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I'm confused, wouldn't this be more of an O(n) instead of an O(log n) issue? If not, then what is the difference? No pointers being used, not even a data structure, just an array of strings. I expected at least a linked list data structure for a phone book. Like sorted in alphabetic order or something.

Correct, OP's example contained an O(n) function:

> For example, the following function is O(n) because the algorithm grows in proportion to its input n: [...]

OP's question was whether there exists a similarly simple example of O(log n), which is not related to what anonymouz was commenting on. (or I'm misunderstanding?)

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