Optimize Initialization Process in Concurrent Merkle Tree

[silentEAG]

Description:

In the file libraries/concurrent-merkle-tree/src/concurrent_merkle_tree.rs at line 109, an empty_node_cache is defined but it is immutable. Even though empty_node_cached generates rightmost_proof and path, it cannot utilize the cache when cache[target] == EMPTY. My understanding is that empty_node_cache should be able to store the results from previous levels and use them for generating the current level, thereby avoiding recursive calls.

Verification:
To verify the issue, insert println!("level: {}", level) in the empty_node_cached func to output the current level. Then, run the following test code:

#[tokio::test(flavor = "multi_thread")]
async fn verify_it() {
    let mut tree1 = ConcurrentMerkleTree::<DEPTH, BUFFER_SIZE>::new();
    let _ = tree1.initialize().unwrap();
}

For better observation of the output, insert a line after each node generation:

for (i, node) in path.iter_mut().enumerate() {
	*node = empty_node_cached::<MAX_DEPTH>(i as u32, &empty_node_cache);
	println!("");
}

When running the cargo test with stdout, you will observe:

level: 0

level: 1
level: 0

level: 2
level: 1
level: 0

level: 3
level: 2
level: 1
level: 0

level: 4
level: 3
level: 2
level: 1
level: 0

...

This pattern introduces an O(n(n+1)/2) computational overhead which is unnecessary.