Dynamic arrays

Let’s build a very simple word processor. What data structure should we use to store the text as our user writes it?

Strings are stored as arrays, right? So we should use an array?

Here’s where that gets tricky: when we allocate an array in a low-level language like C or Java, we have to specify upfront how many indices we want our array to have.

There’s a reason for this—the computer has to reserve space in memory for the array and commit to not letting anything else use that space. We can’t have some other program overwriting the elements in our array!

The computer can’t reserve all its memory for a single array. So we have to tell it how much to reserve.

But for our word processor, we don’t know ahead of time how long the user’s document is going to be! So what can we do?

Just make an array and program it to resize itself when it runs out of space! This is called a dynamic array, and it’s built on top of a normal array.

Python, Ruby, and JavaScript use dynamic arrays for their default array-like data structures. In Javascript, they’re called “arrays.” Other languages have both. For example, in Java, array is a static array (whose size we have to define ahead of time) and ArrayList is a dynamic array.

Here’s how it works:

When you allocate a dynamic array, your dynamic array implementation makes an underlying static array. The starting size depends on the implementation—let’s say our implementation uses 10 indices:

Say you append 4 items to your dynamic array:

At this point, our dynamic array contains 4 items. It has a length of 4. But the underlying array has a length of 10.

We’d say this dynamic array’s size is 4 and its capacity is 10.

The dynamic array stores an end_index to keep track of where the dynamic array ends and the extra capacity begins.

If you keep appending, at some point you’ll use up the full capacity of the underlying array:

Next time you append, the dynamic array implementation will do a few things under the hood to make it work:

1. Make a new, bigger array. Usually twice as big.

Why not just extend the existing array? Because that memory might already be taken. Say we have Spotify open and it’s using a handful of memory addresses right after the end of our old array. We’ll have to skip that memory and reserve the next 20 uninterrupted memory slots for our new array:


2. Copy each element from the old array into the new array.

3. Free up the old array. This tells the operating system, “you can use this memory for something else now.”

4. Append your new item.

We could call these special appends “doubling” appends since they require us to make a new array that’s (usually) double the size of the old one.

Appending an item to an array is usually an O(1) time operation, but a single doubling append is an O(n) time operation since we have to copy all n items from our array.

Does that mean an append operation on a dynamic array is always worst-case O(n) time? Yes. So if we make an empty dynamic array and append n items, that has some crazy time cost like O(n^2) or O(n!)?!?! Not quite.

While the time cost of each special O(n) doubling append doubles each time, the number of O(1) appends you get until the next doubling append also doubles. This kind of “cancels out,” and we can say each append has an average cost or amortized cost of O(1). 

Given this, in industry we usually wave our hands and say dynamic arrays have a time cost of O(1) for appends, even though strictly speaking that’s only true for the average case or the amortized cost.

In an interview, if we were worried about that O(n)-time worst-case cost of appends, we might try to use a normal, non-dynamic array.

The advantage of dynamic arrays over arrays is that you don’t have to specify the size ahead of time, but the disadvantage is that some appends can be expensive. That’s the tradeoff.

But what if we wanted the best of both worlds…  See Linked List


Array are implemented using a few different data structures under the hood, which one is utilized at a given moment is given by heuristics that describe the sort of data stored in the array.  Two of the ways arrays are implemented in JavaScript are HashMaps and Dynamic Arrays.  For this exercise please use static arrays and pseudocode (made up coding language) to create dynamic array implementations of a few of the methods found on the JavaScript array interface and analysis the big O runtime of each.

Here is a link talking about what arrays are in JavaScript and a list of all the methods.  Pick out some of the methods you are familiar with to implement with pseudocode.

Array – JavaScript | MDN (mozilla.org)

Here are a few we recommend doing as well, share your pseudocode and big O runtimes with your mentor.

Array.prototype.at(): Returns the array item at the given index. Accepts negative integers, which count back from the last item.

Array.prototype.filter(): Returns a new array containing all elements of the calling array for which the provided filtering function returns true.

Array.prototype.find(): Returns the found element in the array, if some element in the array satisfies the testing function, or undefined if not found.

Array.prototype.forEach(): Calls a function for each element in the array.

Array.prototype.includes(): Determines whether the array contains a value, returning true or false as appropriate.

Array.prototype.map(): Returns a new array containing the results of calling a function on every element in this array.

Array.prototype.pop(): Removes the last element from an array and returns that element.

Array.prototype.push(): Adds one or more elements to the end of an array, and returns the new length of the array.

Array.prototype.sort(): Sorts the elements of an array in place and returns the array.