Section Recap

Look at what you can do now:

$1.$ Build 1D (one-dimensional) and 2D prefix sum arrays

$2.$ Answer any range sum query in $O(1)$ time

$3.$ Combine prefix sums with HashMaps for counting problems

$4.$ Use prefix/suffix products when division isn't allowed

$5.$

Apply inclusion-exclusion for 2D rectangle queries This technique is a building block. You'll use it inside DP (dynamic programming) transitions, with binary search, and in string algorithms. But the core formula never changes: $pref[r] - pref[l-1]$.