Estructuras de Datos: Objetos y Arreglos

En dos ocasiones me preguntaron - “Disculpe, Sr. Babbage, si pongo números incorrectos en la máquina, ¿van a salir las respuestas correctas?” [...] No puedo terminar de comprender el tipo de confusión de ideas que podrían provocar esta pregunta. Charles Babbage, Passages from the Life of a Philosopher (1864)

Números, Booleanos y cadenas son los ladrillos de los que están hechas las estructuras de datos. Pero no podrás construir mucha casa de un solo ladrillo. Los objetos nos permiten agrupar valores-incluyendo otros objetos-permitiéndonos construir estructuras más complejas.

Los programas que hemos construido hasta ahora han sido seriamente limitados debido al hecho de que estaban operando únicamente en tipos de datos simples. Este capítulo agregará a tu caja de herramientas un entendimiento básico de las estructuras de datos. Al finalizarlo, sabrás lo suficiente para empezar a escribir algunos programas de utilidad.

El capítulo trabajará a lo largo de un ejemplo de programación más o menos realista, introduciendo conceptos conforme apliquen al problema en cuestión. El código de ejemplo muchas veces se construirá sobre funciones y variables que fueron presentadas previamente en el texto.

El sandbox de programación en línea para el libro eloquentjavascript.net/code proporciona una manera de correr el código en el contexto de un capítulo en espacífico. Si decides trabajar en los ejemplos en otro entorno, asegúrate de descargar primero el código completo de este capítulo desde la página del sandbox.

La ardillalobo

De vez en cuando, comúnmente entre las ocho y las diez de la noche, Jacques se transforma en un pequeño y peludo roedor con una frondosa cola.

Por un lado, Jacques esta bastante contento de no tener la clásica licantropía. Convertirse en una ardilla suele causar menos problemas que convertirse en un lobo. En vez de tener que preocuparse por comerse accidentalmente a un vecino (eso sería extraño), le preocupa el ser deborado por el gato del vecino. Después de un par de ocasiones donde se despertó, desnudo y desorientado, en una apenas delgada rama en la cima de un roble, se ha asegurado de cerrar puertas y ventanas de su cuarto por las noches y poner algunas nueces en el suelo para mantenerse ocupado.

Eso resuelve los problemas del gato y el roble. Pero Jacques aún sufre de su enfermedad. Los momentos irregulares en que se presenta la transformación le hacen sospechar que pudieran ser detonadas por algo. Por algún tiempo, creyó que sucedía sólo en los dias que había tocado árboles. Así que dejó de tocar árboles de manera definitiva e incluso evitó acercarse a ellos. Pero el problema presistió.

Cambiando a una perspectiva un poco más científica, Jacques planea empezar un registro diario de todo lo que hizo ese día y si tuvo o no una transformación. Con estos datos espera limitar las condiciones que disparan las transformaciones.

La primer cosa que hace es diseñar una estructura de datos para almacenar esta información.

Conjuntos de datos

Para trabajar con un pedazo de datos digitales, primero tendremos que encontrar una forma de representarlo en la memoria de nuestra máquina. Digamos, como un pequeño ejemplo, que queremos representar una colección de números: 2, 3, 5, 7 y 11.

Podríamos ponernos creativos usando cadenas-despues de todo, las cadenas pueden ser de cualquier longitud, así que podríamos pone mucha información en ellas-y usar "2 3 5 7 11" como nuestra representación. Pero esto es extraño. De alguna forma tendrías que extaer los dígitos y convertirlos de vuelta a números para accesarlos.

Afortunadamente, Javascript proporciona un tipo de dato específico para almacenar secuencias de valores. Se le llama arreglo y se escribe como una lista de valores entre corchetes, separados por comas.

var listOfNumbers = [2, 3, 5, 7, 11];
console.log(listOfNumbers[1]);
// → 3
console.log(listOfNumbers[1 - 1]);
// → 2

La notación para obtener los elementos dentro de un arreglo también utiliza corchetes. Un par de corchetes inmediátamente después de una expresión, con otra expresión dentro de los corchetes. buscará el elemento en la expresión de la izquierda que corresponda al índice dado por la expresión en corchetes.

El primer índice de un arreglo es cero, no uno. Así que el primer elemento puede leerse usando listOfNumbers[0]. Si no tienes antecedentes en programación, acostumbrarte a esta convención puede tomarte algún tiempo. Pero el zero-based counting tiene una larga tradición en tecnología y mientras la convención se siga de manera consistente (que se ha hecho, en Javascript), funciona bien.

Propiedades

Hemos visto algunas expresiones sospechosas como myString.length (para obtener la longitud de una cadena) y Math.max (la función máximo) en ejemplos pasados. Estas son expresiones que accesan una propiedad de algún valor. En el primer caso, accesamos la propiedad length de el valor en myString. En el segundo, accesamos la propiedad llamada max en el objeto Math (que es una colección de valores y funciones relacionadas con las matemáticas).

Casi todos los valores de Javascript tienen propiedades. Las excepciones son null y undefined. Si intentas acceder una propiedad de alguno de estos nonvalues, recibirás un error.

null.length;
// → TypeError: Cannot read property 'length' of null

Las dos maneras comúnes de acceder a propiedades en Javascript es con un punto y con corchetes. Ambas value.x y value[x] acceden una propiedad en value—pero no necesariamente la misma propiedad. La diferencia radica en cómo se interpreta x. Cuando usamos un punto, la parte después del punto debe ser un nombre de variable válido y nombra de manera directa a la propiedad. Cuando usamos corchetes, la expresión dentro de los corchetes es evaluada para obtener el nombre de la propiedad. Mientras que value.x busca la propiedad de value llamada “x”, value[x] intenta evaluar la expresión x y usa el resultado como el nombre de la propiedad.

