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How Does a Merkle Tree Structure Potentially Improve the Efficiency of Cryptographic Proof?

A Merkle tree structure can improve the efficiency of cryptographic proof by allowing a smart contract to verify the inclusion of a specific piece of data within a larger dataset without processing the entire set. The contract only needs the Merkle root (a single hash) and a small path of hashes (the Merkle proof).

This is useful for oracles reporting many data points in one transaction, as it reduces the on-chain data and computational overhead for verification.

How Does the Merkle Tree Structure Contribute to the Efficiency of Cryptographic Proof?
How Is a Merkle Proof Used to Verify a Transaction without Downloading the Entire Blockchain?
How Is the Merkle Tree Structure Used to Verify Transactions Efficiently?
Can a Merkle Proof Be Used to Verify the Integrity of an Options Contract Data Feed?