This is a homework question, but I think there's something missing from it. It asks:

Provide a sequence of m keys to fill a hash table implemented with linear probing, such that the time to fill it is minimum.

And then

Provide another sequence of m keys, but such that the time fill it is maximum. Repeat these two questions if the hash table implements quadratic probing

I can only assume that the hash table has size m, both because it's the only number given and because we have been using that letter to address a hash table size before when describing the load factor. But I can't think of any sequence to do the first without knowing the hash function that hashes the sequence into the table.

If it is a bad hash function, such that, for instance, it hashes every entry to the same index, then both the minimum and maximum time to fill it will take O(n) time, regardless of what the sequence looks like. And in the average case, where I assume the hash function is OK, how am I suppossed to know how long it will take for that hash function to fill the table?

Aren't these questions linked to the hash function stronger than they are to the sequence that is hashed?

As for the second question, I can assume that, regardless of the hash function, a sequence of size m with the same key repeated m-times will provide the maximum time, because it will cause linear probing from the second entry on. I think that will take O(n) time. Is that correct?

Thanks