Así que si sabes que la propiedad que te interesa se llama “length”, usas value.length. Si deseas extraer la propiedad nombrada por el valor almacenado en la variable i, usas value[i]. Y debido a que el nombre de las propiedades puede ser cualquier cadena, si quieres accesar una propiedad llamada “2” o “John Doe”, debes utilizar corchetes:value[2] or value["John Doe"]. Así lo harías incluso si conoces el nombre preciso de la propiedad de antemano, ya que ni “2” ni “John Doe” son nombres válidos de variables y por lo tanto no pueden accesarse a traves de la notación con punto.

Los elementos en un arreglo se almacenan en propiedades. Debido a que los nombres de estas propiedades son números y usualmente necesitamos obtener su nombre de una variable, tenemos que usar la sintaxis de corchetes para accesarlos. La propiedad length de un arreglo nos dice cuantos elementos contiene. Este nombre de propiedad es un nombre de variable válido, y conocemos su nombre por anticipado, así que para encontrar la longitud de un arreglo, comúnmente escribiremos array.length ya que es más fácil de escribir que array["length"].

Métodos

Ambos objetos, las cadenas y los arreglos contienen, adicionalmente a la propiedad length, un número de propiedades que refieren a valores de tipo función.

var doh = "Doh";
console.log(typeof doh.toUpperCase);
// → function
console.log(doh.toUpperCase());
// → DOH

Todas las cadenas tienen una propiedad toUpperCase. Cuando es llamada, regresará una copia de la cadena en la que todas las letras han sido convertidas a mayúsculas. También existe toLowerCase. Puedes adivinar que es lo que hace.

Curiosamente, a pesar de que la llamada a toUpperCase no pasa ningun argumento, la funcion del algun modo tiene acceso a la cadena "Doh", el valor cuya propiedad hemos llamado. Como funciona esto es decrito en el Capitulo 6.

Las propiedades que contienen funciones son generalmente llamadas metodos del valor al que pertenecen. Como , “toUpperCase es un metodo de una cadena”.

Este ejemplo demuestra algunos de los métodos que los objetos de tipo array tienen:

var mack = [];
mack.push("Mack");
mack.push("the", "Knife");
console.log(mack);
// → ["Mack", "the", "Knife"]
console.log(mack.join(" "));
// → Mack the Knife
console.log(mack.pop());
// → Knife
console.log(mack);
// → ["Mack", "the"]

El metodo push puede ser usado para añadir valores al final de un arreglo. El metodo pop hace lo opuesto: remueve el valor al final del arreglo y lo retorna. Un arreglo de cadenas puede ser aplanado a una sola cadena con el metodo join. El argumento dado a join determina el texto que es pegado entre los elementos del arreglo.

Objetos

De regreso a la ardillalobo. Un conjunto de registro de entradas puede ser representado como un arreglo. Pero las entradas no consisten solamente en un numero o una cadena-cada entrada necesita almacenar una lista de actividades y un valor Booleano que indique si Jacques se convirtió en una ardilla. Idealmente, nos gustaría agrupar esos valores juntos en un unico valor y despues poner esos valores agrupados en un arreglo de registro de entradas.

Los valores del tipo object son colecciones arbitrarias de propiedades y podemos agregar o eliminar esas propiedades como nos parezca. Una manera de crear un objeto es usar notación de llaves.

var day1 = {
  squirrel: false,
  events: ["work", "touched tree", "pizza", "running", "television"]
};
console.log(day1.squirrel);
// → false
console.log(day1.wolf);
// → undefined
day1.wolf = false;
console.log(day1.wolf);
// → false

Dentro de las llaves, podemos dar una lista de propiedades separadas por comas. Cada propiedad está escrita como un nombre, seguida por dos puntos, seguida por una expresión que provee un valor para la propiedad. Los espacios y saltos de línea no son significantes. Cuando un objeto abarca multiples líneas, marcandolos como en el ejemplo anterior, esto mejora la legibilidad del codigo. Las propiedades cuyos nombres no son nombres validos de variables o numeros validos tienen que ser encerradas en comillas.

var descriptions = {
  work: "Went to work",
  "touched tree": "Touched a tree"
};

Esto significa que las llaves tienen dos significados en JavaScript. Al inicio de una sentencia, inician un bloque de sentencias. En cualquier otra posición, describen un objeto. Afortunadamente, casí nunca es util iniciar una declaración con un objeto de tipo llave, y en programas típicos, no hay ambigüedad entre estos dos usos.

Leer una propiedad que no existe producirá el valor undefined, lo que paso la primera vez que intentamos leer la propiedad lobo en el ejemplo anterior.

Es posible asignar un valor a una expresión de tipo propiedad con el operador =. Esto reemplazará el valor de la propiedad si existía o creará una nueva propiedad en el objeto si no la había.

Para volver brevemente a nuestro modelo de tentáculos de asociacion de variables. Asociación de variables similares. Ellos captan valores, pero otras variables y propiedades podrían estar llevandose a cabo en los mismos valores. Tú puedes pensar en objetos como los pulpos con cualquier número de tentáculos, cada uno de los cuales tiene un nombre inscrito en ella.

