usaco-guide/content/Silver/Silver_Psum.md

Silver - Prefix Sums

(started by eric wei; not done)

The Task

Given an array of size N, answer Q queries of the following form: Find the sum of all elements between indices i and j.

• CSES Range Sum Queries I

Tutorials

(This technique is also known as cumulative sum or partial sums.) See Ch 11 of https://www.overleaf.com/project/5e73f65cde1d010001224d8a

• CPH 9.1
• aka Cumulative Sum, Partial Sums
• 2D

Extensions

2D Prefix Sums

Given a 2-Dimension array of size NxM, answer Q queries of the following form: Find the sum of all elements within the rectangle of indices (x1,y1) to (x2,y2).

• CSES Forest Queries

Difference Array

Consider the array formed by a_i-a_{i-1}.

• USACO Painting the Barn (i should find an easier one because this is hard)

Prefix Minimum, Etc.

Using