62 lines
2.1 KiB
Text
62 lines
2.1 KiB
Text
---
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id: tree-euler
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title: "Euler Tour Technique"
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author: "?"
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prerequisites:
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- Silver - Depth First Search
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- Gold - Static Range Queries
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- Gold - Point Update Range Sum
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description: Flattening a tree into an array.
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frequency: 2
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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("CSES", "Subtree Queries", "1137", "Easy", false, ["Euler-Tree"], "equivalent to https://judge.yosupo.jp/problem/vertex_add_subtree_sum"),
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new Problem("CSES", "Path Queries", "1138", "Easy", false, ["Euler-Tree","PURS"], "equivalent to https://judge.yosupo.jp/problem/vertex_add_path_sum"),
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],
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lca: [
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new Problem("CSES", "Company Queries II", "1688", "Easy", false, ["LCA"], ""),
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new Problem("CSES", "Distance Queries", "1135", "Easy", false, ["LCA"], ""),
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],
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problems: [
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new Problem("Gold", "Cow Land", "921", "Normal", false, ["Euler-Tree","PURS", "HLD"], ""),
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new Problem("Gold", "Milk Visits", "970", "Normal", false, ["Euler-Tree", "LCA"], ""),
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new Problem("Plat", "Promotion Counting", "696", "Normal", false, ["Euler-Tree","PURS"], ""),
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new Problem("ojuz", "IOI Regions", "IOI09_regions", "Hard", false, ["Euler-Tree", "Binary Search"], ""),
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new Problem("Plat", "Snow-Cow", "973", "Hard", false, ["Euler-Tree","PURS"], ""),
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]
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}
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};
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## Introduction
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<problems-list problems={metadata.problems.sample} />
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If we can preprocess a rooted tree such that every subtree corresponds to a contiguous range on an array, we can do updates and range queries on it!
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### Tutorial
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<resources>
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<resource source="CPH" title="18.2 - Subtrees & Paths" starred>introduces tree traversal array</resource>
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</resources>
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## LCA
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<problems-list problems={metadata.problems.lca} />
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### Tutorial
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<resources>
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<resource source="CPH" title="18.3 - Least Common Ancestor (Method 2)" starred></resource>
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<resource source="cp-algo" title="Reducing LCA to RMQ" url="graph/lca.html" starred></resource>
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</resources>
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(implementation)
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## Problems
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<problems-list problems={metadata.problems.problems} /> |