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
910
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
550
Redis design ideas and usage specifications
halfrost
0
410
Golang message streaming practice in Eleme
halfrost
0
390
SQL practical optimization
halfrost
0
380
Fundamentals of Cryptography
halfrost
0
300
The practice of spatial index in geographic service
halfrost
0
380
Getting started with Machine Learning
halfrost
0
280
Functional Reactive Programming
halfrost
0
310
Eleme Report
halfrost
1
360
Other Decks in Programming
See All in Programming
ベクトル検索システムの気持ち
monochromegane
29
8.7k
生産性アップのためのAI個人活用
kunoyasu
0
480
List とは何か? / PHPerKaigi 2025
meihei3
0
520
RubyKaigiで手に入れた HHKB Studioのための HIDRawドライバ
iberianpig
0
340
GDG Super.init(version=6) - From Where to Wear : 모바일 개발자가 워치에서 발견한 인사이트
haeti2
0
550
Gunma.web #55
tinykitten
0
130
家族・子育て重視/沖縄在住を維持しながらエンジニアとしてのキャリアをどのように育てていくか?
ug
0
230
Return of the Full-Stack Developer
simas
PRO
1
310
Develop Faster With FrankenPHP
dunglas
2
2.3k
複雑なフォームと複雑な状態管理にどう向き合うか / #newt_techtalk vol. 15
izumin5210
4
2.7k
php-fpm がリクエスト処理する仕組みを追う / Tracing-How-php-fpm-Handles-Requests
shin1x1
5
810
PHPでお金を扱う時、終わりのない 謎の1円調査の旅にでなくて済む方法
nakka
3
980
Featured
See All Featured
VelocityConf: Rendering Performance Case Studies
addyosmani
328
24k
Making Projects Easy
brettharned
116
6.1k
JavaScript: Past, Present, and Future - NDC Porto 2020
reverentgeek
47
5.3k
Embracing the Ebb and Flow
colly
84
4.6k
Into the Great Unknown - MozCon
thekraken
35
1.7k
Building an army of robots
kneath
304
45k
Product Roadmaps are Hard
iamctodd
PRO
52
11k
Mobile First: as difficult as doing things right
swwweet
223
9.5k
Fight the Zombie Pattern Library - RWD Summit 2016
marcelosomers
233
17k
4 Signs Your Business is Dying
shpigford
183
22k
Art, The Web, and Tiny UX
lynnandtonic
298
20k
Distributed Sagas: A Protocol for Coordinating Microservices
caitiem20
331
21k
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