Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
Segment Tree Basics
Search
halfrost
January 15, 2020
Programming
0
940
Segment Tree Basics
halfrost
January 15, 2020
Tweet
Share
More Decks by halfrost
See All by halfrost
Redis multi-data center two-way synchronization
halfrost
0
580
Redis design ideas and usage specifications
halfrost
0
420
Golang message streaming practice in Eleme
halfrost
0
410
SQL practical optimization
halfrost
0
400
Fundamentals of Cryptography
halfrost
0
310
The practice of spatial index in geographic service
halfrost
0
400
Getting started with Machine Learning
halfrost
0
300
Functional Reactive Programming
halfrost
0
320
Eleme Report
halfrost
1
370
Other Decks in Programming
See All in Programming
今ならAmazon ECSのサービス間通信をどう選ぶか / Selection of ECS Interservice Communication 2025
tkikuc
11
2.8k
Claude Codeの使い方
ttnyt8701
1
130
来たるべき 8.0 に備えて React 19 新機能と React Router 固有機能の取捨選択とすり合わせを考える
oukayuka
2
820
セキュリティマネジャー廃止とクラウドネイティブ型サンドボックス活用
kazumura
1
190
LINEヤフー データグループ紹介
lycorp_recruit_jp
0
760
Effect の双対、Coeffect
yukikurage
5
1.4k
Java on Azure で LangGraph!
kohei3110
0
160
アンドパッドの Go 勉強会「 gopher 会」とその内容の紹介
andpad
0
250
AWS CDKの推しポイント 〜CloudFormationと比較してみた〜
akihisaikeda
3
290
Datadog RUM 本番導入までの道
shinter61
1
310
実践ArchUnit ~実例による検証パターンの紹介~
ogiwarat
2
280
Cursor Meetup Tokyo ゲノミクスとCursor: 進化と制約のあいだ
koido
2
1.1k
Featured
See All Featured
XXLCSS - How to scale CSS and keep your sanity
sugarenia
248
1.3M
The Myth of the Modular Monolith - Day 2 Keynote - Rails World 2024
eileencodes
26
2.8k
Embracing the Ebb and Flow
colly
86
4.7k
Practical Tips for Bootstrapping Information Extraction Pipelines
honnibal
PRO
20
1.3k
Measuring & Analyzing Core Web Vitals
bluesmoon
7
490
The Success of Rails: Ensuring Growth for the Next 100 Years
eileencodes
45
7.4k
Building Applications with DynamoDB
mza
95
6.5k
[Rails World 2023 - Day 1 Closing Keynote] - The Magic of Rails
eileencodes
35
2.3k
Designing for Performance
lara
609
69k
Code Review Best Practice
trishagee
68
18k
Typedesign – Prime Four
hannesfritz
42
2.7k
Learning to Love Humans: Emotional Interface Design
aarron
273
40k
Transcript
Segment Tree 基础篇
Range Minimum/Maximum Query •需求:在饿了么的⼀个⽤户的历史订单中,找出该⽤户指定⼀段 时间内单笔订单最贵/最便宜的订单 One problem •O(n), when query
K —> ∞ times ?
Range Minimum/Maximum Query •需求:在饿了么的⼀个⽤户的历史订单中,求出找出该⽤户指定 ⼀段时间内累积消费总⾦额 Another problem •O(n), when query
K —> ∞ times ? •prefixSum, time O(n), query O(1)
Range Minimum/Maximum Query •需求:在 12306 ⽹站上,统计⼀条线路上任意指定两个站点之间 的可售出的票数总和 One more thing
•O(n), when query K —> ∞ times ? •prefixSum, time O(n), update O(n), query O(1)
How to ? Range Minimum/Maximum Query 5 O(log n) or
O(1) ?
Presentation agenda 6 What How to use Leetcode example What
is segment tree 2 3 1 How Example
Define Segment Tree 7 1. ❌ Complete Binary Tree 2.
∈ Balanced Binary Tree 3. As Full binary tree
How many node Segment Tree 8 0-level : 1 1-level
: 2 2-level : 4 3-level : 8 4-level : 16 (n-1)—level :2^(n-1) n-level:2^n Σ 0-(n-1) level:Σ = 2^n - 1 ≈ n-level => 2n Mathematical Induction:Σ = 4n (n = 2^k or n = 2^k + 1)
How many node Segment Tree 9 •When n≥3, [1,n] segment
split [1,n] into 2*⌊log (n-1)⌋ sub- Interval •4n ≥ 2*⌊log (n-1)⌋ <= 2n ≥ log (n-1) <= 4^n ≥ n-1
How to create Segment Tree 10
How to query Segment Tree 11 ❗
How to update Segment Tree 12 ❗
How to update Segment Tree 13 •Update [2,3] ? •❌
O(n)
How to update Segment Tree 14 •Update [2,3] ? •✅O(log
n)
How to update Segment Tree 15
How to query Segment Tree 16 •push_down
How to update Segment Tree 17 •push_down + push_up
How to low space Segment Tree 18 •Leetcode 715
Compared ST VS Array 19 20% 80% 60% 40% 2585
785 Update: Array O(n) | Segment Tree O(log n) Query: Array O(n) | Segment Tree O(log n)
Segment Tree 20 Example
Segment Tree 21 Example
Segment Tree 22 Example
Boyer-Moore Majority Vote Algorithm 23 Example
Segment Tree 24 Example
Segment Tree 25 Example •judge threshold •count = map[1:[0 1
4 5] 2:[2 3]] •eg: 1 in [0,5] count , twice binary search, find [lowerBound, upperBound) •(upperBound - lowerBound) ≥ threshold
Segment Tree 26 •Leetcode 327. Count of Range Sum •Leetcode
715. Range Module •Leetcode 699. Falling Squares & 732. My Calendar III •Leetcode 850. Rectangle Area II •Leetcode 218. The Skyline Problem Exercise
Advance 27 15% 35% 50% •One point update (update: min/change,
query: sum/min) •Interval update (update: min/change, query: sum/hash) •Discretization •Interval merge •Scan line •Binary Index Tree