usaco-guide/content/5_Gold/Tree_Euler.mdx

---
id: tree-euler
title: "Euler Tour on Tree"
author: "?"
prerequisites: 
 - Silver - Depth First Search
 - Gold - Static Range Queries
 - Gold - Point Update Range Sum
description: Subtree updates and queries as well as a way to compute lowest common ancestors.
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"),
    ],
    lca: [
      new Problem("CSES", "Company Queries II", "1688", "Easy", false, ["LCA"], ""),
    ],
    problems: [
      new Problem("CSES", "Distance Queries", "1135", "Easy", false, ["LCA"], ""),
      new Problem("CSES", "Path Queries", "1138", "Easy", false, ["Euler-Tree","PURS"], "equivalent to https://judge.yosupo.jp/problem/vertex_add_path_sum"),
      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} />

### Tutorial

  - CPH 18.2 - Subtrees & Paths

## LCA

### Tutorial

 - CPH 18.3 - Least Common Ancestor
  - [cp-algorithms - LCA with Sparse Table](https://cp-algorithms.com/graph/lca.html)

(implementation)

## Problems

<problems-list problems={metadata.problems.problems} />