change_polynomial, a Python code which uses a polynomial multiplication algorithm to count the ways of making various sums using a given number of coins.
In this version of the change making problem, the order of the coins is significant. In other words, if we are using exactly 3 coins to make 16 cents, then we count 6 separate solutions: (1,5,10), (1,10,5), (5,1,10), (5,10,1), (10,1,5) and (10,5,1). Similarly, we count three essentialy equivalent solutions to forming the sum of 7 cents.
If the user wishes to determine the number of ways of forming sums using anywhere from 0 up to COIN_NUM coins, inclusive, then it is only necessary to include a coin of value 0 in the denomination list.
The computer code and data files described and made available on this web page are distributed under the MIT license
change_polynomial is available in a MATLAB version and an Octave version and a Python version.
change_diophantine, a Python code which sets up a Diophantine equation to solve the change making problem, which counts the number of ways a given sum can be formed using coins of various denominations.
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