Es un operador unitario que, cuando se aplica a una expresión acceso a la propiedad, eliminará la propiedad con el nombre del objeto. Esto no es una cosa común a hacer, pero es posible.

var anObject = {left: 1, right: 2};
console.log(anObject.left);
// → 1
delete anObject.left;
console.log(anObject.left);
// → undefined
console.log("left" in anObject);
// → false
console.log("right" in anObject);
// → true

El operador binario 'in', cuando se aplica a una cadena y un objeto, devuelve un valor booleano que indica si ese objeto tiene esa propiedad. La diferencia entre el establecimiento de una propiedad a undefined, y el hecho de eliminarlo es que, en el primer caso, el objeto todavía tiene la propiedad (que simplemente no tiene un valor muy interesante), mientras que en el segundo caso la propiedad ya no está presente y devolverá falso.

Arrays, then, are just a kind of object specialized for storing sequences of things. If you evaluate typeof [1, 2], this produces "object". You can see them as long, flat octopuses with all their arms in a neat row, labeled with numbers.

image::img/octopus-array.jpg[alt="Artist's representation of an array"]

So we can represent Jacques’ journal as an array of objects.

var journal = [
  {events: ["work", "touched tree", "pizza",
            "running", "television"],
   squirrel: false},
  {events: ["work", "ice cream", "cauliflower",
            "lasagna", "touched tree", "brushed teeth"],
   squirrel: false},
  {events: ["weekend", "cycling", "break",
            "peanuts", "beer"],
   squirrel: true},
  /* and so on... */
];

== Mutability ==

We will get to actual programming real soon now. But first, there's one last piece of theory to understand.

We've seen that object values can be modified. The types of values discussed in earlier chapters, such as numbers, strings, and Booleans, are all immutable—it is impossible to change an existing value of those types. You can combine them and derive new values from them, but when you take a specific string value, that value will always remain the same. The text inside it cannot be changed. If you have reference to a string that contains "cat", it is not possible for other code to change a character in that string to make it spell "rat".

With objects, on the other hand, the content of a value can be modified by changing its properties.

When we have two numbers, 120 and 120, we can consider them precisely the same number, whether or not they refer to the same physical bits. But with objects, there is a difference between having two references to the same object and having two different objects that contain the same properties. Consider the following code:

var object1 = {value: 10};
var object2 = object1;
var object3 = {value: 10};

console.log(object1 == object2);
// → true
console.log(object1 == object3);
// → false

object1.value = 15;
console.log(object2.value);
// → 15
console.log(object3.value);
// → 10

(((tentacle (analogy))))(((variable,model of)))The object1 and object2 variables grasp the same object, which is why changing object1 also changes the value of object2. The variable object3 points to a different object, which initially contains the same properties as object1 but lives a separate life.

(((== operator)))(((comparison,of objects)))(((deep comparison)))JavaScript's == operator, when comparing objects, will return true only if both objects are precisely the same value. Comparing different objects will return false, even if they have identical contents. There is no “deep” comparison operation built into JavaScript, which looks at object's contents, but it is possible to write it yourself (which will be one of the link:04_data.html#exercise_deep_compare[exercises] at the end of this chapter).

== The lycanthrope's log ==

(((weresquirrel example)))(((lycanthropy)))(((addEntry function)))So Jacques starts up his JavaScript interpreter and sets up the environment he needs to keep his ((journal)).

// include_code

var journal = [];

function addEntry(events, didITurnIntoASquirrel) {
  journal.push({
    events: events,
    squirrel: didITurnIntoASquirrel
  });
}

And then, every evening at ten—or sometimes the next morning, after climbing down from the top shelf of his bookcase—he records the day.

addEntry(["work", "touched tree", "pizza", "running",
          "television"], false);
addEntry(["work", "ice cream", "cauliflower", "lasagna",
          "touched tree", "brushed teeth"], false);
addEntry(["weekend", "cycling", "break", "peanuts",
          "beer"], true);

Once he has enough data points, he intends to compute the ((correlation)) between his squirrelification and each of the day's events and ideally learn something useful from those correlations.

(((correlation)))Correlation is a measure of ((dependence)) between ((variable))s (“variables” in the statistical sense, not the JavaScript sense). It is usually expressed as a coefficient that ranges from -1 to 1. Zero correlation means the variables are not related, whereas a correlation of one indicates that the two are perfectly related—if you know one, you also know the other. Negative one also means that the variables are perfectly related but that they are opposites—when one is true, the other is false.

(((phi coefficient)))For binary (Boolean) variables, the phi coefficient (ϕ) provides a good measure of correlation and is relatively easy to compute. To compute ϕ, we need a ((table)) n that contains the number of times the various combinations of the two variables were observed. For example, we could take the event of eating ((pizza)) and put that in a table like this:

image::img/pizza-squirrel.svg[alt="Eating pizza versus turning into a squirrel",width="7cm"]

ϕ can be computed using the following formula, where n refers to the table:

ifdef::html_target[]

++++

endif::html_target[]

ifdef::tex_target[]

pass:[\begin{equation}\varphi = \frac{n{11}n{00}-n{10}n{01}}{\sqrt{n{1\bullet}n{0\bullet}n{\bullet1}n{\bullet0}}}\end{equation}]

endif::tex_target[]

The notation (!html n~01~!)(!tex pass:[$n{01}$]!) indicates the number of measurements where the first variable (squirrelness) is false (0) and the second variable (pizza) is true (1). In this example, (!html _n~01~!)(!tex pass:[$n_{01}$]!) is 9.

