Start by clarifying the requirements: hash function, tree structure (binary or n-ary), and operations (build, update, verify). Then outline the recursive construction: hash leaves, pair and hash upwards until a single root hash. Finally, discuss implementation details, complexity, and potential optimizations.
Pro tip: Mention that Merkle trees enable efficient verification of large data sets and are used in systems like Git and blockchains; this shows you understand real-world applications beyond the algorithm itself.
Ask about the hash function (e.g., SHA-256), tree arity (binary is common), and whether the tree needs to support dynamic updates or just static construction. Also confirm if odd number of leaves should be handled by duplicating the last leaf or promoting it.
Define a Node class with hash value, left and right child pointers (for binary tree), and optionally a reference to the original data. For leaves, store the hash of the data block.
Recursively compute hashes: for each leaf, hash the data; for internal nodes, concatenate children's hashes and hash the result. Handle odd number of nodes by duplicating the last node or carrying it up.
For verification, provide a function that takes a leaf, its index, and a proof (list of sibling hashes) to recompute the root. For updates, recompute hashes along the path from the leaf to the root.
State time complexity: O(n) to build, O(log n) to verify or update. Mention space complexity O(n). Discuss optimizations like caching intermediate hashes or using a balanced tree for dynamic updates.
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