I am building a sparse matrix II, however, when I assign some of its elements by zeros they are being stored with zero values unless I use dropzeros(II).

1- Why using sparse(II) below not dropping zeros from II?
2- Is there a way to set (as default) at the first of my code that assigning zeros will not be stored into II?

Thanks for your reply!
This is because I have a for loop and inside it I change the value of II and then calculate X = A \II. So, I want to avoid using dropzeros(II) in the loop.

for i:11000
# change in II
II = dropzeros(II)
X = A \II
end

Note that you should do dropzeros!(II) and not II=dropzeros(II). In any case, this is not advisable if performance is a concern.
The real reason is that removing/inserting a single entry in SparseArrayCSC is very slow (O(n)) where n is the number of nonzeros. So that loop would be reeeally slow (O(n^2)). True, there is an overhead in dropzeros! for finding where the new zero is, but it would still be O(n^2) without that. Do you really need remove it? It’s probably faster by just setting it to zero.

well, constructing the sparse matrix would be also slow (possibly slower!), so I wouldn’t advise that. Note that dropzeros! would not be needed in this case. But it’s really easy to benchmark, just use the BenchmarkTools package with the @btime macro. e.g.

In general, constructing sparse matrices element-by-element with A[i,j] = val is extremely slow. If you want to construct matrices element-by-element, use the sparse(I,J,V) constructor.

(Changing entries of a sparse matrix without changing the sparsity pattern is fast, though.)