Notes: Algorithms

Lower Bound:

Any algorithm must take Ω(g(n)) time to solve the problem.

Upper Bound: No More than
Lower Bound: No Less than

My First Adsense Earning

After one year, I finally got my Adsense earning. Thanks to all the visitors of my blog. This motivates me to scan and upload some more of my physics problem solutions.

Chuang Tzu

Take a foot-long stick, cut it in half every day, you'd never come to the end.” -Chuang Tzu

Given the most powerful tools today, cutting a foot-long stick half every day would only take you roughly 50 days to reach the point where you only have a single nucleon to work with. Technically it is the end, since until now no one has been able to separate quarks from each other. A nucleon of course is made of up three quarks. In this sense, Chuang Tzu is wrong.

However, it can be argued that you can try to separate quarks, albeit very briefly, by colliding two nucleons after accelerating it close to the speed of light. By doing this you would just create more particles. In an effort to further “divide” a nucleon, you will end up having extra particles to worry about (Are they still part of the stick or not?, Do I have to continue “cutting” these in half too?, etc..). In this sense, you'd never come to an end. You will always have a particle which isn't elementary as we know it (quarks, leptons or guage bosons) to “cut”. If you take this line of argument, Chuang Tzu is correct.

Install ROOT on Macbook Air 2010 11" Running OSX Lion

I. Getting the source

To install ROOT from source you first have to get the tar file containing the source. This tar file can be found in the usual ROOT download area (ftp://root.cern.ch/root). The files are named
root-.source.tar.gz.

Here's a short summary:

1) Get access to the FTP area (substitute any FTP client and appropriate
   email address below):

     prompt% ftp root.cern.ch
     User: anonymous
     Password:

2) Go to the directory, and prepare for binary transfer of files:

     ftp> cd /root
     ftp> bin

3) Get the sources tar-ball (substitute the appropriate version
   number), and exit FTP client:

     ftp> get root-.source.tar.gz
     ftp> bye

4) Unpack the distribution:

     prompt% gzip -dc root_v5.32.00.source.tar.gz | tar -xf -

II. Getting ready to build

You may want to compile features into ROOT, which depends on third party libraries. For OS X, all  you need to do is install Xcode. To install Xcode,

1) Go to the App Store then search Xcode. Click install (This will actually download Xcode installer instead of installing it).

2) When it is "done", go to the Applications folder and click on the "Install Xcode" file to install Xcode.


III. Install ROOT

1) Run the following commands to install ROOT:

       ./configure macosx64 --prefix=/usr/local
       make -j2
       gmake install