27 lines
980 B
Markdown
27 lines
980 B
Markdown
# 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](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
|
|
- 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](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
|