HTables_8
During open addressing, if the number of probes exceeds 1, expected run time complexity of the hash table becomes O(____).
(number of probes = k, size of table =n)

Question

HTables_8
During open addressing, if the number of probes  exceeds 1, expected run time complexity of the hash table becomes O(____).
(number of probes = k, size of table =n)

BlackTom AI · Accepted Answer

The question asks about the expected run time complexity of an open addressing hash table when the number of probes exceeds 1, with notation: number of probes = k and table size = n.
Option by option analysis:
- Option "k": While the time to resolve a single lookup/insert in open addressing grows with how many probes you must perform, the standard way to express the overall expected complexity for a hash table operation is in terms of the table size n (and load factor), not directly in terms of k. Saying O(k) would be precise if you are analyzing a single operation in isolation as a function of the number of probes, but the question’s framing emphasizes the typical overall expected complexity as a function of the table size, given that k can vary up to n. Therefore, labeling the complexity as O(k) does not align with the expected-parameter convention used here.
- Option "n": This choice reflects the idea that as probing increases with a nontrivial number of probes, you may end up inspecting a sizable portion of the table. In many analyses of open addressing under nontrivial probe counts, the expected cost grows with the table size, approaching linear in n in the worst or near-worst scenarios. Thus, O(n) is a reasonable and commonly cited expression for the expected time when probes are not bounded by a small constant and the load factor is substantial.
- Option "1": This would imply constant-time performance regardless of probes, which contradicts the open addressing behavior where additional probes directly contribute to more work. Hence it is incorrect for nontrivial probe counts.
- Option "n2": Interpreting as O(n^2) would imply a quadratic time growth with table size, which is not consistent with standard open addressing analyses where the cost grows roughly linearly with table size in typical high-probe scenarios, not quadratically.

In summary, since the question frames the expected complexity in terms of the table size n under nontrivial probing, option "n" is the most fitting choice among the given options. The other options either misrepresent how probe count translates to overall cost (k), or state an implausible constant (1), or exaggerate to a quadratic growth (n2).

HTables_8 During open addressing, if the number of probes exceeds 1, expected run time complexity of the hash table becomes O(____). (number of probes = k, size of table =n)

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