Classic array manipulation

The title alone is ambiguous, so first ask for the operation and desired result. If it is the common workload of adding value v to every index in inclusive range [l, r] and returning the final maximum, avoid touching every element. Allocate a difference array, add v at l and subtract v at r + 1 when in bounds, then take a running prefix sum and track its maximum. Each update is O(1), and the final reconstruction is O(n), giving O(n + q) time for q updates and O(n) space. Confirm zero- versus one-based input indices and use a wide numeric type because many updates can overflow a small integer. Do not claim this approach applies if the confirmed operations are point updates or arbitrary queries.