Start by clarifying requirements and edge cases, then design the Merkle tree with a clear hashing scheme (e.g., SHA-256) and define node structure. Implement the core functions—build tree, get root, generate proof, verify proof—and analyze time/space complexity. Finally, discuss real-world applications like blockchain and distributed systems, highlighting trade-offs.
Pro tip: Mention that proof verification only requires the root hash and the proof, not the full tree, and emphasize the logarithmic proof size. Also, discuss how to handle odd numbers of nodes (e.g., duplicate last node) to show attention to detail.
Ask about data block size, hash function, handling of empty input, odd number of leaves, and whether the tree should be balanced. Confirm that proof verification should work without the full tree.
Define leaf nodes as hashes of data blocks, internal nodes as hashes of concatenated child hashes. Decide on a consistent hashing scheme (e.g., SHA-256) and how to handle odd nodes (e.g., promote or duplicate).
Write functions to build the tree from a list of blocks, compute the root hash, generate an inclusion proof for a given block (list of sibling hashes), and verify a proof given a root hash and block.
Discuss time complexity: O(n) to build, O(log n) to generate/verify proof. Space: O(n) for tree, O(log n) for proof. Mention trade-offs like using a balanced tree vs. other structures.
Explain how Merkle trees are used in blockchain (e.g., Bitcoin), distributed systems (e.g., IPFS, Cassandra), and version control (e.g., Git) for efficient data verification and integrity.
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