Minimum length subarray with sum k

Match the technique to the guarantees

The title omits two essential details. If all numbers are positive and the task is shortest subarray with sum at least k, expand a window and shrink from the left while its sum remains at least k, recording the shortest valid length. If the task is exact sum k, use prefix sums: when current prefix is P, an earlier prefix P-k creates a qualifying subarray; retain the latest or earliest index depending on the requested objective. Negative values invalidate the usual shrinking-window monotonicity.

State the invariant

For the positive at-least form, removing a left value only decreases sum, so once the window is valid it is safe to shrink greedily. With arbitrary integers and sum at least k, use prefix sums plus an increasing deque of candidate prefix indices; discard dominated prefixes and pop from the front when their difference reaches k. That is O(n) time and O(n) space. The positive sliding-window variant is O(n) time and O(1) space. Test no solution, one element, exact versus greater-than behavior, and negative values before presenting code.