Say, the smallest item in a hash table for which item.key is larger than given_item.key. Well, keys in a hash table are hashed. This implies that unless you'r

Say, the smallest item in a hash table for which item.key is larger than given_item.key. Well, keys in a hash table are hashed. This implies that unless you're searching for a specific key (e.g. "42") rather than a condition (e.g. "smallest key greater than 42") then the time complexity is necessarily O(N).