Question

The sum of a range

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.

Since the end boundary is inclusive, you’ll need to use the <= operator rather than simply < to check for the end of your loop.

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.

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.

Reversing an array

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.

A 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.

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.

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.

Deep comparison

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 === .

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 .

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.

This is a book about getting computers to do what you want them to do. Computers are about as common as screwdrivers today, but they contain a lot more hidden complexity and thus are harder to operate and understand. To many, they remain alien, slightly threatening things.