Sliding window Modifed version

“Modified sliding window” is not a complete problem statement, so an interviewer-quality response begins by clarifying the range condition, whether values can be negative, and whether we count windows or optimize one. Then define a precise invariant. For example, with at most K distinct values, maintain a frequency map and a distinct counter; with replacements allowed, maintain the maximum character frequency; with a sum bound and non-negative values, maintain the running sum. Add the right element, repair the invariant by removing left elements, and update the answer only when the window has the intended meaning. The linear bound comes from each element entering and leaving at most once, not from a nested loop magically being constant. If the modification permits negative numbers or arbitrary non-monotonic validity, say that prefix sums, deques, or another method may be necessary. Typical time is O(n) and space is O(number of tracked values).