Comments on the Assumption

Very odd assumption (even somewhat ill-defined).

Stronger (less general, worse) than the assumption in randomized quicksort. There, we showed that the randomization in the algorithm made it so no particular input elicits worst-case behavior.

Weaker (more general, better) than the assumption needed to show non-randomized quicksort efficient. There, we'd need to assume that the probability of a bad input (reversed list) was small.

Here, we are putting a restriction on the combination of our hash function and our inputs. The better our hash function is, the less we care about the key sequence.


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