change_polynomial, a MATLAB code which uses a polynomial algorithm to count the number of 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.
change_diophantine, a MATLAB 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.
change_dynamic, a MATLAB code which uses dynamic programming to solve the change making problem, which counts the number of ways a given sum can be formed using coins of various denominations.
change_greedy, uses the greedy method to seek a solution to the change making problem, which tries to match a given amount by selecting coins of various denominations.
change_making, a dataset directory which contains test data for the change making problem;
combination_lock, a MATLAB code which simulates the process of determining the secret combination of a lock.
combo, a MATLAB code which includes many combinatorial routines.
football_dynamic, a MATLAB code which uses dynamic programming to count the ways of achieving a given score in football.
mcnuggets, a MATLAB code which counts M(N), the number of ways a given number N of Chicken McNuggets can be assembled, given that they are only available in packages of 6, 9, and 20.
partition_brute, a MATLAB code which uses brute force to seek solutions of the partition problem, splitting a set of integers into two subsets with equal sum.
partition_greedy, a MATLAB code which uses a greedy algorithm to seek a solution of the partition problem, in which a given set of integers is to be split into two groups whose sums are as close as possible.
polynomial_multiply, a MATLAB code which multiplies two polynomials p(x) and q(x).
satisfy, a MATLAB code which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem.
subset, a MATLAB code which enumerates, generates, ranks and unranks combinatorial objects including combinations, partitions, subsets, index sets, and trees.
subset_sum, a MATLAB code which seeks solutions of the subset sum problem, in which it is desired to find a subset of a set of integers which has a given sum.
tsp_brute, a MATLAB code which is given a city-to-city distance table, and solves a (small) traveling salesperson problem (TSP), using brute force.
tsp_descent, a MATLAB code which is given a city-to-city distance table, chooses an initial tour at random, and then tries simple variations, seeking to quickly find a tour of lower cost for the traveling salesperson problem (TSP).
tsp_greedy, a MATLAB code which is given a city-to-city distance table,, and solves a small traveling salesperson problem (TSP) using the greedy algorithm. It picks a starting city at random, and then successively visits the nearest unvisited city.
tsp_random, a MATLAB code which is given a city-to-city distance table, seeks a solution of the Traveling Salesperson Problem (TSP), by randomly generating round trips that visit every city, returning the tour of shortest length.