Ubuntu forgot password

If you don't remember any of your Ubuntu passwords while logging in,
then,
from the boot menu,
select -> Recovery Mode(Ubuntu, not Windows),
then select -> drop root shell
You will get a shell where you would be logged in as root.
There type :
passwd <username>
and change the password.
Reboot.
done.

Non recursive algorithm for Post Order Traversal

For Pre,Post and In order traversals of a Binary tree,

it is very easy to write recursive programs/algorithms.

But when it comes to a non-recursive solution, it becomes

rather difficult. Though pre-order and in-order traversals

have non-recursive algorithms, which are slightly easier

to implement/understand, post-order is a tough nut to

crack.

Not any more.
Here is an easy to understand non-recursive algorithm

for post-order traversal :

Fact I : Post order traversal(Left-Right-Root) is the exact opposite

of Root-Right-Left traversal(RoRiL)(Prove it!).

Fact II : And a non-recursive algo for Pre-order(RoLRi) is equally good

for RoRiL.

So, just use the non-recursive algo for RoRiL(which is similar to Pre-order)

and traverse it backwards.(that's the post order traversal)

(Pre-order Non Recursive Algorithm)

Rabbit poupulation Fibonacci sequence

Question :
A young pair of rabbits (one of each sex) is placed on an island. A pair
of rabbits does not breed until they are 2 months old. After they are
2 months old, each pair of rabbits produces another pair each month.
Find a recurrence relation for the number of rabbits on the island
after n months, assuming that no rabbits ever die.

Solution :
Suppose there are A_n rabbits after n months.
Then number of rabbits born in (n+1)th month is : A_n+1 - A_n.
A_n+2
= 2*number of rabbits in nth month + number of rabbits born in (n+1)th month.
= 2*A_n + A_n+1 - A_n
= A_n + A_n+1
= Fibonacci sequence

Fibonacci sequence, rabbit population

Question :
A young pair of rabbits (one of each sex) is placed on an island. A pair
of rabbits does not breed until they are 2 months old. After they are
2 months old, each pair of rabbits produces another pair each month.
Find a recurrence relation for the number of rabbits on the island
after n months, assuming that no rabbits ever die.

Solution :
Suppose there are A_n rabbits after n months.
Then number of rabbits born in (n+1)th month is : A_n+1 - A_n.
A_n+2
= 2*number of rabbits in nth month + number of rabbits born in (n+1)th month.
= 2*A_n + A_n+1 - A_n
= A_n + A_n+1
= Fibonacci sequence

0 is same as '\0'

void main(){
char check[10];
check[0] = 'a';
check[1] = 'b';
check[2] = 0;
printf("%s\n",check);
}
will produce the same output as :

void main(){
char check[10];
check[0] = 'a';
check[1] = 'b';
check[2] = '\0';
printf("%s\n",check);
}

since ascii code of '\0' is 0,
whereas ascii code of '0' is 48.

php dom xml problem

Problem :
Warning: domdocument::domdocument() [domdocument.domdocument]: Entity: line 1: parser error : Start tag expected, '<' not found in C:\xampp\htdocs\xyz.php on line 8.

solution :
php_domxml.dll extension has to be commented in the php.ini file under apache/bin.(or
whatever php.ini file is loaded for you, find out through phpinfo()).

source.

Vim : stop making a tilda/tilde file

I came across two ways to do it:
(i) :set nobackup and :set nowritebackup
but it didn't work for me.

(ii) :set backupdir=$VIMRUNTIME/vim_backup
it worked for me. Bascially create a directory, where the backup files(tilda files)
will be created. Surprisingly, the backup files are not being created here.
And nowhere else.

I am using gvim on Windows btw.

A software for theorem proving

http://isabelle.in.tum.de/