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usaco-guide/content/5_Gold/Tree_Euler.mdx
2020-06-26 23:07:31 -04:00

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