The problem is: What is the big O of a piece of code like this given than array.length is O(N)?

for i… N array.length
—>for j… N array.length
——>for k… N array.length

My approach was to imagine it first for the case we usually know, when array.length is O(1).
If you think of it graphically, the first two loops can be seen as a 2D matrix. Every i,j in the matrix represents the big O of one step.
Then if we “zoom in” into any of those steps, we see that every “1″ unrolls into a O(N) operation because of the third loop. So in total we come up with O(N^3).

for i… N array.length
—>for j… N array.length
——>for k… N array.length

_________N_____

   j0   j1  j2  j3  j4
i0 1   1   1   1   1
i1 1   1   1   1   1 ...    |
i2 1   1   1   1   1        N
i3 1   1   1   1   1        |
i4 1   1   1   1   1                    <--O(N*N ) = O(N^2)
            |
           /\  (exploding a step)
          /  \
              _
      k0 1    |                         <--O(N)
      k1 1    N
      k2 1    |
      k3 1                           So O(N * N^2) = O(N^3)

Now I imagined it for the case of our problem, when array.length takes O(N). In the i,j matrix every step now is not “1″ but “2N+1″ because it includes 2 array.length (one for the i loop and another for the j loop). Then if we “zoom in” into any of those steps, we see that every “2N+1″ becomes “2N+N^2″ since the third loop is now O(N^2). So the total of the i,j matrix is O(N^4).

for i… N array.length
—>for j… N array.length
——>for k… N array.length

________________N______

      j0       j1         j2
i0 ( 2N+1)  ( 2N+1)   ( 2N+1)
i1 ( 2N+1)  ( 2N+1)   ( 2N+1)         |
i2 ( 2N+1)  ( 2N+1)   ( 2N+1)         N
i3 ( 2N+1)  ( 2N+1)   ( 2N+1)         |
i4 ( 2N+1)  ( 2N+1)   ( 2N+1)       <-- O((2N+1)*(N)) = O(N^2)
                  |
                 /\   (exploding a step)
                /  \  

            k0 1+N   |              <--  O(N*(N+1)) = O(N^2)
            k1 1+N   N
            k2 1+N   |
            k3 1+N                

                                        So O(N^2 * N^2) = O(N^4)

My case

How to

For more details checkout the foremost tool.

Context

I was at a Google Chrome Extension event , and thought of how it would interact with the media that connects to your computer, and would extensions be able to access your filesystem to grab let say, pictures from a USB?
The answer is as usual, “yes and no.” Since the extensions are javascript, for security reasons extensions are sandboxed, so javascript by itself is not able to access the filesystem but it can load dll’s that can access it.

I got curious because:

1) Chrome OS does interact with the filesystem to provide all the same access to media(Eg. USBN Drive) that a regular OS provides.
2) Chrome browser extensions will potentially need to expand to interact with the user’s media.
3) So will this sandbox need to be breached or not?

Idea

A bubble (or jail-like filesystem) where a chunk of the filesystem is assigned to the extension so that it can interact with the media safely, similar to a jail

Idea for a simple jailed filesystem for applications of Google Chrome OS and Chrome Browser Extensions

Is this idea stupid or not? Feel free to comment!
.

Thanks Orlando for the explanation of current state of affairs of the javascript sandbox!

Sounds like an easy task right? Not really.

After trying several of the existing tools including some mentioned in techcruch I realized what 4 what I would call “common sense” features still lacking in exiting apps.

While I truly appreciate there being free apps at all to use, I would rather use no tool than a handicapped one. Anyone share the same feeling?

1. Task indentation: Yes, this IS important because if we do not split a major task into several more tangible ones that task will probably never get done.
2. Collaboration: For simple project collaboration this is essential. I want to be able to add and cross out tasks at the same time as someone else working in the project. It shouldn’t require a full-featured project management software to have todo lists collaboration.
3. Import and Export:  If migrating from some old form of todo list (yes it could be notepad), it is useful to have a way to import these lists. I struggled forever trying to import lists from Gmail’s task app and failed to import indented tasks.
4. Fresh uncluttered feel: Yes this is another overlooked “feature” but it is so important. If I am going to have a todo list I dont want it to be yet another tormenting and overwhelming factor in my life. I need a todo list that would say “yes! life is simple..do one task at a time..see the lots of white space?? see the lack of clutter?? see the tasks how clear they are?? you can do it!.” =)

Gmail Tasks App: This is by far the most intuitive yet simple app I have been able to use for more than a day. Its integration with a product I already use is ever better, less clicks to get things done. Yet it lacks collaboration. I can send an email with my task list but there is no way to update the list simultaneously.

Remember the Milk (RTM): Simple and lost of white space, but lacks the ability to indent tasks! You will see RTM recommended even in lifehacker.

