Welcome to our exciting TypeScript lesson! Today, you'll tackle a fascinating programming challenge that will enhance your problem-solving skills using TypeScript. This exercise involves working with arrays while employing advanced techniques like sorting and the two-pointer method. Let's dive right in!

Your challenge is to create a TypeScript function to work on two equally long arrays, A and B. The arrays have a length between 1 and 1000, and each element is a unique positive integer ranging from 1 to 1,000,000. Your task involves the following steps:

1. For each element B[i] in the array B, double its value to get 2 * B[i].
2. Identify the closest number to 2 * B[i] in array B, naming it B[j].
3. For each index i, retrieve the value at index j in array A and assign it to the new array.
4. Return a new array where each element corresponds to A[j] based on the closest value found in B.

To illustrate this, let's consider an example:

After executing your function, the resulting array should appear as follows:

Let's begin solving this problem by constructing a sorted structure for array B. We'll use TypeScript type annotations to define an array of objects, where each object contains the elements (value) from B and their respective indices (index).

Here’s how to start our TypeScript function with type annotations included:

In this section, we define BElement to clearly structure B_sorted as an array of objects with defined types, which aids in improving the readability and type safety of our code.

With our sorted array (B_sorted) prepared, we proceed by initializing the right pointer, j, and the result array, res. These will assist in navigating within the bounds of B_sorted and collecting our results, respectively. TypeScript enhances this process by providing type annotations for these variables.

The core logic of this problem is implemented here. Using a loop, we iterate over each element in B_sorted. For every element, the function computes the target, which is twice the value of the current element. We adjust the position of the pointer j to locate the closest number smaller than or equal to the target.

Now, using the indices captured in B_sorted, we modify the elements in A to form our result array res. TypeScript ensures that all operations adhere to the designated types.

Here is the complete TypeScript solution for this task, which successfully implements the outlined logic:

Congratulations on completing the lesson! You have successfully translated a complex problem into TypeScript, utilizing its robust type system to create type-safe arrays and pointers. The use of advanced programming techniques, like sorting and the two-pointer method, further enriched your TypeScript skills and solidified your understanding of functional problem-solving. We encourage you to continue practicing these techniques in varied scenarios to fully master them. Enjoy your coding journey with TypeScript!