Combinatorial optimization | Number theory | Recreational mathematics

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. (Wikipedia).

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Related pages

Pseudo-polynomial time | Knapsack problem | List of knapsack problems | Dynamic programming | Integer | Weak NP-completeness | Package-merge algorithm | Partition problem | Coin problem | Greedy algorithm | Fast Fourier transform | Special case