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    As an example for a similar data structure with worse worst-case complexity, consider hash tables: O(1) typical lookup speed (most of the time, can find correct element immediately), but O(n) worst case (might have to search all elements). Commented Oct 5, 2021 at 17:35
  • 2
    @amon Yes exactly. If your hashing algorithm is bad, it devolves into a linear search of an unsorted list. Commented Oct 5, 2021 at 17:37
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    Adding to the fun, it's often also helpful to look at the prerequisites of an algorithm. Binary search is O(log n), but it requires that the input be sorted first. A linear search of an unsorted list is O(n), but it (obviously) doesn't require that the input be sorted. And, that's before real-world complications kick in, too. Commented Oct 6, 2021 at 4:37
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    I think you've made an error with the example - with 16 elements, the worst-case will examine 4 of them; the average case almost 3 (and both scale proportionally to log n, but with different constants of proportion). Commented Oct 6, 2021 at 15:04
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    I guess the key point is that average and worst-case scale the same way, but average is usually some fraction of worst-case. Commented Oct 6, 2021 at 15:36