Toddledo: Finally found one app that has almost everything  I need yet its looks needs much more improvement.  It makes me feel as if the task generating monster is going to devour me.

Blah blah List: popups = more clicks. This is a no-no.

Tada list by 37 signals:  Again, lacks task indentation.

Any suggestions? Right now my best option is Google docs. It is collaborative, integrates with other google apps I already use, and it is easily accessed from igoogle.

Let me know what tools you use!

So this is a post about yet more intellectual masturbation yay! HOW TO STORE THE PREV AND NEXT POINTERS OF A NODE IN A DOUBLE LINKTED LIST IN A SINGLE ADDRESS.

Intro

In a double linked list there is the concept of a pointer to the previous and the next nodes. What we want to do here is store the addresses to the previous and next nodes in a single address using an XOR old trick.  To show you how this works we only need these two pieces of node which I got from a neat little explanation here. This code is meant for counting the nodes of the double linked list but in generally shows how to traverse the list encoding and decoding the previous and next addresses.

typedef struct node {
   struct node *diff;

   int data;
} node;

Here *diff refers to the XOR of the addresses od previous and next pointer.

unsigned long countNodes()
{
   unsigned long nodes = 0;
   node *curr, *prev, *temp;

   prev = NULL;
   curr = nodeHead;
   while (curr)
     {
	nodes ++;
	temp = curr;
	curr = XOR(prev, temp->diff);
	prev = temp;
     }

  return nodes;
}


Example

Lets say you have a linked list with nodes A, B, C.

• And Node A is at address 100000
• And diff has address XOR (prev,next)= XOR (000000, B) = XOR (000000, 101110)  = 101110. 
   

• Then we go into the loop inside countNodes() and in the first iteration this is what the state looks like :

              temp = A = 100000

              curr = XOR ( prev,  diff )  = XOR ( 000000,  101110) = 101110

              prev = temp = 100000

So now curr, which is the equivalent of the next node,  is pointing at B’s address ( 101110) and we have decoded this address using 2 main things:

1. The diff variable in node A that contains the XOR of prev and next of A.
2. A varibale prev that keeps track of that the previous node’s address was. 

Keep in mind that although we are using 2 variables (and thus addresses) for figuring out what next is, we really only store one as part of each node since from these 2 vars one is reused every iterations, and thats the prev var.

cool aint it? : )

Why do we women shop?. This is a list compiled from my own experience, friends and people I have known through the years. These are what I have considered the key reasons but I am open to suggestions.

Creative need: we crave beauty and beautiful things. We have a “sweet tooth” for pretty things, for colors, shapes and contrasts. Our seventh sense is that of aesthetics (since our six is for understanding those from Mars) and this sense must be feed periodically. Jade’s blog, cravinganthropologie had me do some serious thinking about this.

Anthropologie is one of those places that I visit to get my “fix” of beauty but buy nothing from, always leaves a void of “all those pretty things I want but should not buy”. Yet I keep visiting because something is better than nothing. This store is a trip to my grandmother’s house, Alice’s Wonderland, a help-Africa recycling project and a girl at home popurry. Here are a few observations you might identify with:

So Saturday morning we wake up and realize it is time for a “pimp my ride” session, and me, myself and I are the ride. This is a case where we consider ourselves the canvas that we can use to get creative about, buying that necklace that matches the blouse…and the body.

Would we be satisfied simply arranging accessories and not buying them? Although there is certainly a satisfaction to this, buying the item feels like the signature on an oil painting, the culminating event and final touch of the masterpiece we created. You cant just paint and not sign, you must buy.

Anxiety: This is similar to eating when you are anxious about work you are doing, about a personal issue, anything you cannot find an immediate resolution to. This leads to the next point, procrastination. But before let me note that plenty of actresses are compulsive shoppers, among many reasons out of anxiety and possibly work related stress. Also, women from low income families spend great amount of time and money (considering their financial status) shopping. Of course it is not at brand stores they go to shop. Instead they go to Ross, Walmart, Target..you name it. Anxieties of a different kind hit this group, and they find relief on buying a lot of many cheap things.

Procrastination: We all know about procrastination, it is that self deceiving process you undergo when you must do X but instead you find a million tasks to complete before you even attempt doing X. Some of us become such creative procrastinators that we manage to accomplish inhuman amounts of work while on the run from X. It is not surprising that shopping is sometimes another escape for procrastination, surely an effective one since it could extend for hours.

That guilt feeling: How many times you go to the store and pick a few pretty shirts but on the way to the cashier….guilt grabs you and makes you put them down and away? We hold them in your hands until the last minute, and hope guilt doesn’t strike. Guilt to spend more money, guilt to spend on those overpriced jeans we love, guilt to not be able to control ourselves, guilt, guilt. What do we do about guilt? We bring our girl friends over to help dissipate our guilty sensation, “why not buy if they are buying?,” “She just told me to get that purple blouse,” “I must treat myself”.

