What is the Prefix Sum technique?

Prefix Sum

javascript

1
Preprocessing complexity: O(n).
2
Range query complexity: O(1).
3
Auxiliary space: O(n) for a separate prefix array.
4
Prefix sums are useful when many range queries are performed against mostly static data.
5
The technique can be extended to frequency counts and multidimensional grids.

Difficulty: 5/10

Topics: range sum queries, array preprocessing, cumulative sums

0-2 years experience

1
Given an array of integers, how would you compute the sum of elements between indices i and j inclusive in O(1) time after a one‑time preprocessing step?
2
If you need to answer many sub‑array sum queries, what preprocessing would you perform and how would you answer each query?
3
What, if anything, changes in your approach when the array contains negative numbers?

2-5 years experience

1
We have a live leaderboard where scores are updated frequently and we need to report the total score for any range of users. How would you modify the prefix‑sum approach to handle updates efficiently?
2
During a code review, a teammate's implementation of range‑sum queries using prefix sums fails when the array length is zero. How would you debug and fix it?
3
Explain the trade‑offs between using a simple prefix‑sum array versus a Fenwick tree for range‑sum and point‑update operations.

5-8 years experience

1
Design a service that stores time‑series data for millions of sensors and must serve range‑sum queries with sub‑millisecond latency. How would you structure storage and use prefix sums or related techniques at scale?
2
Our analytics pipeline processes batches of logs and we need to compute cumulative metrics per day. How would you ensure the prefix‑sum computation remains correct when data arrives out‑of‑order or needs to be recomputed after a schema change?
3
Discuss how you would handle integer overflow and precision when using prefix sums on 64‑bit counters in a distributed system.

8+ years experience

1
We are migrating a legacy reporting system that uses ad‑hoc loops for aggregations to a new architecture. How would you evaluate whether introducing a prefix‑sum based materialized view is worth the engineering effort across multiple teams?
2
In a multi‑tenant data warehouse, different tenants have varying retention policies. How would you design a prefix‑sum strategy that supports efficient roll‑up and purge while minimizing storage duplication?
3
Consider a global e‑commerce platform where daily sales totals are pre‑aggregated using prefix sums. How would you orchestrate incremental updates and ensure consistency across regions during a rolling deployment?