Question: You aim to design an efficient algorithm (polynomial complexity) to find the optimal (lowest) number of coins to give in the coin change problem. You

You aim to design an efficient algorithm (polynomial complexity) to find the optimal (lowest) number of coins to give in the coin change problem. You realised that this is a combinatorial optimisation problem, and only brute-force algorithm can guarantee that you will find the optimal solution.

(1)Why does the brute-force algorithm does not satisfy efficiency requirement, in other words does not have a polynomial complexity?

(2)What complexity class this problem belongs to? What does that mean in terms of complexity to find a solution and verify it for this problem?

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