The value (!html n~1•~!)(!tex pass:[$n{1\bullet}$]!) refers to the sum of all measurements where the first variable is true, which is 5 in the example table. Likewise, (!html _n~•0~!)(!tex pass:[$n_{\bullet0}$]!) refers to the sum of the measurements where the second variable is false.

(((correlation)))(((phi coefficient)))So for the pizza table, the part above the division line (the dividend) would be 1×76 - 4×9 = 40, and the part below it (the divisor) would be the square root of 5×85×10×80, or (!html √340000!)(!tex pass:[$\sqrt{340000}$]!). This comes out to ϕ ≈ 0.069, which is tiny. Eating ((pizza)) does not appear to have influence on the transformations.

== Computing correlation ==

(((array,as table)))(((nesting,of arrays)))We can represent a two-by-two ((table)) in JavaScript with a four-element array ([76, 9, 4, 1]). We could also use other representations, such as an array containing two two-element arrays ([[76, 9], [4, 1]]) or an object with property names like "11" and "01", but the flat array is simple and makes the expressions that access the table pleasantly short. We'll interpret the indices to the array as two-((bit)) ((binary number)), where the leftmost (most significant) digit refers to the squirrel variable and the rightmost (least significant) digit refers to the event variable. For example, the binary number 10 refers to the case where Jacques did turn into a squirrel, but the event (say, "pizza") didn't occur. This happened four times. And since binary 10 is 2 in decimal notation, we will store this number at index 2 of the array.

(((phi coefficient)))(((phi function)))This is the function that computes the ϕ coefficient from such an array:

// test: clip // include_code strip_log

function phi(table) {
  return (table[3] * table[0] - table[2] * table[1]) /
    Math.sqrt((table[2] + table[3]) *
              (table[0] + table[1]) *
              (table[1] + table[3]) *
              (table[0] + table[2]));
}

console.log(phi([76, 9, 4, 1]));
// → 0.068599434

(((square root)))(((Math.sqrt function)))This is simply a direct translation of the ϕ formula into JavaScript. Math.sqrt is the square root function, as provided by the Math object in a standard JavaScript environment. We have to sum two fields from the table to get fields like (!html n~1•~!)(!tex pass:[$n_{1\bullet}$]!) because the sums of rows or columns are not stored directly in our data structure.

(((JOURNAL data set)))Jacques kept his journal for three months. The resulting ((data set)) is available in the coding sandbox for this chapter(!book (http://eloquentjavascript.net/code#4[_eloquentjavascript.net/code#4_])!), where it is stored in the JOURNAL variable, and in a downloadable http://eloquentjavascript.net/code/jacques_journal.js[file].

(((tableFor function)))(((hasEvent function)))To extract a two-by-two ((table)) for a specific event from this journal, we must loop over all the entries and tally up how many times the event occurs in relation to squirrel transformations.

// include_code strip_log

function hasEvent(event, entry) {
  return entry.events.indexOf(event) != -1;
}

function tableFor(event, journal) {
  var table = [0, 0, 0, 0];
  for (var i = 0; i < journal.length; i++) {
    var entry = journal[i], index = 0;
    if (hasEvent(event, entry)) index += 1;
    if (entry.squirrel) index += 2;
    table[index] += 1;
  }
  return table;
}

console.log(tableFor("pizza", JOURNAL));
// → [76, 9, 4, 1]

(((array,searching)))(((indexOf method)))The hasEvent function tests whether an entry contains a given event. Arrays have an indexOf method that tries to find a given value (in this case, the event name) in the array and returns the index at which it was found or -1 if it wasn't found. So if the call to indexOf doesn't return -1, then we know the event was found in the entry.

(((array,indexing)))The body of the loop in tableFor figures out which box in the table each journal entry falls into by checking whether the entry contains the specific event it's interested in and whether the event happens alongside a squirrel incident. The loop then adds one to the number in the array that corresponds to this box on the table.

We now have the tools we need to compute individual ((correlation))s. The only step remaining is to find a correlation for every type of event that was recorded and see whether anything stands out. But how should we store these correlations once we compute them?

== Objects as maps ==

(((weresquirrel example)))(((array)))One possible way is to store all the ((correlation))s in an array, using objects with name and value properties. But that makes looking up the correlation for a given event somewhat cumbersome: you'd have to loop over the whole array to find the object with the right name. We could wrap this lookup process in a function, but we would still be writing more code, and the computer would be doing more work than necessary.

[[object_map]] (((object)))(((square brackets)))(((object,as map)))(((in operator)))A better way is to use object properties named after the event types. We can use the square bracket access notation to create and read the properties and can use the in operator to test whether a given property exists.

var map = {};
function storePhi(event, phi) {
  map[event] = phi;
}

storePhi("pizza", 0.069);
storePhi("touched tree", -0.081);
console.log("pizza" in map);
// → true
console.log(map["touched tree"]);
// → -0.081

(((data structure)))A ((map)) is a way to go from values in one domain (in this case, event names) to corresponding values in another domain (in this case, ϕ coefficients).

There are a few potential problems with using objects like this, which we will discuss in link:06_object.html#prototypes[Chapter 6], but for the time being, we won't worry about those.

(((for/in loop)))(((for loop)))(((object,looping over)))What if we want to find all the events for which we have stored a coefficient? The properties don't form a predictable series, like they would in an array, so we cannot use a normal for loop. JavaScript provides a loop construct specifically for going over the properties of an object. It looks a little like a normal for loop but distinguishes itself by the use of the word in.

for (var event in map)
  console.log("The correlation for '" + event +
              "' is " + map[event]);
// → The correlation for 'pizza' is 0.069
// → The correlation for 'touched tree' is -0.081

[[analysis]] == The final analysis ==

(((journal)))(((weresquirrel example)))(((gatherCorrelations function)))To find all the types of events that are present in the data set, we simply process each entry in turn and then loop over the events in that entry. We keep an object phis that has correlation coefficients for all the event types we have seen so far. Whenever we run across a type that isn't in the phis object yet, we compute its correlation and add it to the object.

