Abstract. We investigate the structure of the currencies (systems of coins) for which the greedy change-making algorithm always finds an optimal solution (that is, a one with minimum number of coins). We present a series of necessary conditions that must be satisfied by the values of coins in such systems. We also uncover some relations between such currencies and their sub-currencies.
Recently, Niewiarowska and Adamaszek REF investigate the structure of canonical coin systems and present a series of suf cient conditions of non-canonical coin systems.
Combinatorics of the change-making problem
Mathematics Computer Science