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Logic & Puzzles

An algorithm repeatedly processes a dataset. If a potential function, defined as the sum of unprocessed data elements, strictly decreases with each iteration, which consequence follows?

A)Algorithm requires infinite iterations
B)Algorithm must eventually terminate
C)Algorithm converges to local optimum
D)Algorithm achieves global optimum

💡 Explanation

The algorithm must eventually terminate because a strictly decreasing potential function that is bounded below cannot decrease indefinitely; this is the essence of the Invariant method. Therefore, termination is guaranteed rather than indefinite looping, which would violate the decreasing potential function requirement.

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