Sliding Window Technique Problem

Problem A sliding-window problem: given an array and a window definition, compute an aggregate over contiguous subarrays — e.g. the maximum sum of a subarray of fixed size k, or the smallest window satisfying a given constraint.

Input / Output

• Input: array nums of integers, plus a window size k (fixed-size variant) or a target condition (variable-size variant)
• Output: the required aggregate — max/min sum, count of qualifying windows, or the length of the smallest/longest valid window

Constraints

• 1 <= nums.length <= 10^5, so an O(n*k) brute force will time out
• 1 <= k <= nums.length
• Values may be negative in the fixed-size variant; the variable-size shrink trick requires non-negative values

Example

• Input: nums = [2,1,5,1,3,2], k = 3 → Output: 9 (window [5,1,3])
• Tricky case: nums = [-1,-2,-3], k = 2 → -3; the answer must be seeded from the first window, not from 0