# python_combinatorics

python_combinatorics, a Python code which considers a variety of problems in combinatorics involving counting, combinations, permutations, and so on.

### Related Data and codes:

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_01_brute, a Python code which uses brute force to solve small versions of the 0/1 knapsack problem;

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;

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.

Last revised on 07 February 2023.