// test: clip // include_code strip_log

function gatherCorrelations(journal) {
  var phis = {};
  for (var entry = 0; entry < journal.length; entry++) {
    var events = journal[entry].events;
    for (var i = 0; i < events.length; i++) {
      var event = events[i];
      if (!(event in phis))
        phis[event] = phi(tableFor(event, journal));
    }
  }
  return phis;
}

var correlations = gatherCorrelations(JOURNAL);
console.log(correlations.pizza);
// → 0.068599434

(((correlation)))Let's see what came out.

// test: no

for (var event in correlations)
  console.log(event + ": " + correlations[event]);
// → carrot:   0.0140970969
// → exercise: 0.0685994341
// → weekend:  0.1371988681
// → bread:   -0.0757554019
// → pudding: -0.0648203724
// and so on...

(((for/in loop)))Most correlations seem to lie close to zero. Eating carrots, bread, or pudding apparently does not trigger squirrel-lycanthropy. It does seem to occur somewhat more often on weekends, however. Let's filter the results to show only correlations greater than 0.1 or less than -0.1.

// start_code // test: no

for (var event in correlations) {
  var correlation = correlations[event];
  if (correlation > 0.1 || correlation < -0.1)
    console.log(event + ": " + correlation);
}
// → weekend:        0.1371988681
// → brushed teeth: -0.3805211953
// → candy:          0.1296407447
// → work:          -0.1371988681
// → spaghetti:      0.2425356250
// → reading:        0.1106828054
// → peanuts:        0.5902679812

A-ha! There are two factors whose ((correlation)) is clearly stronger than the others. Eating ((peanuts)) has a strong positive effect on the chance of turning into a squirrel, whereas brushing his teeth has a significant negative effect.

Interesting. Let's try something.

// include_code strip_log

for (var i = 0; i < JOURNAL.length; i++) {
  var entry = JOURNAL[i];
  if (hasEvent("peanuts", entry) &&
     !hasEvent("brushed teeth", entry))
    entry.events.push("peanut teeth");
}
console.log(phi(tableFor("peanut teeth", JOURNAL)));
// → 1

Well, that's unmistakable! The phenomenon occurs precisely when Jacques eats ((peanuts)) and fails to brush his teeth. If only he weren't such a slob about dental hygiene, he'd have never even noticed his affliction.

Knowing this, Jacques simply stops eating peanuts altogether and finds that this completely puts an end to his transformations.

(((weresquirrel example)))All is well with Jacques for a while. But a few years later, he loses his ((job)) and is eventually forced to take employment with a ((circus)), where he performs as The Incredible Squirrelman by stuffing his mouth with peanut butter before every show. One day, fed up with this pitiful existence, Jacques fails to change back into his human form, hops through a crack in the circus tent, and vanishes into the forest. He is never seen again.

== Further arrayology ==

(((array,methods)))(((method)))Before finishing up this chapter, I want to introduce you to a few more object-related concepts. We'll start by introducing some generally useful array methods.

(((push method)))(((pop method)))(((shift method)))(((unshift method)))We saw push and pop, which add and remove elements at the end of an array, link:04_data.html#array_methods[earlier] in this chapter. The corresponding methods for adding and removing things at the start of an array are called unshift and shift.

var todoList = [];
function rememberTo(task) {
  todoList.push(task);
}
function whatIsNext() {
  return todoList.shift();
}
function urgentlyRememberTo(task) {
  todoList.unshift(task);
}

(((task management example)))The previous program manages lists of tasks. You add tasks to the end of the list by calling rememberTo("eat"), and when you're ready to do something, you call whatIsNext() to get (and remove) the front item from the list. The urgentlyRememberTo function also adds a task but adds it to the front instead of the back of the list.

(((array,searching)))(((indexOf method)))(((lastIndexOf method)))The indexOf method has a sibling called lastIndexOf, which starts searching for the given element at the end of the array instead of the front.

console.log([1, 2, 3, 2, 1].indexOf(2));
// → 1
console.log([1, 2, 3, 2, 1].lastIndexOf(2));
// → 3

Both indexOf and lastIndexOf take an optional second argument that indicates where to start searching from.

(((slice method)))(((array,indexing)))Another fundamental method is slice, which takes a start index and an end index and returns an array that has only the elements between those indices. The start index is inclusive, the end index exclusive.

console.log([0, 1, 2, 3, 4].slice(2, 4));
// → [2, 3]
console.log([0, 1, 2, 3, 4].slice(2));
// → [2, 3, 4]

(((string,indexing)))When the end index is not given, slice will take all of the elements after the start index. Strings also have a slice method, which has a similar effect.

(((concatenation)))(((concat method)))The concat method can be used to glue arrays together, similar to what the + operator does for strings. The following example shows both concat and slice in action. It takes an array and an index, and it returns a new array that is a copy of the original array with the element at the given index removed.

function remove(array, index) {
  return array.slice(0, index)
    .concat(array.slice(index + 1));
}
console.log(remove(["a", "b", "c", "d", "e"], 2));
// → ["a", "b", "d", "e"]

== Strings and their properties ==

(((string,properties)))We can read properties like length and toUpperCase from string values. But if you try to add a new property, it doesn't stick.

var myString = "Fido";
myString.myProperty = "value";
console.log(myString.myProperty);
// → undefined

Values of type string, number, and Boolean are not objects, and though the language doesn't complain if you try to set new properties on them, it doesn't actually store those properties. The values are immutable and cannot be changed.

