subset_sum, a Python 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_TABLE works by a kind of dynamic programming approach, constructing a table of all possible sums from 1 to S. The storage required is N * S, so for large S this can be an issue.
SUBSET_SUM_FIND works by brute force, trying every possible subset to see if it sums to the desired value. It uses the bits of a 32 bit integer to keep track of the possibilities, and hence cannot work with more N = 31 weights.
The computer code and data files made available on this web page are distributed under the GNU LGPL license.
subset_sum 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 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.
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;
mcnuggets, a Python 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 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.
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_sum_backtrack, a Python code which uses backtracking to solve the subset sum problem, 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.
tsp_brute, a Python code which reads a file of city-to-city distances and solves the traveling salesperson problem, using brute force.
tsp_descent, a Python 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 Python code which reads a file of city-to-city distances and solves the traveling salesperson problem, using a greedy algorithm.
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.