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
540
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
Return of the Full-Stack Developer
simas
PRO
1
300
技術好きなエンジニアが "リーダーへの進化" によって得たものと失ったもの
pospome
5
1.3k
Effective Signals in Angular 19+ Rules and Helpers
manfredsteyer
PRO
0
160
requirements with math
moony
0
490
研究開発と実装OSSと プロダクトの好循環 / A virtuous cycle of research and development implementation OSS and products
linyows
1
180
RCPと宣言型ポリシーについてのお話し
kokitamura
2
130
私の愛したLaravel 〜レールを超えたその先へ〜
kentaroutakeda
11
2.7k
GDG Super.init(version=6) - From Where to Wear : 모바일 개발자가 워치에서 발견한 인사이트
haeti2
0
520
SLI/SLOの設定を進めるその前に アラート品質の改善に取り組んだ話
tanden
2
420
PHPによる"非"構造化プログラミング入門 -本当に熱いスパゲティコードを求めて- #phperkaigi
o0h
PRO
0
720
Devin入門と最近のアップデートから見るDevinの進化 / Introduction to Devin and the Evolution of Devin as Seen in Recent Update
rkaga
0
380
Functional APIから再考するLangGraphを使う理由
os1ma
4
630
Featured
See All Featured
[Rails World 2023 - Day 1 Closing Keynote] - The Magic of Rails
eileencodes
33
2.1k
Keith and Marios Guide to Fast Websites
keithpitt
411
22k
Site-Speed That Sticks
csswizardry
4
440
The Power of CSS Pseudo Elements
geoffreycrofte
75
5.7k
The Myth of the Modular Monolith - Day 2 Keynote - Rails World 2024
eileencodes
22
2.6k
Code Reviewing Like a Champion
maltzj
521
39k
Building Adaptive Systems
keathley
40
2.4k
GraphQLの誤解/rethinking-graphql
sonatard
69
10k
Thoughts on Productivity
jonyablonski
69
4.5k
GitHub's CSS Performance
jonrohan
1030
460k
Designing Experiences People Love
moore
140
23k
For a Future-Friendly Web
brad_frost
176
9.6k
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