Question

For what values of n is algorithm B at least 1,000 times more efficient than algorithm A? (Enter your answer as a single inequality solved for n).

a) n > 1000
b) n < 1000
c) n ≥ 1000
d) n ≤ 1000

Answer 1

To determine when algorithm B is at least 1,000 times more efficient than algorithm A, the correct inequality is n ≥ 1000. The correct answer is option c).

Step-by-step explanation:

To determine for what values of n algorithm B is at least 1,000 times more efficient than algorithm A, we must come up with an inequality that represents this condition. Being '1,000 times more efficient' means that for algorithm B to be at least as efficient as algorithm A.

Algorithm A's performance metric, or time complexity, should be 1,000 times worse (larger) than that of algorithm B. If we let T(A) represent the time complexity of algorithm A and T(B) the time complexity of algorithm B, the condition can be formalized as T(A) ≥ 1000 × T(B).

However, without specific expressions for T(A) and T(B), we cannot solve for n directly. Typically, these expressions are functions of n, the size of the input. Given that 'at least 1,000 times' implies a threshold that must be met or exceeded, the correct inequality for n would be n ≥ 1000, which corresponds to option c) n ≥ 1000.