You can generate that input only when needed. So whenever the sorting algorithm asks whether A[i] > A[i+1], you can perform the comparison there and then. So the answer to your question is yes.

The input is always needed, the neural net is an iterative algorithm that views the "local information" gathered from the array on every time step. It's asking continuously whether e.g. `A[i] > A[i+1]`.

No, the neural net needs to receive a feature vector before each instruction in order to sort the array. So whenever you want to sort things, you need to create that vector over and over.