55 lines
1.9 KiB
Text
55 lines
1.9 KiB
Text
---
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id: PURQ
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title: "Point Update Range Query"
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author: Benjamin Qi
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prerequisites:
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description: Range queries for any associative operation over an array with updates using segment tree.
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frequency: 1
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---
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import { Problem } from "../models";
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export const metadata = {
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problems: {
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sample: [
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new Problem("YS", "Point Set Range Composite", "point_set_range_composite", "Intro", false, ["PURQ"], ""),
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],
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general: [
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new Problem("CSES", "Range Minimum Queries II", "1649", "Intro", false, ["PURQ"], ""),
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new Problem("Gold", "Springboards", "995", "Normal", false, ["PURQ"], "min segtree"),
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new Problem("Plat", "Nocross", "721", "Normal", false, ["PURQ"], "LIS variation"),
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new Problem("Plat", "Slingshot", "816", "Hard", false, ["PURQ"], ""),
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]
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}
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};
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<problems-list problems={metadata.problems.sample} />
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<br/>
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A **segment tree** allows you to do point update and range query in $O(\log N)$ time each for any associative operation.
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### Tutorials
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<info-block title="Pro Tip">
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For gold, you only need to know the basics (ex. sum, min queries). You can skip more advanced applications such as **lazy propagation** for now.
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</info-block>
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<resources>
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<resource source="CSA" title="Segment Trees" url="segment_trees" starred>interactive</resource>
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<resource source="CF" title="Efficient and easy segment trees" url="blog/entry/18051" starred>simple implementation</resource>
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<resource source="CPH" title="9.3 - Segment Trees" starred>same implementation as above</resource>
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<resource source="CPC" title="3 - Data Structures" url="03_data_structures" starred>see slides after union-find</resource>
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<resource source="cp-algo" title="Segment Tree" url="data_structures/segment_tree.html" starred></resource>
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<resource source="PAPS" title="11.2.3"></resource>
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</resources>
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### Problems
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Can also try solving some of the BIT questions with segtree.
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<problems-list problems={metadata.problems.general} />
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