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Suppose we want to make change for n cents, using the least number of coins of denominations 1, 10, and 25 cents. Consider the following
Suppose we want to make change for n cents, using the least number of coins of denominations 1, 10, and 25 cents. Consider the following greedy strategy: suppose the amount left to change is m; take the largest coin that is no more than m; subtract this coin's value from m, and repeat. Either give a counter example, to prove that this algorithm can output a non-optimal solution or prove that this algorithm always outputs an optimal solution
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