Sliding Window Maximum Sum

This challenge focuses on implementing the sliding window technique in Python to find the maximum sum of a subarray of a fixed size. The sliding window pattern is a powerful algorithmic technique used for efficiently processing contiguous subarrays or substrings. Mastering it will equip you to solve many common array and string manipulation problems.

Problem Description

Given an array of integers nums and an integer k, find the maximum sum of any contiguous subarray of size k.

Requirements:

• You must use the sliding window technique to solve this problem.
• The subarray must be contiguous (elements must be adjacent in the original array).
• The size of the subarray is fixed at k.

Expected Behavior: Your function should return a single integer representing the largest sum found among all subarrays of size k. If the input array is empty or k is greater than the length of the array, you should handle this gracefully (e.g., return 0 or raise an error, as per constraints).

Edge Cases:

• k is equal to the length of nums.
• k is 1.
• The array nums contains negative numbers.
• The array nums is empty.
• k is 0 or negative.

Examples

Example 1:

Input: nums = [1, 3, -1, -3, 5, 3, 6, 7], k = 3
Output: 16
Explanation:
The subarrays of size 3 are:
[1, 3, -1] -> sum = 3
[3, -1, -3] -> sum = -1
[-1, -3, 5] -> sum = 1
[-3, 5, 3] -> sum = 5
[5, 3, 6] -> sum = 14
[3, 6, 7] -> sum = 16
The maximum sum is 16.

Example 2:

Input: nums = [10, 4, 2, 5, 6, 1, 8], k = 2
Output: 14
Explanation:
The subarrays of size 2 are:
[10, 4] -> sum = 14
[4, 2] -> sum = 6
[2, 5] -> sum = 7
[5, 6] -> sum = 11
[6, 1] -> sum = 7
[1, 8] -> sum = 9
The maximum sum is 14.

Example 3:

Input: nums = [-2, 1, -3, 4, -1, 2, 1, -5, 4], k = 4
Output: 6
Explanation:
The subarray [4, -1, 2, 1] has a sum of 6, which is the maximum sum for any subarray of size 4.

Constraints

• 1 <= k <= nums.length
• -10^4 <= nums[i] <= 10^4
• The input nums will be a list of integers.
• The input k will be an integer.
• Your solution should aim for a time complexity of O(n), where n is the length of nums.

Notes

The sliding window technique involves maintaining a "window" of a fixed size that moves across the data structure. For this problem, the window will represent the current subarray of size k. As the window slides one element to the right, you'll efficiently update the sum instead of recalculating it from scratch for each new subarray. Consider how you can update the sum by subtracting the element leaving the window and adding the element entering the window.