# knapsack_01

knapsack_01, a MATLAB code which uses brute force to solve small versions of the 0/1 knapsack problem.

In the 0/1 knapsack problem, we are given a knapsack with carrying capacity C, and a set of N items, with the I-th item having a weight of W(I). We want to pack as much total weight as possible into the knapsack without exceeding the weight limit. We do this by specifying which items we will not take (0) or take (1).

This library uses a simple brute force or exhaustive search method, which is guaranteed to get the optimal solution, but which is not efficient for large values of N.

### Languages:

knapsack_01 is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

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### Source Code:

• knapsack_01.m seeks the optimal solution of the 0/1 knapsack problem using exhaustive search.
• subset_gray_next.m computes all possible subsets of a set of N objects, one at a time.

Last revised on 06 February 2019.