (sum > target).

  4. Update Minimum Length: Each time you find a valid window (sum > target), check if its length is smaller than the previously recorded minimum length.

  5. Continue Until End of Array: Repeat the process until the end pointer has traversed the entire array.

Sample Code:

using System;

class SmallestSubarrayFinder
{
    public static int MinSubArrayLen(int target, int[] nums)
    {
        int minLength = int.MaxValue;
        int currentSum = 0;
        int start = 0;

        for (int end = 0; end < nums.Length; end++)
        {
            currentSum += nums[end]; // Expand the window by including nums[end]

            // Shrink the window as long as the current sum is greater than the target
            while (currentSum > target)
            {
                minLength = Math.Min(minLength, end - start + 1); // Update min length
                currentSum -= nums[start]; // Shrink the window from the left
                start++;
            }
        }

        return minLength == int.MaxValue ? 0 : minLength; // Return 0 if no valid subarray found
    }

    static void Main()
    {
        int[] nums = { 2, 3, 1, 2, 4, 3 };
        int target = 7;
        int result = MinSubArrayLen(target, nums);

        if (result > 0)
        {
            Console.WriteLine($"The length of the smallest subarray with sum greater than {target} is: {result}");
        }
        else
        {
            Console.WriteLine("No valid subarray found.");
        }
    }
}

How It Works:

  1. Initialization: minLength is set to the maximum possible value to ensure any found subarray will be smaller. currentSum starts at 0, and start is initialized at the beginning of the array.

  2. Outer Loop: The end pointer iterates through the array, expanding the window by adding nums[end] to currentSum.

  3. Inner Loop: When currentSum exceeds the target, the inner loop begins:

    • It updates minLength if the current window size (from start to end) is smaller than the previously recorded size.
    • It then reduces currentSum by subtracting nums[start] and moves the start pointer to the right to attempt to find a smaller valid subarray.

  4. Final Result: After the loops, if minLength is still the maximum value, it means no valid subarray was found, and we return 0. Otherwise, we return the length of the smallest subarray.

Time Complexity:

  • O(n): Each element is processed at most twice (once by the end pointer and once by the start pointer).
  • O(1): The space complexity is constant as we only use a few extra variables.

This method is efficient and effective for finding the smallest subarray with a sum greater than a given value.