Abstract

The change-making problem is the problem of representing a given value with the fewest coins possible. We investigate the problem of determining whether the greedy algorithm produces an optimal representation of all amounts for a given set of coin denominations 1 = c1 < c2 < ... < c m . Chang and Gill [1] show that if the greedy algorithm is not always optimal, then there exists a counterexample x in the range c3 ≤ x < cm(c m cm−1+ c m − 3cm1/cm−cm− 1.

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