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Coin change problem algorithm from wikipedia


Change-making problem

The change-making problem addresses the question of finding the minimum number of coins (of certain denominations) that add up to a given amount of money. It is a special case of the integer knapsack problem, and has applications wider than just currency.
It is also the most common variation of the coin change problem, a general case of partition in which, given the available denominations of an infinite set of coins, the objective is to find out the number of possible ways of making a change for a specific amount of money, without considering the order of the coins.
It is weakly NP-hard, but may be solved optimally in pseudo-polynomial time by dynamic programming.[1][2]

Mathematical definition

Non-currency examples

Methods of solving

Related problems

See also


Further reading