Just a social thing: Stores are another place to “hang out” just like a mall is. You share likes and dislikes about the items you find, or get your friend to tell you how amazing that dress looks on you. It becomes a female bonding experience.

If shopping has become a problem for you, don’t feel bad, just do something about it, now. Read my post about how to stop for suggestions.

Author’s notes: This post is a result of me obsessing lately about why we are drawn to buy this or the other. Having been raised in a country (Cuba) where there was no window shopping, little commerce and complete lack of advertisement, shopping is still a constantly evolving theme in my life. I am afraid that my cold eye as an outsider will soon run out so I must make note of this which I see.

Dedicated to my grandfather, Gregorio Arteaga.

Recuerdo la calidez de las calles de la Habana vieja cuando pretendia ser turista en mi propio pais, pero era inutil. La brisa marina me reconocia como hija y despeinaba mis cabellos al caminar sobre las geometricas aguas de adoquines. Buscaba mis raices, respirando la humedad, jugando a adivinar la proxima flor que creceria entre las grietas de los ladrillos de la vieja catedral. Esa era yo. Un duende perdido entre paredes y brisas de otros tiempos. Muchas cosas me preguntaba; por que las mujeres vestian como en tiempos de la colonizacion para ser retratadas con turistas? Extranarian el tiempo de exclavitud?

Es una revolucion de artistas sin firma lo que se observa si uno se aventura entre los artesanos de la Catedral. Junto a aromas a madera fresca, vez rostros humildes que acompanan esculpturas con suaves razgos africanos, tal como tallados con los dedos de Dios. Estos rostros de ingenieros, pintores, arquitectos y desocupados tal parece que no saben de su ingenio. Insisten en vender sus creaciones a los visitantes que entre naravillas no saben que escoger. Muchos se han convertido en artistas porque necesitan dinero. Sus manos que antes ojeaban paginas de fisica mecanica ahora entretienen a turistas con artesanias casuales. Sin duda los ideales del ser humano cambian cuando las necesidades basicas no estan satisfechas, cuando sus estomagos crujen como bestias. Despues de sonar con carreras exitosas, un dia despertarorn con la simple necesidad de comer, y vestirse. solo eso y nada mas. Se vieron obligados a descubrir un sin fin de creativas manas en ellos, porque sus estomagos crujian como bestias. Realmente somos criaturas simples.

Todos traen sus tesoros al gran bazar de la plaza de la Catedral para ganarse unos centavos. Algunos traen los libros de sus heroes de infancia, libros sobre el Che y Marti que ya no le dan valor. A otros les bastan sus dotes musicales para impresionar al publico y con guitarras ardientes le cantan a la belleza de su tierra y mujeres.

Al doblar la esquina de la Catedral de La Habana se encuentra la Basilica Menor de un tal santo “Francisco de Asis”, una de mis memorias inolvidables. Se esconde de la multitud y sirve re refugio a pensadores solitarios. Recuerdo que al entrar, hasta mis pies se extendian figuras cubistas coloreadas por los vitrales de fondo y casi alcanzaba a ver las siluetas de monjes disfrutando la paz del silencio entre el viejo claustro de columnas toscanas. En alguna enciclopedia lei que una mantra sutil de cantos religiosos se hospedaba en este lugar, y su eco, atrapado por las columnas ingeniosamante disenadas, permanecia prisionero.

Hoy muchos ya no piensan en historia, arte ni ciencia, pero el aliento a Habana vieja les alimenta el alma. Ahora solo se sientan por doquier a hablar de temas prohibidos, o caminan por las calles roidas con un ojo en el suelo y otro en en cielo, temiendo que un vecino los bautice con agua infernal desde algun balcon. En cambio, los ninos, ajenos a las preocupaciones humanas, corretean por la callejuelas tropezando con los transeuntes y vendiendo Habanos a los turistas como les encargo su madre.

No es extrano tropezar con un historiador del arte que sufre en ricones la prostitucion de la vieja Habana, o un loco pregonando insensateces. Como explicar que en los balocones de marmol donde antes se sentaban senoras de tercipelo ahora se sientan viejas desdentadas? “Ironia”, se llama esta pagina de la hisotria. No les son utiles los muebles de caoba y cedro or el piso de marmol negro a estas senoras que anoran comida. Con cucharas de plata beben una sopa de agua azucarada en la manana y agua salada en la noche.

Es esta cultura descavellada la que le da la magia a la Habana, donde cada persona es un brochazo de un impresionista llamado Orate. “Gris, que te quiero Gris”, diria Garcia Lorca si visitara mi pais. Siempre te recordare.

Writer’s Note: Many like me have had the need to write about the reality of the cuban people. One of the most fascinating yet raw books I have read was El hombre, la hembra y el hambre, by Daina Chaviano. Check it out for an account of the humane and inhumane side of the story.