Hello there! Are you ready to solve another engaging problem today? We have a practical task that will enhance your problem-solving skills. It involves critical aspects of programming — dealing with arrays and using techniques such as hashmaps, sorting, and the two-pointer method. So, let's jump in!

Alright, our task is as follows. Suppose you have two equally long arrays, A and B, with a length varying from 1 to 1000, with each element being a unique positive integer ranging from 1 up to 10^6. Your challenge is to craft a Python function that identifies the closest number in array B to 2 * B[i] for each i. Once this number is identified, say for the specific i it is B[j], we want to create an array from A[j]s in the order of increasing is.

To illustrate this, let's consider an example. We have:

A = [10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110]
B = [4, 12, 3, 9, 6, 1, 5, 8, 37, 25, 100]

After running your function, the resulting array should look like this:

[80, 100, 50, 20, 20, 60, 40, 20, 110, 90, 110]

Let's walk through the first few steps:

The first item in B is 4 at index=0. Double of this number is 8. The closest number to 8 in array B is 8 which is at index=7. The number at the same index in array A is 80, so we add 80 to our new array.

The second item in B is 12 at index=1. Double of this number is 24. The closest number to 24 in B is 25 which is at index=9. Corresponding index in A has the number 100. So, we add 100 to our new array.

The third item in B is 3 at index=2. Double of this number is 6. The closest number to 6 in B is 6 which is at index=4. Corresponding index in A has the number 50. So, we add 50 to our new array.

We continue this process for the rest of the elements in B.

Let's embark on our solution-building journey by constructing a sorted list for array B. This list will include pairs of values (val) and their corresponding indices (idx) from array B. Here, val represents the element in B, while idx denotes the index at which val is found in array B.

This sorted list will act similar to a hashmap, storing 'value-index' pairs. It not only organizes the data for efficient retrieval but also makes it easier for us to traverse the list. Here's the introductory part of our Python function, including the complete sorted list:

def find_and_replace(A, B):
    B_sorted = sorted([(val, idx) for idx, val in enumerate(B)], key=lambda x: x[0]) 

In the above code, we generate a list of tuples comprising the values from 'B' and their respective indices using the enumerate function. Then, the sorted function arranges these tuples in ascending order of their values.