>RunTimeFix
BookStudyPracticeInterviewsYouTubeCoursesAbout
Log inGet Started
Topics/Prefix Sums & Difference Arrays
beginner level

Prefix Sums & Difference Arrays

Quick Answer

What is Prefix Sums & Difference Arrays?

Prefix sums transform range sum queries from O(n) to O(1) after O(n) preprocessing. This simple yet powerful technique appears in countless contest problems. RunTimeFix covers 1D prefix sums (subarray sum queries), 2D prefix sums (submatrix sum queries), suffix sums and suffix aggregates, and difference arrays (the inverse operation that enables O(1) range updates). These aren't just contest tricks — prefix sums are used in production systems for analytics, image processing, and cumulative statistics.

  • prefix sums
  • prefix sum array
  • difference array
  • 2D prefix sums
  • range sum query
  • cumulative sum

Study Material for Prefix Sums & Difference Arrays

Ch 13: Prefix Sums & Difference Arrays

1D Prefix Sums · 2D Prefix Sums · Suffix Sums & Suffix Aggregates · Difference Arrays

Related Topics

AlgorithmsTwo Pointers & Sliding WindowSegment Tree & Fenwick Tree
Was this helpful?

Published by RunTimeFix · Comprehensive guides for competitive programming

>RunTimeFix

Practical programming education. Books, videos, courses, and hands-on learning for competitive programming, DSA, and software engineering.

RunTimeFix

  • About
  • YouTube
  • Book
  • Study Library
  • Courses

Learn

  • Competitive Programming
  • DSA
  • Development
  • Databases

Legal

  • Privacy
  • Terms
  • Refund Policy

RunTimeFix — debug → solve → run

© 2026 RunTimeFix. All rights reserved.