(((string,methods)))(((slice method)))(((indexOf method)))(((string,searching)))But these types do have some built-in properties. Every string value has a number of methods. The most useful ones are probably slice and indexOf, which resemble the array methods of the same name.

console.log("coconuts".slice(4, 7));
// → nut
console.log("coconut".indexOf("u"));
// → 5

One difference is that a string's indexOf can take a string containing more than one character, whereas the corresponding array method looks only for a single element.

console.log("one two three".indexOf("ee"));
// → 11

(((whitespace)))(((trim method)))The trim method removes whitespace (spaces, newlines, tabs, and similar characters) from the start and end of a string.

console.log("  okay \n ".trim());
// → okay

(((length property,for string)))(((charAt method)))(((string,indexing)))We have already seen the string type's length property. Accessing the individual characters in a string can be done with the charAt method but also by simply reading numeric properties, like you'd do for an array.

var string = "abc";
console.log(string.length);
// → 3
console.log(string.charAt(0));
// → a
console.log(string[1]);
// → b

[[arguments_object]] == The arguments object ==

(((arguments object)))(((length property)))(((parameter)))(((optional argument)))(((array-like object)))Whenever a function is called, a special variable named arguments is added to the environment in which the function body runs. This variable refers to an object that holds all of the arguments passed to the function. Remember that in JavaScript you are allowed to pass more (or fewer) arguments to a function than the number of parameters the function itself declares.

function noArguments() {}
noArguments(1, 2, 3); // This is okay
function threeArguments(a, b, c) {}
threeArguments(); // And so is this

(((length property)))The arguments object has a length property that tells us the number of arguments that were really passed to the function. It also has a property for each argument, named 0, 1, 2, and so on.

indexsee:[pseudo array,array-like object] (((array,methods)))If that sounds a lot like an array to you, you're right, it is a lot like an array. But this object, unfortunately, does not have any array methods (like slice or indexOf), so it is a little harder to use than a real array.

function argumentCounter() {
  console.log("You gave me", arguments.length, "arguments.");
}
argumentCounter("Straw man", "Tautology", "Ad hominem");
// → You gave me 3 arguments.

(((journal)))(((console.log)))(((variadic function)))Some functions can take any number of arguments, like console.log. These typically loop over the values in their arguments object. They can be used to create very pleasant interfaces. For example, remember how we created the entries to Jacques’ journal.

addEntry(["work", "touched tree", "pizza", "running",
          "television"], false);

Since he is going to be calling this function a lot, we could create an alternative that is easier to call.

function addEntry(squirrel) {
  var entry = {events: [], squirrel: squirrel};
  for (var i = 1; i < arguments.length; i++)
    entry.events.push(arguments[i]);
  journal.push(entry);
}
addEntry(true, "work", "touched tree", "pizza",
         "running", "television");

(((arguments object,indexing)))This version reads its first argument (squirrel) in the normal way and then goes over the rest of the arguments (the loop starts at index 1, skipping the first) to gather them into an array.

== The Math object ==

(((Math object)))(((Math.min function)))(((Math.max function)))(((Math.sqrt function)))(((minimum)))(((maximum)))(((square root)))As we've seen, Math is a grab-bag of number-related utility functions, such as Math.max (maximum), Math.min (minimum), and Math.sqrt (square root).

[[namespacepollution]] (((namespace)))(((namespace pollution)))(((object)))The Math object is used simply as a container to group a bunch of related functionality. There is only one Math object, and it is almost never useful as a value. Rather, it provides a _namespace so that all these functions and values do not have to be global variables.

(((variable,naming)))Having too many global variables “pollutes” the namespace. The more names that have been taken, the more likely you are to accidentally overwrite the value of some variable. For example, it's not unlikely that you'll want to name something max in one of your programs. Since JavaScript's built-in max function is tucked safely inside the Math object, we don't have to worry about overwriting it.

Many languages will stop you, or at least warn you, when you are defining a variable with a name that is already taken. JavaScript does neither, so be careful.

(((Math.cos function)))(((Math.sin function)))(((Math.tan function)))(((Math.acos function)))(((Math.asin function)))(((Math.atan function)))(((Math.PI constant)))(((cosine)))(((sine)))(((tangent)))(((PI constant)))(((pi)))Back to the Math object. If you need to do ((trigonometry)), Math can help. It contains cos (cosine), sin (sine), and tan (tangent), as well as their inverse functions, acos, asin, and atan, respectively. The number π (pi)—or at least the closest approximation that fits in a JavaScript number—is available as Math.PI. (There is an old programming tradition of writing the names of ((constant)) values in all caps.)

// test: no

function randomPointOnCircle(radius) {
  var angle = Math.random() * 2 * Math.PI;
  return {x: radius * Math.cos(angle),
          y: radius * Math.sin(angle)};
}
console.log(randomPointOnCircle(2));
// → {x: 0.3667, y: 1.966}

If sines and cosines are not something you are very familiar with, don't worry. When they are used in this book, in link:13_dom.html#sin_cos[Chapter 13], I'll explain them.

(((Math.random function)))(((random number)))The previous example uses Math.random. This is a function that returns a new pseudorandom number between zero (inclusive) and one (exclusive) every time you call it.

