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usaco-guide/content/6_Plat/RURQ.mdx
2020-06-26 20:33:06 -04:00

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---
id: RURQ
title: "Range Update Range Query"
author: Benjamin Qi
prerequisites:
- Gold - Point Update Range Query
description: Lazy updates on segment trees and two binary indexed trees in conjunction.
frequency: 1
---
import { Problem } from "../models";
export const metadata = {
problems: {
bitSample: [
new Problem("SPOJ", "Horrible Queries", "HORRIBLE", "Easy", false, ["BIT-Range"], ""),
],
bitProb: [
new Problem("CSES", "Polynomial Queries", "1736", "Normal", false, ["BIT-Range"], "equivalent to https://dmoj.ca/problem/acc3p4"),
],
lazySample: [
new Problem("CSES", "Range Updates & Sums", "1735", "Easy", false, ["Lazy SegTree"], ""),
],
lazySegTree: [
new Problem("YS", "Range Affine Range Sum", "range_affine_range_sum", "Easy", false, ["Lazy SegTree"], ""),
new Problem("Plat", "Counting Haybales", "578", "Easy", false, ["Lazy SegTree"], ""),
new Problem("Old Gold", "The Lazy Cow", "418", "Easy", false, ["Lazy SegTree"], ""),
],
lazySegCnt: [
new Problem("CSES", "Area of Rectangles", "1741", "Hard", false, ["Lazy SegTree"], ""),
new Problem("HR", "Strange Tree", "https://www.hackerrank.com/contests/openbracket-2017/challenges/special-path-on-a-strange-tree/problem", "Hard", false, ["Lazy SegTree"]),
],
segTreeBeats: [
new Problem("YS", "Range Chmin Chmax Add Range Sum", "range_chmin_chmax_add_range_sum", "Very Hard", false, ["SegTreeBeats"], ""),
],
}
};
## BIT Revisited
<problems-list problems={metadata.problems.bitSample} />
Binary Indexed Trees can support range increments in addition to range sum queries.
### Tutorial
<resources>
<resource source="GFG" title="Range Update Point Query" url="binary-indexed-tree-range-updates-point-queries/"></resource>
<resource source="GFG" title="Range Update Range Query" url="binary-indexed-tree-range-update-range-queries/"></resource>
</resources>
[My Implementation](https://github.com/bqi343/USACO/blob/master/Implementations/content/data-structures/1D%20Range%20Queries%20(9.2)/BITrange.h)
### Problems
<problems-list problems={metadata.problems.bitProb} />
## Lazy Segment Tree
<problems-list problems={metadata.problems.lazySample} />
### Tutorial
- CPH 28.1 (Segment Trees Revisited)
### Problems
<problems-list problems={metadata.problems.lazySegTree} />
## Lazy Segment Tree - Counting Minimums
use segment tree that keeps track of minimum and # of minimums
<problems-list problems={metadata.problems.lazySegCnt} />
## Segment Tree Beats
### Tutorial
<resources>
<resource source="CF" title="Intro to Segment Tree Beats" url="blog/entry/57319"></resource>
</resources>
### Problems
<problems-list problems={metadata.problems.segTreeBeats} />
(300iq insane problem)