---
id: seg-ext
title: "More Applications of Segment Tree"
author: Benjamin Qi
prerequisites: 
 - Gold - Static Range Queries
 - Gold - Point Update Range Query
description: "?"
frequency: 3
---

import { Problem } from "../models";

export const metadata = {
  problems: {
    walkSam: [
      new Problem("CSES", "Hotel Queries", "1143", "Easy", false, ["PURQ"], "walk"),
    ],
    walk: [
      new Problem("Old Gold", "Seating", "231", "Normal", false, [], "walk on max segtree"),
      new Problem("Plat", "Balancing", "624", "Normal", false, [], "walk"),
    ],
    combSam: [
      new Problem("CSES", "Subarray Sum Queries", "1190", "Normal", false, ["PURQ"], "comb"),
    ],
    comb: [
      new Problem("Plat", "High Card Low Card", "577", "Normal", false, ["PURQ", "Greedy"], "comb"),
      new Problem("POI", "Cards", "https://szkopul.edu.pl/problemset/problem/qpsk3ygf8MU7D_1Es0oc_xd8/site/?key=statement", "Normal", false, [], "comb"),
      new Problem("Old Gold", "Marathon", "495", "Normal", false, [], "comb"),
      new Problem("Old Gold", "Optimal Milking", "365", "Normal", false, [], "comb"),
    ],
    waveletSam: [
      new Problem("YS", "Range K-th Smallest", "range_kth_smallest", "Hard", false, ["Wavelet"], ""),
    ],
    wavelet: [
      new Problem("Kattis", "Easy Query", "easyquery", "Hard", false, ["Wavelet"], ""),
      new Problem("DMOJ", "Ninjaclasher's Wrath 2", "globexcup19s4", "Hard", false, ["Wavelet"], ""),
    ],
  }
};

## Walking on a Segment Tree

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

You want to support queries of the following form on an array $a_1,\ldots,a_N$ (along with point updates).

> Find the first $i$ such that $a_i\ge x$.

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.

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

## Combining

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

(solution to above problem)

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

## Wavelet Tree

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

### Tutorial

<resources>
  <resource source="CF" title="Intro to New DS: Wavelet Trees" url="blog/entry/52854"></resource>
</resources>

### Problems

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