knapsack_greedy, a MATLAB code which uses a greedy algorithm to estimate a solution of the knapsack problem.
The computer code and data files described and made available on this web page are distributed under the MIT license
knapsack_greedy 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 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 MATLAB 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 MATLAB code which uses a polynomial multiplication algorithm to count the ways of making various sums using a given number of coins.
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.
knapsack_01, a MATLAB code which uses brute force to solve small versions of the 0/1 knapsack problem;
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 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 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.
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 reads a file of city-to-city distances and solves the traveling salesperson problem, using brute force.
tsp_descent, a MATLAB code which is given a city-to-city distance map, 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 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.