Bitcoin nodes do not store merkle trees, so there is nothing to save.

The particular layout you suggest has poor locality. E.g. the first node above 0 is at 8 instead of being as soon as it could possibly be, at 2. Even in ram access locality matters. (at least to the extent that performance matters at all)

It also only works for trees which are fully populated at every level-- ones where the size is a power of two-- or otherwise it requires padding up to the next power of two size which wastes a *lot* of space.

First, thank you Sir for replying:

1-I was not sure about Transactions Merkle Trees, that's why I asked at the last paragraph; if not stored for each block, then no use in TX Merkle Tree. As I said, I originally suggested it for the Utreexo design.

-but in any case, where is the transaction Merkle Tree is stored?since I think the number of transactions do not deviate too much from powers of 2. With the current average it could be 2¹¹ or 2¹¹ + 2⁹, from what I understand the numbers will increase after applying Schnorr signature but still near powers of2; and even easier to handle than UTXOS as it's not dynamic.

2-The Utreexo design works by keeping logN roots of only complete full binary trees (a forest) to make sure there's at max 2logN nodes in any proof: all the roots + the regular proof from the tree the UTXO in

(it's like a binary representation of a number, u can always partition a number to a summation of powers of2.

**So, whatever way he is storing the trees in his forest they are always full binary trees**.

3-I don't understand what u meant about the example; if u mean it's not the typical way they compact a tree to 1D array in data structures literature, I made it this way to visualize it more easy; when u insert or delete u need to look the true parent (for 0&1 it's 8), while

in the proof fetching which I wrote a Pseudocode u need

9 for 0&1 (not 8), and 8 for 2&3.

They did say that was one of their problems in addition to space saving (if no care for space saving, they would have stored 3pointers :2 to children & 1 to aunt or niece)

So this way they can reach parent/aunt/sibling/... whatever they want with the right math indexing.

4-I thought this 2D (like half pyramid side for the forest, where the 2D array looks like a horizontal right angle triangle layer for each power of2 tree) is easier and do the job of saving the pointers. If they can compact it even more into 1D and get all the math indexing, shift when insert/delete correct ( I'm not sure which makes less shifts with insert/delete the 2D or 1D)fine, but the way it seems they still use pointers.