python_combinatorics, a Python code which considers a variety of problems in combinatorics involving counting, combinations, permutations, and so on.
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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.
combo, a Python code which includes many combinatorial routines.
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.
football2_diophantine, a Python code which uses diophantine analysis to count the ways of achieving a given score in football, ignoring the ordering of events.
football2_dynamic, a Python code which uses dynamic programming to count the ways of achieving a given score in football, respecting the order of events.
knapsack, a dataset directory which contains test data for the knapsack problem; we consider n items of given value and weight, and a knapsack with a weight limit. We wish to select items to store in the knapsack which maximize the total value.
knapsack_01_brute, a Python code which uses brute force to solve small versions of the 0/1 knapsack problem;
knapsack_brute, a Python code which uses brute force to solve small versions of the knapsack problem, in which N items are available, each with given value and weight. A thief's knapsack can carry no more than Wmax pounds. The thief seeks a selection of items to carry in the knapsack of maximum total value.
knapsack_dynamic, a Python code which uses dynamic programming to solve a knapsack problem.
knapsack_greedy, a Python code which uses a greedy algorithm to estimate a solution of the knapsack problem;
knapsack_random, a Python code which randomly chooses a subset of N items, each with given value and weight. It then evaluates whether this is a feasible solution to a problem in which a thief's knapsack can carry no more than Wmax pounds, and it is desired to maximum the total value of the selected items.
knapsack_rational, a Python code which solves the rational knapsack problem, in which a knapsack of limited weight capacity is filled with profitable items. This variation of the knapsack problem allows a fractional part of an item to be included in the knapsack. The result is an upper bound on the maximum possible profit for the knapsack problem.
knapsack_values, a Python code which returns some simple examples of the knapsack problem, in which N items are available, each with given value V and weight W. A thief's knapsack can carry no more than K pounds. The thief seeks a selection S of items to carry in the knapsack of maximum total value.
matrix_chain_brute, a Python code which finds the cost of the most efficient ordering to use when multiplying a sequence of matrices, using brute force.
matrix_chain_dynamic, a Python code which finds the cost of the most efficient ordering to use when multiplying a sequence of matrices, using dynamic programming.
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 brute force to seek solutions of the partition problem, splitting a set of integers 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_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 is given a city-to-city distance map, and solves the traveling salesperson problem (TSP), using brute force.
tsp_descent, a Python 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 Python code which is given a city-to-city distance map, picks a starting city, and then successively visits the nearest unvisited city.
tsp_random, a Python code which is given a city-to-city distance map, and then randomly samples a number of possible tours, to quickly seek a tour of lower length.