Alice and Bob Experimenting with Algorithm ZETA

Alice and Bob's Algorithm Study

Alice and Bob are experimenting with an algorithm ZETA. Alice conducted an empirical study and concluded that ZETA is definitely Omega(n logn) in terms of its efficiency. On the other hand, Bob's study suggests that the algorithm is definitely O(n²). This discrepancy in their findings sparks a discussion about the true time complexity of algorithm ZETA.

Statement Analysis

Statement: Algorithm ZETA is definitely O(n).

Final answer:

Alice believes the algorithm ZETA has a lower bound of Omega(n logn) while Bob claims an upper bound of O(n²). There is no sufficient information to support the algorithm being O(n). Instead, ZETA's time complexity is at least n logn and at most n².

Explanation:

The question is centered on determining the time complexity of an algorithm called ZETA based on empirical studies presented by two individuals, Alice and Bob. Alice claims that the algorithm is Omega(n logn), which means the algorithm's running time grows at least as fast as n logn for large enough n. Bob states the algorithm is O(n²), indicating that the running time does not grow faster than the function n².

Based on these claims, the correct statement is not provided in the original question. It would be incorrect to conclude that the algorithm is definitely O(n) given the previous statements made by Alice and Bob. Without additional information, it is only safe to say that ZETA's complexity is bounded below by n logn (per Alice's claim) and above by n² (per Bob's claim).