# knapsack_dynamic

knapsack_dynamic, a Python code which uses dynamic programming to solve a knapsack problem.

All the problem data, weights, values, and knapsack capacity, must be integers.

### Languages:

knapsack_dynamic is available in a MATLAB version and an Octave versionand a Python version.

### Related Data and Programs:

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.

combination_lock, a Python code which simulates the process of determining the secret combination of a lock.

combo, a Python code which includes many combinatorial routines.

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 to a 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.

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, 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_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 table, and solves the traveling salesperson problem, using brute force.

tsp_greedy, a Python code which is given a city-to-city distance table, 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.

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.

### Source Code:

Last revised on 02 November 2022.