Problem Description

The problem requires creating a class ArrayWrapper that encapsulates an array of integers. This class should offer two specific behaviors:

1. When two instances of ArrayWrapper are added together using the + operator, the result should be an integer representing the sum of all elements in both arrays wrapped by the instances.

2. When the String() function is invoked on an instance of ArrayWrapper, it should return a string representing the elements in the array, formatted as a comma-separated list enclosed within brackets.

To summarize, the ArrayWrapper class needs to handle two types of operations: arithmetic addition and string conversion, going beyond the typical array functionality.

Intuition

To address the two requested features of the ArrayWrapper class, we need to implement two key methods:

1. The valueOf() method: In JavaScript and TypeScript, the valueOf() method is called when an object is used in a context that expects a primitive value. By overriding this method, we can return the pre-calculated sum of the array's elements whenever the + operator is used on an instance of ArrayWrapper.

2. The toString() method: This method is invoked when we attempt to convert an object to a string, such as when passing an object to the String() function. Overriding the toString() method allows us to return the array elements as a formatted string, which matches the second behavior requirement.

The solution starts by initializing two instance variables in the constructor: nums to store the array of integers and s to store the sum of the array's elements. This sum is computed upfront using the reduce() function to avoid repeated calculations during addition operations.

In the valueOf() method, the sum s is returned so that it can be used in arithmetic operations. When two ArrayWrapper instances are added, this method is automatically called, and the sums of both instances are added together.

In the toString() method, a string representation of the array is constructed using template literals, ensuring the format [1,2,3] is achieved, where the actual numbers come from the stored nums array.

By implementing these methods, ArrayWrapper instances gain the ability to handle addition and string conversion in the desired manner.

Solution Approach

The implementation of the ArrayWrapper class leverages the object-oriented features of TypeScript. Let's walk through the different parts of the implementation and dive into the algorithms, data structures, and patterns used:

• Constructor: The constructor is a special method for creating and initializing objects created with a class. In this case, the constructor accepts an array of integers. Inside the constructor, we have the following steps:

  1. The input array is stored in the private instance variable nums. The keyword private ensures that this variable cannot be accessed directly from outside the class, encapsulating the data.
  2. The sum of the array's elements is calculated using the reduce() function and stored in the private instance variable s. The reduce() function is a higher-order function that accumulates a value by applying a function to each element of an array, in this case, summing up their values.

• valueOf() Method: This method is overridden to fulfill the requirement of returning the sum of the array's elements when the + operator is used. There is no explicit call to this method in the code—the JavaScript (and by extension TypeScript) runtime calls it automatically when an object is used in a context that requires a primitive value (i.e., during arithmetic operations).

• toString() Method: This method is also overridden to meet the requirement of returning a string formatted as a comma-separated list enclosed within brackets whenever the String() function is used. Here, we are using template literals to create the desired string representation of the array.

The combination of these methods allows the ArrayWrapper class to behave correctly for addition and string conversion operations. Once an instance of ArrayWrapper is created, both methods work transparently to provide the functionality without further intervention. This is an example of how overriding built-in JavaScript methods can create custom behavior for operators and functions that normally work with primitive values.

Example Walkthrough

Let's consider a small example to illustrate the solution approach for the ArrayWrapper class. Suppose we initialize two instances of ArrayWrapper with the arrays [1, 2, 3] and [4, 5].

Here's how we could express it in code:

let arrayOne = new ArrayWrapper([1, 2, 3]);
let arrayTwo = new ArrayWrapper([4, 5]);

Now, let's walk through the two behaviors as per the solution approach:

1. When we use the + operator on these instances:

   let sum = arrayOne + arrayTwo;

   Internally, TypeScript will attempt to convert arrayOne and arrayTwo to primitive values, triggering the valueOf() method on each instance. This will return the sum of the elements within each ArrayWrapper.

   For our example, arrayOne.valueOf() will return 6 (since 1+2+3 = 6), and arrayTwo.valueOf() will return 9 (since 4+5 = 9). The result assigned to sum will be their collective sum: 15.

2. When we pass an instance of ArrayWrapper to the String() function:

   let str = String(arrayOne);

   This triggers the toString() method on arrayOne which constructs and returns a string in the format of a comma-separated list, encapsulated in brackets. For arrayOne, the toString() method will produce the string "[1,2,3]".

Now that we have a grasp of the process, let's translate this into the markdown template provided for documentation purposes:

Consider two instances of `ArrayWrapper`, one with the array `[1, 2, 3]` and the other with `[4, 5]`.

```typescript
let arrayOne = new ArrayWrapper([1, 2, 3]);
let arrayTwo = new ArrayWrapper([4, 5]);

Arithmetic Addition Using the + Operator

When we calculate the sum of these two ArrayWrapper instances:

let sum = arrayOne + arrayTwo;

arrayOne + arrayTwo triggers the valueOf() method on both arrayOne and arrayTwo. The sum for arrayOne is 6, while for arrayTwo, it is 9. These sums are then added to give us the total sum, 15, which is the value of sum.

String Conversion Using the String() Function

When we convert arrayOne to a string:

let str = String(arrayOne);

This invocation calls the toString() method on arrayOne, resulting in the string representation "[1,2,3]". This format is achieved by constructing the string with template literals, matching the array within brackets and separated by commas.

This walkthrough provides a clear example of the intended functionalities of the `ArrayWrapper` class: performing arithmetic addition and converting to a string representation.

Solution Implementation

Time and Space Complexity

Time Complexity

For the ArrayWrapper constructor, we have the following operations and their complexities:

• Initializing nums with an array of length n: O(1) (assignment operation)
• Calculating the sum of the nums array with reduce: O(n) where n is the number of elements in the nums array.

Since these are the only two operations in the constructor and the reduce function dominates the time complexity, the overall time complexity for the construction of an ArrayWrapper instance is O(n).

The valueOf method simply returns the sum (this.s), which was pre-computed in the constructor. Thus, the time complexity for this operation is O(1).

The toString method creates a string representation of the array. This operation goes over the array of length n and constructs a string. The time complexity of this method is typically O(n) because it is dependent on the length of the input array.

Space Complexity

• The space complexity for storing nums is O(n), where n is the length of the input array.
• The sum s is just a single number, so it takes O(1).

Hence, the overall space complexity for an instance of the ArrayWrapper class is O(n) due to the storage of the nums array.