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:

TypeScript
Copy to clipboard
1const A: number[] = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110];
2const B: number[] = [4, 12, 3, 9, 6, 1, 5, 8, 37, 25, 100];

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

TypeScript
Copy to clipboard
1const result: number[] = [80, 100, 50, 20, 20, 60, 40, 20, 110, 90, 110];

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:

TypeScript
Copy to clipboard
1type BElement = { value: number; index: number };
2
3function findAndReplace(A: number[], B: number[]): number[] {
4    let B_sorted: BElement[] = [];
5    for (let i = 0; i < B.length; i++) {
6        B_sorted.push({ value: B[i], index: i });
7    }
8    B_sorted.sort((a, b) => a.value - b.value);

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.

TypeScript
Copy to clipboard
1    let j: number = 0; // TypeScript enforces number type for pointer
2    let res: number[] = new Array(A.length); // Result array with number type

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.

TypeScript
Copy to clipboard
1    for (let i = 0; i < B.length; i++) {
2        let target: number = 2 * B_sorted[i].value; // Calculate target number
3        while (j < B.length - 1 && B_sorted[j + 1].value < target) {
4            j++; // Adjust pointer to find closest number less than the target
5        }
6        if (j < B.length - 1 &&
7            Math.abs(B_sorted[j + 1].value - target) < Math.abs(target - B_sorted[j].value)) {
8            j++; // Increment pointer if next number is closer to the target
9        }

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.

TypeScript
Copy to clipboard
1        res[B_sorted[i].index] = A[B_sorted[j].index];  
2        // Align and assign the correct elements to the result array
3    }
4
5    return res;
6}

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

TypeScript
Copy to clipboard
1type BElement = { value: number; index: number };
2
3function findAndReplace(A: number[], B: number[]): number[] {
4    let B_sorted: BElement[] = [];
5    for (let i = 0; i < B.length; i++) {
6        B_sorted.push({ value: B[i], index: i });
7    }
8    B_sorted.sort((a, b) => a.value - b.value);
9
10    let j: number = 0; // Pointer as a number type
11    let res: number[] = new Array(A.length); // Result array with number type
12
13    for (let i = 0; i < B.length; i++) {
14        let target: number = 2 * B_sorted[i].value; // Calculate target number
15        while (j < B.length - 1 && B_sorted[j + 1].value < target) {
16            j++; // Adjust pointer to find closest number
17        }
18        if (j < B.length - 1 && 
19            Math.abs(B_sorted[j + 1].value - target) < Math.abs(target - B_sorted[j].value)) {
20            j++; // Increment pointer for closer match
21        }
22        res[B_sorted[i].index] = A[B_sorted[j].index];  
23    }
24
25    return res;
26}
27
28const A: number[] = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110];
29const B: number[] = [4, 12, 3, 9, 6, 1, 5, 8, 37, 25, 100];
30const result: number[] = findAndReplace(A, B);
31console.log(result); // Output: [80, 100, 50, 20, 20, 60, 40, 20, 110, 90, 110].

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!