Summation Prove (Intro. to Algo. Open Course Episode 5) in Quick Sort
2017-09-24 18:59
357 查看
When I prove the expectation of Randomized Quick Sort, I use the following fact. Therefore, I need to prove it.
Prove:
Sn=∑k=2n−1klgk≤12n2lgn−18n2
Solve:
∑k=2n−1klgk<∫n−12klgkdk<∫n2klgkdk(klgk>0)
Integration by parts
Sn<12k2lgk|n2−12∫n2k21kln2dk=12n2lgn−2lg2−(ln24n2−ln2)=12n2lgn−ln24n2+ln2−2<12n2lgn−ln24n2(ln2−2<0)<12n2lgn−18n2(ln2>12)
The problem is solved.
Prove:
Sn=∑k=2n−1klgk≤12n2lgn−18n2
Solve:
∑k=2n−1klgk<∫n−12klgkdk<∫n2klgkdk(klgk>0)
Integration by parts
Sn<12k2lgk|n2−12∫n2k21kln2dk=12n2lgn−2lg2−(ln24n2−ln2)=12n2lgn−ln24n2+ln2−2<12n2lgn−ln24n2(ln2−2<0)<12n2lgn−18n2(ln2>12)
The problem is solved.
相关文章推荐
- Intro-to-algo (counting sort, radix sort, decis...
- How to search a table in a store proc and open the store proc
- Error:Failed to resolve: junit:junit:4.12 <a href="open.dependency.in.project.structure">Show in Pro
- QT29 how to use QWebView and open web page in QWebView
- Open Baidu webpage and type in Chinese characters to start searching, press “Back” button to go to B
- What does Quick Sort look like in Python?
- Lamp环境下编写PHP代码时出现错误:Warning: Unknown: failed to open stream: Permission denied in Unknown on line 0
- How to change the name in open with list / File association.
- (转) Quick Guide to Build a Recommendation Engine in Python
- “unable to open user login file\\服务器项目管理目录\data\logedin\用户名.log ”
- Cannot open virtual machine:This virtual machine appears to be in use
- Use PSO to find minimum in OpenCASCADE
- The best way to configure the student course table in Hibernate
- 8 quick ways to clear up drive space in Windows 10
- How to open PDF files in sharepoint
- linux下的LAMP环境中的问题:failed to open stream: Permission denied in
- Silktest2011:How to get Browser type in openagent model?
- Apply Newton Method to Find Extrema in OPEN CASCADE
- How to open UITextView web links in a UIWebView instead of Safari?
- How To Open Block Material in SAP MM?