The Range Update Problem

New problem: you have an array, and you need to add a value $v$ to all elements from index $l$ to $r$. You'll do this many times, then read the final array.

Naive approach: loop from $l$ to $r$, add $v$ to each element. Each update takes $O(n)$ time. Can you do better? Yes. Difference arrays let you perform range updates in $O(1)$.