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As a final example of recursion in practice, let s have a look at the algorithm called binary search. You probably know of the game where you are supposed to guess what someone is thinking about by asking 20 yes-or-no questions. To make the most of your questions, you try to cut the number of possibilities in (more or less) half. For example, if you know the subject is a person, you might ask Are you thinking of a woman You don t start by asking Are you thinking of John Cleese unless you have a very strong hunch. A version of this game for those more

Note There are two ways to create a password_hash through the API. You can set a basic md5 hash such as

Tip If you are new to MySQL, we highly recommend that you also install MySQL Query Browser and MySQL Administrator, which both can be downloaded from the MySQL Developer Zone page. MySQL Administrator, as its name implies, can be used for managing your MySQL sever. MySQL Query Browser allows you to run SQL queries and scripts from a graphical user interface. Both applications are available for Linux, Windows, and Mac OS X. If you re using OS X, a good application for both managing your databases and executing queries is CocoaMySQL (www.theonline.org/cocoamysql/).

the following:

Open a console window and execute the following command to start MySQL: $ mysqld_safe --user=mysql & The command starts the MySQL server in the background using the mysql user. Verify that you can connect to the database with the following command: $ mysql -u root You should see the following: Welcome to the MySQL monitor. Commands end with ; or \g. Your MySQL connection id is 2 to server version: 5.0.19-standard Type 'help;' or '\h' for help. Type '\c' to clear the buffer. mysql>

numerically inclined is to guess a number For example, your partner is thinking of a number between 1 and 100, and you have to guess which one it is Of course, you could do it in a hundred guesses, but how many do you really need As it turns out, you only need seven questions The first one is something like Is the number greater than 50 If it is, then you ask Is it greater than 75 You keep halving the interval until you find the number You can do this without much thought The same tactic can be used in many different contexts One common problem is to find out whether a number is to be found in a (sorted) sequence, and even to find out where it is.

$data = array( 'firstname' => 'John', 'lastname' => 'Doe', 'password_hash' => md5('secret') );

Ruby on Rails needs a database driver to communicate with the MySQL server. Ruby on Rails comes with a pure Ruby MySQL driver, but we want to use the native C driver written by Tomita Masahiro, as it is considerably faster.

Again, you follow the same procedure: Is the number to the right of the middle of the sequence If it isn t, Is it in the second quarter (to the right of the middle of the left half) and so on You keep an upper and a lower limit to where the number may be, and keep splitting that interval in two with every question The point is that this algorithm lends itself naturally to a recursive definition and implementation Let s review the definition first, to make sure we know what we re doing: If the upper and lower limits are the same, they both refer to the correct position of the number, so return it Otherwise, find the middle of the interval (the average of the upper and lower bound), and find out if the number is in the right or left half.

You can also include a salt through the following method:

Note Each database requires a different driver, since there is no standard protocol. For more information