Problem Description

The problem requires us to extend the functionality of all arrays in TypeScript by adding a custom method called last. This method should return the last element of the array when called. If the array is empty, meaning it has no elements, the method should return -1. It is mentioned that we can assume the array is the result of JSON.parse, which indicates that we are dealing with an array of elements that originated from a JSON string.

The method array.last() will thus become a universal method that can be applied to any array instance within the TypeScript environment after we've added this functionality.

Intuition

To implement a new method that can be used on all arrays, we can extend the built-in Array prototype in TypeScript. Prototypes in JavaScript (and by extension, TypeScript) are part of the language's prototypal inheritance system. By adding a method to Array.prototype, we actually add that method to all arrays because they inherit methods from their prototype.

The last method needs to do the following:

• Check if the array is empty. If it is, return -1.
• If the array is not empty, return the last element.

We can check if the array is empty by looking at its length property. If length is 0, the array is empty.

To access the last element of the array, we can use the existing method at(-1), which is a part of modern JavaScript that allows us to access the last element by providing -1 as the index. If this at method is not supported or if we need to be compatible with environments that do not support modern features, we can use this[this.length - 1] to access the last element of the array using the classical approach.

By defining Array.prototype.last as a function, we ensure that any array created or existing will have the last method available.

We use TypeScript's declare global to extend the global Array interface so that TypeScript knows about our new method and does not throw type errors when attempting to use last() on an array. Inside this declaration, we indicate that last is either going to return an element of the array's type T or -1.

The Array.prototype.last function definition follows this interface, using a ternary operator to either return the last element if the array is not empty or -1 otherwise.

Solution Approach

The solution makes use of the prototypal inheritance feature of JavaScript, as well as TypeScript's ability to declare types and interfaces that will allow us to extend native objects.

Here's how the implementation works step-by-step:

1. Adding a new method to a native object: We start by declaring a global enhancement to the Array type. This is achieved through TypeScript's declare global which will not affect runtime behavior but allows us to tell TypeScript about the new shape of the Array interface.

   declare global {
       interface Array<T> {
           last(): T | -1;
       }
   }

   Here we're telling TypeScript that we're adding a new method last that will return either the last element of the array, of type T, or the number -1.

2. Implementing the last Method: The functionality of this method is attached to the Array prototype. Attaching properties or methods to a prototype means all instances of the prototype will have access to those properties or methods.

   Array.prototype.last = function () {
       return this.length ? this.at(-1) : -1;
   };

3. Logic within the last Method: The last method checks whether the array upon which it's called (this) has any elements by checking this.length. If the length is not zero, meaning the array has at least one element, it returns the last element using this.at(-1). Otherwise, if the array is empty (length === 0), it returns -1.

4. ESNext Feature: The at method utilized here is a part of ESNext (proposed features for ECMAScript beyond its current edition). It allows for direct access to the array element at a given index, including negative indices which count backwards from the last item.

5. No Reference Solution Approach: The reference solution approach is not provided in the description; however, based on the problem description and solution code, the aforementioned steps define the algorithm and approach used clearly.

6. Exporting as a TypeScript Module: Lastly, the solution includes export {};, which is necessary to treat the file as a module, which in turn allows the global declaration augmentation. Without treating the file as a module, you could unintentionally pollute the global namespace.

Algorithmically, this is a very straightforward approach: enhancement involves extending an existing data structure (the Array) with an additional method. The pattern used here is augmentation of a native prototype, which is a powerful feature of JavaScript that needs to be used carefully to avoid unexpected side-effects, especially when extending native objects.

Example Walkthrough

Let's consider a small example to illustrate the solution approach detailed in the content provided.

Suppose we have two arrays, one with several elements, and one that is empty:

let numbersArray = [10, 20, 30, 40, 50];
let emptyArray = [];

To utilize the last method that we plan to add to the Array prototype, we would perform the following steps:

1. Declare and Define the last Method: First, we declare the method in the global scope, telling TypeScript about this new method we're going to create. Then, we actually define the method on the Array prototype as shown earlier.

2. Applying the last Method to Arrays: After adding the last method to the Array prototype, it becomes available on all array instances, including numbersArray and emptyArray.

3. Calling the last Method on our Arrays:

   • When numbersArray.last() is called, the method checks if numbersArray is empty. Since its length is not zero (it has elements), it will return the last element, which is 50.

   let lastElementOfNumbers = numbersArray.last(); // expected to return 50

   • When emptyArray.last() is called, the method looks at the length of emptyArray, finds it to be 0, and thus returns -1, indicating that the array is empty.

   let lastElementOfEmpty = emptyArray.last(); // expected to return -1

By following these steps, we have enhanced all array instances in our TypeScript environment with a new last method that adheres to the logic described. This method is now part of the array's prototype chain, so any array created or that exists within the TypeScript runtime has access to it. The export {} at the end of our TypeScript file ensures that the module's augmented type declaration does not leak into the global scope unintentionally.

Using this method, developers can now reliably get the last element of any array or handle the case when the array is empty without needing to write additional logic each time this common task is required.

Solution Implementation

Time and Space Complexity

Time Complexity

The time complexity for the last method is O(1). This is because the method simply accesses the last element of the array if the array is not empty, using the Array.prototype.at(-1) method, which is a constant-time operation.

Space Complexity

The space complexity for the last method is O(1). The method does not use any additional space that is dependent on the input size. It simply returns the existing value from the array or the number -1.