75 lines
2.3 KiB
Text
75 lines
2.3 KiB
Text
---
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id: seg-ext
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title: "More Applications of Segment Tree"
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author: Benjamin Qi
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prerequisites:
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- Gold - Static Range Queries
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- Gold - Point Update Range Query
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description: "?"
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frequency: 3
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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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walkSam: [
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new Problem("CSES", "Hotel Queries", "1143", "Easy", false, ["PURQ"], "walk"),
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],
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walk: [
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new Problem("Old Gold", "Seating", "231", "Normal", false, [], "walk on max segtree"),
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new Problem("Plat", "Balancing", "624", "Normal", false, [], "walk"),
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],
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combSam: [
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new Problem("CSES", "Subarray Sum Queries", "1190", "Normal", false, ["PURQ"], "comb"),
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],
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comb: [
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new Problem("Old Gold", "Marathon", "495", "Easy", false, [], "comb"),
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new Problem("Old Gold", "Optimal Milking", "365", "Normal", false, [], "comb"),
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new Problem("POI", "Cards", "https://szkopul.edu.pl/problemset/problem/qpsk3ygf8MU7D_1Es0oc_xd8/site/?key=statement", "Normal", false, [], "comb"),
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new Problem("Plat", "High Card Low Card", "577", "Normal", false, ["PURQ", "Greedy"], "comb"),
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],
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waveletSam: [
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new Problem("YS", "Range K-th Smallest", "range_kth_smallest", "Normal", false, ["Wavelet"], ""),
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],
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wavelet: [
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new Problem("Kattis", "Easy Query", "easyquery", "Hard", false, ["Wavelet"], ""),
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new Problem("DMOJ", "Ninjaclasher's Wrath 2", "globexcup19s4", "Hard", false, ["Wavelet"], ""),
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],
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}
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};
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## Walking on a Segment Tree
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<problems-list problems={metadata.problems.walkSam} />
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You want to support queries of the following form on an array $a_1,\ldots,a_N$ (along with point updates).
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> Find the first $i$ such that $a_i\ge x$.
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Of course, you can do this in $O(\log^2N)$ time with a max segment tree and binary searching on the first $i$ such that $\max(a_1,\ldots,a_i)\ge x$. But try to do this in $O(\log N)$ time.
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<problems-list problems={metadata.problems.walk} />
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## Combining
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<problems-list problems={metadata.problems.combSam} />
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(solution to above problem)
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<problems-list problems={metadata.problems.comb} />
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## Wavelet Tree
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<problems-list problems={metadata.problems.waveletSam} />
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### Tutorial
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<resources>
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<resource source="CF" title="Intro to New DS: Wavelet Trees" url="blog/entry/52854"></resource>
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</resources>
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### Problems
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<problems-list problems={metadata.problems.wavelet} />
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