Answer
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Work Step by Step
Because it uses the phrase “Pick a collection of numbers” without specifying how, it’s non-deterministic — as if the algorithm magically “guesses” the right subset.
So, in the non-deterministic model, its running time is polynomial, because verifying that a chosen subset sums to 125 is quick.
The mystery algorithm is non-deterministic.
In the non-deterministic model, it has polynomial time complexity (because checking a guessed subset is quick).
In the deterministic model, finding such a subset would take nonpolynomial (exponential) time, since there are
$2^n$ possible subsets to test.
