Prefix Sums#

This chapter will introduce you to a technique called prefix sums. This technique can make calculations much faster and efficient. The chapter will explain how cumulative aggregation works and how it can help you optimize your operations.

Prefix sums are like building blocks that can be used to create many different algorithms. They make it easier to handle cumulative values and allow you to solve complex problems much more efficiently than before.

What this chapter covers:

  1. Introduction to Prefix Sums: Establish the groundwork by understanding the essence of prefix sums, their role in performance enhancement, and the scenarios where they shine.

  2. Prefix Sum Array Construction: Dive into the mechanics of constructing a prefix sum array, unlocking the potential to access cumulative values efficiently.

  3. Range Sum Queries: Explore how prefix sums revolutionize calculating sums within a given range, enabling quick and consistent results.

  4. Subarray Sum Queries: Delve into the technique’s application in efficiently determining the sum of elements within any subarray of an array.

  5. Prefix Sum Variants: Discover the versatility of prefix sums in solving problems related to averages, running maximum/minimum values, and more.

  6. Problem-Solving with Prefix Sums: Develop strategies for solving diverse problems by incorporating prefix sums, from optimizing sequence operations to speeding up specific algorithms.