What is the time complexity of prefix sums?

Best case O(n) build. Worst case O(1) per query. Space complexity is O(n).

Prefix sums

easy

prefix[r+1] − prefix[l] cancels the shared head and leaves exactly a[l..r]. One linear pass buys constant-time range sums for every query afterwards.

Best O(n) buildWorst O(1) per querySpace O(n)

Loading the prefix sums engine…

Range updates in O(1), materialised once at the end.

Prefix sums in one array, driven by the lowest set bit.

Range queries and point updates, both O(log n).