Range Queries

  • Antti LaaksonenEmail author
Part of the Undergraduate Topics in Computer Science book series (UTICS)


In this chapter, we discuss data structures for efficiently processing range queries on arrays. Typical queries are range sum queries (calculating the sum of values) and range minimum queries (finding the minimum value). Section 9.1 focuses on a simple situation where the array values are not modified between the queries. In this case it suffices to preprocess the array so that we can efficiently determine the answer for any possible query. We will first learn to process sum queries using a prefix sum array, and then we will discuss the sparse table algorithm for processing minimum queries. Section 9.2 presents two tree structures that allow us to both process queries and update array values efficiently. A binary indexed tree supports sum queries and can be seen as a dynamic version of a prefix sum array. A segment tree is a more versatile structure that supports sum queries, minimum queries, and several other queries. The operations of both the structures work in logarithmic time.

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of HelsinkiHelsinkiFinland

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