// test: no

console.log(Math.random());
// → 0.36993729369714856
console.log(Math.random());
// → 0.727367032552138
console.log(Math.random());
// → 0.40180766698904335

(((pseudorandom number)))(((random number)))Though computers are deterministic machines—they always react the same way if given the same input—it is possible to have them produce numbers that appear random. To do this, the machine keeps a number (or a bunch of numbers) in its internal state. Then, every time a random number is requested, it performs some complicated deterministic computations on this internal state and returns part of the result of those computations. The machine also uses the outcome to change its own internal state so that the next “random” number produced will be different.

(((rounding)))(((Math.floor function)))If we want a whole random number instead of a fractional one, we can use Math.floor (which rounds down to the nearest whole number) on the result of Math.random.

// test: no

console.log(Math.floor(Math.random() * 10));
// → 2

Multiplying the random number by 10 gives us a number greater than or equal to zero, and below 10. Since Math.floor rounds down, this expression will produce, with equal chance, any number from 0 through 9.

(((Math.ceil function)))(((Math.round function)))There are also the functions Math.ceil (for “ceiling”, which rounds up to a whole number) and Math.round (to the nearest whole number).

== The global object ==

(((global object)))(((window variable)))(((global scope)))(((scope)))(((object)))The global scope, the space in which global variables live, can also be approached as an object in JavaScript. Each global variable is present as a ((property)) of this object. In ((browser))s, the global scope object is stored in the window variable.

// test: no

var myVar = 10;
console.log("myVar" in window);
// → true
console.log(window.myVar);
// → 10

== Summary ==

Objects and arrays (which are a specific kind of object) provide ways to group several values into a single value. Conceptually, this allows us to put a bunch of related things in a bag and run around with the bag, instead of trying to wrap our arms around all of the individual things and trying to hold on to them separately.

Most values in JavaScript have properties, the exceptions being null and undefined. Properties are accessed using value.propName or value["propName"]. Objects tend to use names for their properties and store more or less a fixed set of them. Arrays, on the other hand, usually contain varying numbers of conceptually identical values and use numbers (starting from 0) as the names of their properties.

There are some named properties in arrays, such as length and a number of methods. Methods are functions that live in properties and (usually) act on the value they are a property of.

Objects can also serve as maps, associating values with names. The in operator can be used to find out whether an object contains a property with a given name. The same keyword can also be used in a for loop (for (var name in object)) to loop over an object's properties.

== Exercises ==

=== The sum of a range ===

(((summing (exercise))))The link:00_intro.html#intro[introduction] of this book alluded to the following as a nice way to compute the sum of a range of numbers:

// test: no

console.log(sum(range(1, 10)));

(((range function)))(((sum function)))Write a range function that takes two arguments, start and end, and returns an array containing all the numbers from start up to (and including) end.

Next, write a sum function that takes an array of numbers and returns the sum of these numbers. Run the previous program and see whether it does indeed return 55.

(((optional argument)))As a bonus assignment, modify your range function to take an optional third argument that indicates the “step” value used to build up the array. If no step is given, the array elements go up by increments of one, corresponding to the old behavior. The function call range(1, 10, 2) should return [1, 3, 5, 7, 9]. Make sure it also works with negative step values so that range(5, 2, -1) produces [5, 4, 3, 2].

ifdef::interactive_target[]

// test: no

// Your code here.

console.log(range(1, 10));
// → [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
console.log(range(5, 2, -1));
// → [5, 4, 3, 2]
console.log(sum(range(1, 10)));
// → 55

endif::interactive_target[]

!!hint!!

(((summing (exercise))))(((array,creation)))(((square brackets)))Building up an array is most easily done by first initializing a variable to [] (a fresh, empty array) and repeatedly calling its push method to add a value. Don't forget to return the array at the end of the function.

(((array,indexing)))(((comparison)))Since the end boundary is inclusive, you'll need to use the <= operator rather than simply < to check for the end of your loop.

(((arguments object)))To check whether the optional step argument was given, either check arguments.length or compare the value of the argument to undefined. If it wasn't given, simply set it to its ((default value)) (1) at the top of the function.

(((range function)))(((for loop)))Having range understand negative step values is probably best done by writing two separate loops—one for counting up and one for counting down—because the comparison that checks whether the loop is finished needs to be >= rather than <= when counting downward.

It might also be worthwhile to use a different default step, namely, -1, when the end of the range is smaller than the start. That way, range(5, 2) returns something meaningful, rather than getting stuck in an ((infinite loop)).

!!hint!!

=== Reversing an array ===

(((reversing (exercise))))(((reverse method)))(((array,methods)))Arrays have a method reverse, which changes the array by inverting the order in which its elements appear. For this exercise, write two functions, reverseArray and reverseArrayInPlace. The first, reverseArray, takes an array as argument and produces a new array that has the same elements in the inverse order. The second, reverseArrayInPlace, does what the reverse method does: it modifies the array given as argument in order to reverse its elements. Neither may use the standard reverse method.

(((efficiency)))(((pure function)))(((side effect)))Thinking back to the notes about side effects and pure functions in the link:03_functions.html#pure[previous chapter], which variant do you expect to be useful in more situations? Which one is more efficient?

ifdef::interactive_target[]

// test: no

// Your code here.

console.log(reverseArray(["A", "B", "C"]));
// → ["C", "B", "A"];
var arrayValue = [1, 2, 3, 4, 5];
reverseArrayInPlace(arrayValue);
console.log(arrayValue);
// → [5, 4, 3, 2, 1]

endif::interactive_target[]

!!hint!!

