Sliding Window technique

Start by asking whether the window size is fixed. A fixed window keeps a running sum, frequency table, or other aggregate: build the first window, then for each shift add the entering value and remove the leaving value. A variable window needs a validity invariant such as “at most K distinct characters” or “sum at most K with non-negative values.” Extend right, update state, and advance left until validity is restored. The answer can be recorded before or after shrinking depending on whether the task asks for valid, maximal, or minimal windows. Never recompute the whole interval after a shift; the gain comes from incremental updates. Since each pointer advances at most n times, these implementations are commonly O(n) time. Space depends on state, often O(1) for numeric aggregates or O(alphabet size) for character counts. Mention empty input and invalid k explicitly.