subset_sum_backtrack, a MATLAB code which uses backtracking to seek solutions of the subset sum problem, in which it is desired to find a subset of integers which has a given sum.
The computer code and data files made available on this web page are distributed under the MIT license
subset_sum_backtrack is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python 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, 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.
knapsack_01_brute, a MATLAB code which uses brute force to solve small versions of the 0/1 knapsack problem;
knapsack_dynamic, a MATLAB code which uses dynamic programming to solve a knapsack problem.
knapsack_greedy, a MATLAB code which uses a greedy algorithm to estimate a solution of the 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.
mcnuggets_diophantine, a MATLAB 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.
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.
satisfy_brute, a MATLAB 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_sum, a MATLAB code which seeks solutions of the subset sum problem, in which it is desired to find a subset of integers which has a given sum.
subset_sum_brute, a MATLAB 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.
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 a number of simple variations, seeking to quickly find a tour of lower cost.
tsp_greedy, a MATLAB code which reads a file of city-to-city distances, picks a starting city, and then successively visits the nearest unvisited city.
tsp_random, a MATLAB code which reads a file of city-to-city distances, and then randomly samples a number of possible tours, to quickly seek a tour of lower length.