(((reversing (exercise))))There are two obvious ways to implement reverseArray. The first is to simply go over the input array from front to back and use the unshift method on the new array to insert each element at its start. The second is to loop over the input array backward and use the push method. Iterating over an array backward requires a (somewhat awkward) for specification like (var i = array.length - 1; i >= 0; i--).

Reversing the array in place is harder. You have to be careful not to overwrite elements that you will later need. Using reverseArray or otherwise copying the whole array (array.slice(0) is a good way to copy an array) works but is cheating.

The trick is to swap the first and last elements, then the second and second-to-last, and so on. You can do this by looping over half the length of the array (use Math.floor to round down—you don't need to touch the middle element in an array with an odd length) and swapping the element at position i with the one at position array.length - 1 - i. You can use a local variable to briefly hold on to one of the elements, overwrite that one with its mirror image, and then put the value from the local variable in the place where the mirror image used to be.

!!hint!!

[[list]] === A list ===

(((data structure)))(((list (exercise))))(((linked list)))(((object)))(((array)))(((collection)))Objects, as generic blobs of values, can be used to build all sorts of data structures. A common data structure is the list (not to be confused with the array). A list is a nested set of objects, with the first object holding a reference to the second, the second to the third, and so on.

// include_code

var list = {
  value: 1,
  rest: {
    value: 2,
    rest: {
      value: 3,
      rest: null
    }
  }
};

The resulting objects form a chain, like this:

image::img/linked-list.svg[alt="A linked list",width="6cm"]

(((structure sharing)))(((memory)))A nice thing about lists is that they can share parts of their structure. For example, if I create two new values {value: 0, rest: list} and {value: -1, rest: list} (with list referring to the variable defined earlier), they are both independent lists, but they share the structure that makes up their last three elements. In addition, the original list is also still a valid three-element list.

Write a function arrayToList that builds up a data structure like the previous one when given [1, 2, 3] as argument, and write a listToArray function that produces an array from a list. Also write the helper functions prepend, which takes an element and a list and creates a new list that adds the element to the front of the input list, and nth, which takes a list and a number and returns the element at the given position in the list, or undefined when there is no such element.

(((recursion)))If you haven't already, also write a recursive version of nth.

ifdef::interactive_target[]

// test: no

// Your code here.

console.log(arrayToList([10, 20]));
// → {value: 10, rest: {value: 20, rest: null}}
console.log(listToArray(arrayToList([10, 20, 30])));
// → [10, 20, 30]
console.log(prepend(10, prepend(20, null)));
// → {value: 10, rest: {value: 20, rest: null}}
console.log(nth(arrayToList([10, 20, 30]), 1));
// → 20

endif::interactive_target[]

!!hint!!

(((list (exercise))))(((linked list)))Building up a list is best done back to front. So arrayToList could iterate over the array backward (see previous exercise) and, for each element, add an object to the list. You can use a local variable to hold the part of the list that was built so far and use a pattern like list = {value: X, rest: list} to add an element.

(((for loop)))To run over a list (in listToArray and nth), a for loop specification like this can be used:

for (var node = list; node; node = node.rest) {}

Can you see how that works? Every iteration of the loop, node points to the current sublist, and the body can read its value property to get the current element. At the end of an iteration, node moves to the next sublist. When that is null, we have reached the end of the list and the loop is finished.

(((recursion)))The recursive version of nth will, similarly, look at an ever smaller part of the “tail” of the list and at the same time count down the index until it reaches zero, at which point it can return the value property of the node it is looking at. To get the zeroeth element of a list, you simply take the value property of its head node. To get element N + 1, you take the Nth element of the list that's in this list's rest property.

!!hint!!

[[exercise_deep_compare]] === Deep comparison ===

(((deep comparison (exercise))))(((comparison)))(((deep comparison)))(((== operator)))The == operator compares objects by identity. But sometimes, you would prefer to compare the values of their actual properties.

Write a function, deepEqual, that takes two values and returns true only if they are the same value or are objects with the same properties whose values are also equal when compared with a recursive call to deepEqual.

(((null)))(((=== operator)))(((typeof operator)))To find out whether to compare two things by identity (use the === operator for that) or by looking at their properties, you can use the typeof operator. If it produces "object" for both values, you should do a deep comparison. But you have to take one silly exception into account: by a historical accident, typeof null also produces "object".

ifdef::interactive_target[]

// test: no

// Your code here.

var obj = {here: {is: "an"}, object: 2};
console.log(deepEqual(obj, obj));
// → true
console.log(deepEqual(obj, {here: 1, object: 2}));
// → false
console.log(deepEqual(obj, {here: {is: "an"}, object: 2}));
// → true

endif::interactive_target[]

!!hint!!

(((deep comparison (exercise))))(((typeof operator)))(((object)))(((=== operator)))Your test for whether you are dealing with a real object will look something like typeof x == "object" && x != null. Be careful to compare properties only when both arguments are objects. In all other cases you can just immediately return the result of applying ===.

(((for/in loop)))(((in operator)))Use a for/in loop to go over the properties. You need to test whether both objects have the same set of property names and whether those properties have identical values. The first test can be done by counting the properties in both objects and returning false if the numbers of properties are different. If they're the same, then go over the properties of one object, and for each of them, verify that the other object also has the property. The values of the properties are compared by a recursive call to deepEqual.

(((return value)))Returning the correct value from the function is best done by immediately returning false when a mismatch is noticed and returning true at the end of the function.

!!hint!!