48 lines
1.6 KiB
Text
48 lines
1.6 KiB
Text
---
|
|
id: PURQ
|
|
title: "Point Update Range Query"
|
|
author: Benjamin Qi
|
|
prerequisites:
|
|
description: Range queries for any associative operation over an array with updates using segment tree.
|
|
frequency: 1
|
|
---
|
|
|
|
import { Problem } from "../models";
|
|
|
|
export const metadata = {
|
|
problems: {
|
|
sample: [
|
|
new Problem("YS", "Point Set Range Composite", "point_set_range_composite", "Intro", false, ["PURQ"], ""),
|
|
],
|
|
probs: [
|
|
new Problem("CSES", "Range Minimum Queries II", "1649", "Intro", false, ["PURQ"], ""),
|
|
new Problem("Gold", "Springboards", "995", "Normal", false, ["PURQ"], "min segtree"),
|
|
new Problem("Plat", "Nocross", "721", "Normal", false, ["PURQ"], "LIS variation"),
|
|
]
|
|
}
|
|
};
|
|
|
|
<problems-list problems={metadata.problems.sample} />
|
|
|
|
A **segment tree** allows you to do point update and range query in $O(\log N)$ time each for any associative operation.
|
|
|
|
<info-block title="Pro Tip">
|
|
|
|
For gold, you only need to know the basics (ex. sum, min queries). More advanced applications (such as *lazy propagation*) are restricted to platinum.
|
|
|
|
</info-block>
|
|
|
|
### Tutorials
|
|
|
|
- CPH 9.3 (Segment Trees)
|
|
- [PAPS 11.2.3](https://www.csc.kth.se/~jsannemo/slask/main.pdf)
|
|
- [Codeforces Tutorial](http://codeforces.com/blog/entry/18051)
|
|
- [CSAcademy Tutorial](https://csacademy.com/lesson/segment_trees/)
|
|
- [cp-algorithms](https://cp-algorithms.com/data_structures/segment_tree.html)
|
|
- [Slides from CPC.3](https://github.com/SuprDewd/T-414-AFLV/tree/master/03_data_structures)
|
|
|
|
### Problems
|
|
|
|
Can also try solving some of the BIT questions w/ segtree.
|
|
|
|
<problems-list problems={metadata.problems.general} />
|