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:
-
Initialize Variables: Start with pointers for the window (
start
andend
), a variable to keep track of the current sum, and a variable to store the minimum length of the subarray. -
Expand the Window: Use the
end
pointer to expand the window by adding elements to the current sum until it exceeds the target sum. -
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 thestart
, update the current sum and check if the window still satisfies the condition (sum > target). -
Update Minimum Length: Each time you find a valid window (sum > target), check if its length is smaller than the previously recorded minimum length.
-
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:
-
Initialization:
minLength
is set to the maximum possible value to ensure any found subarray will be smaller.currentSum
starts at 0, andstart
is initialized at the beginning of the array. -
Outer Loop: The
end
pointer iterates through the array, expanding the window by addingnums[end]
tocurrentSum
. -
Inner Loop: When
currentSum
exceeds the target, the inner loop begins:- It updates
minLength
if the current window size (fromstart
toend
) is smaller than the previously recorded size. - It then reduces
currentSum
by subtractingnums[start]
and moves thestart
pointer to the right to attempt to find a smaller valid subarray.
- It updates
-
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 thestart
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.