usaco-guide/content/2_Silver/6_Silver_Psum.md

---
slug: /silver/prefix-sums
title: "Prefix Sums"
author: Eric Wei (incomplete)
order: 6
---

<div class="syllabus-only">
  Description: Todo
</div>

<!-- END DESCRIPTION -->

## 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](https://cses.fi/problemset/task/1646)

## 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

## 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](https://cses.fi/problemset/task/1652)

### Difference Array

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

 - [USACO Painting the Barn](http://www.usaco.org/index.php?page=viewproblem2&cpid=919) (i should find an easier one because this is hard)

### Prefix Minimum, Etc.

Using
add frontmatter to all modules 2020-06-04 01:42:57 +00:00			`---`
			`slug: /silver/prefix-sums`
update frontmatter for all modules 2020-06-04 05:39:49 +00:00			`title: "Prefix Sums"`
upd silver psum 2020-06-04 02:16:50 +00:00			`author: Eric Wei (incomplete)`
update frontmatter for all modules 2020-06-04 05:39:49 +00:00			`order: 6`
add frontmatter to all modules 2020-06-04 01:42:57 +00:00			`---`

update frontmatter for all modules 2020-06-04 05:39:49 +00:00			`<div class="syllabus-only">`
			`Description: Todo`
			`</div>`
+ hashing, add #s 2020-06-03 20:16:33 +00:00
update frontmatter for all modules 2020-06-04 05:39:49 +00:00			`<!-- END DESCRIPTION -->`
upd silver psum 2020-06-04 02:16:50 +00:00
			`## 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](https://cses.fi/problemset/task/1646)`

			`## Tutorials`

			`(This technique is also known as cumulative sum or partial sums.)`

+ hashing, add #s 2020-06-03 20:16:33 +00:00			`See Ch 11 of https://www.overleaf.com/project/5e73f65cde1d010001224d8a`

upd silver psum 2020-06-04 02:16:50 +00:00			`- CPH 9.1`

			`## 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](https://cses.fi/problemset/task/1652)`

			`### Difference Array`

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

			`- [USACO Painting the Barn](http://www.usaco.org/index.php?page=viewproblem2&cpid=919) (i should find an easier one because this is hard)`

			`### Prefix Minimum, Etc.`

			`Using`