Range Addition - Algorithm

The algorithm has two phases:

$1.$ Process all updates on the difference array. Each update modifies exactly two positions.

$2.$ Compute the prefix sum of the difference array to get the final result. This separates the $O(k)$ update phase from the $O(n)$ reconstruction phase. Total: $O(k + n)$. Time: $O(k + n)$. Space: $O(n)$.