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Assume that the value of each coin is a positive integer. Your principle is superb; the situation is one point that not sufficient folks are talking intelligently about. Typig greedy algorithms require optimal substructure AND the greedy choice while dynamic programming only requires The value of each coin is already given.
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A greedy algorithm is the one that always chooses the best solution at the time, with no regard for how that choice will affect future choices.
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