mcnuggets_diophantine, a Python code which uses Diophantine methods to find the ways a given number N of Chicken McNuggets can be assembled, given that they are only available in packages of 6, 9, and 20.
The computer code and data files described and made available on this web page are distributed under the MIT license
mcnuggets_diophantine 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.
change_dynamic, a Python 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, a Python code which 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_polynomial, a Python code which uses a polynomial multiplication algorithm to count the ways of making various sums using a given number of coins.
diophantine_nd, a Python code which is given a Diophantine equation in N variables, and returns all strictly positive solutions, or all nonnegative solutions.
football_dynamic, a Python code which uses dynamic programming to count the ways of achieving a given score in football.
knapsack_01_brute, a Python code which uses brute force to solve small versions of the 0/1 knapsack problem;
knapsack_greedy, a Python code which uses a greedy algorithm to estimate a solution of the knapsack problem;
partition_brute, a Python code which uses a brute force method to find solutions of the partition problem, in which a set of integers must be split into two subsets with equal sum.
partition_greedy, a Python 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.
satisfy_brute, a Python code which uses brute force to find all assignments of values to a set of logical variables which make a complicated logical statement true.
subset, a Python code which enumerates, generates, ranks and unranks combinatorial objects including combinations, partitions, subsets, index sets, and trees.
subset_sum, a Python 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.
subset_sum_brute, a Python code which uses brute force to solve the subset sum problem, to find a subset of a set of integers which has a given sum.
test_values, a Python code which supplies test values of various mathematical functions, including Abramowitz, AGM, Airy, Bell, Bernoulli, Bessel, Beta, Binomial, Bivariate Normal, Catalan, Cauchy, Chebyshev, Chi Square, Clausen, Clebsch Gordan, Collatz, Cosine integral, Dawson, Debye, Dedekind, dilogarithm, Exponential integral, Elliptic, Error, Euler, Exponential integral, F probability, Fresnel, Frobenius, Gamma, Gegenbauer, Goodwin, Gudermannian, Harmonic, Hermite, Hypergeometric, inverse trigonometic, Jacobi, Julian Ephemeris Date, Kelvin, Laguerre, Laplace, Legendre, Lerch, Lobachevsky, Lobatto, Logarithmic integral, Log normal, McNugget numbers, Mertens, Mittag-Leffler, Moebius, Multinomial, Negative binomial, Nine J, Normal, Omega, Owen, Partition, Phi, Pi, Poisson, Polylogarithm, Polyomino, Prime, Psi, Rayleigh, Hyperbolic Sine integral, Sigma, Sine Power integral, Sine integral, Six J, Sphere area, Sphere volume, Spherical harmonic, Stirling, Stromgen, Struve, Student, Subfactorial, Student probability, Three J, Transport, Trigamma, Truncated normal, van der Corput, von Mises, Weibull, Wright omega, Zeta.
tsp_brute, a Python code which reads a file of city-to-city distances and solves the traveling salesperson problem, using brute force.
tsp_greedy, a Python code which reads a file of city-to-city distances, 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 Python 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.