✨ Merkle tree generation

[bal7hazar]

• Add poseidon version of the merkle tree
• Add proof computation
• Clean and add corresponding tests

Pull Request type

Please check the type of change your PR introduces:

• Bugfix
• Feature
• Code style update (formatting, renaming)
• Refactoring (no functional changes, no API changes)
• Build-related changes
• Documentation content changes
• Other (please describe):

What is the current behavior?

Issue Number: #169
Issue Number: #170

What is the new behavior?

• A new implementation of the MerkleTree using poseidon hash method
• Add a compute_proof method to the MerkleTreeTrait to generate a proof based on leaves and an index
• Rename the previous merkle tree type from MerkleTree to MerkleTreeLegacy
• Merkle tree tests refactoring to clarify tests and add tests according to the new feature

Does this introduce a breaking change?

• Yes
• No

Before the change you could just have:

use alexandria_data_structures::merkle_tree::MerkleTreeTrait;
let mut merkle_tree = MerkleTreeTrait::new();

Now you must specify which kind of merkle tree you want (the legacy version or the new one):

// The new version, using the poseidon hash method
use alexandria_data_structures::merkle_tree::{MerkleTree, HashMethod, MerkleTreeTrait};
let hash_method = HashMethod::Poseidon(());
let mut merkle_tree = MerkleTreeTrait::new(hash_method);

// The legacy version, using the pedersen hash method
use alexandria_data_structures::merkle_tree::{MerkleTree, HashMethod, MerkleTreeTrait};
let hash_method = HashMethod::Poseidon(());
let mut merkle_tree = MerkleTreeTrait::new(hash_method);

Other information

Work load: ~ 8 hours

[bal7hazar]

@LucasLvy could you take the lead on this review please to move forward?