# KNAPSACK_01 Maximal Packing of a Knapsack with Given Items

KNAPSACK_01, a MATLAB library 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 FORTRAN77 version and a MATLAB version and a Python version.

### Related Data and Programs:

CHANGE_MAKING, a MATLAB library which considers the change making problem, in which a given sum is to be formed using coins of various denominations.

COMBINATION_LOCK, a MATLAB program which simulates the process of determining the secret combination of a lock.

COMBO, a MATLAB library which includes many combinatorial routines.

KNAPSACK_01, a dataset directory which contains test data for the 0/1 knapsack problem;

PARTITION_PROBLEM, a MATLAB library which seeks solutions of the partition problem, splitting a set of integers into two subsets with equal sum.

SATISFY, a MATLAB program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem.

SUBSET, a MATLAB library which enumerates, generates, ranks and unranks combinatorial objects including combinations, partitions, subsets, index sets, and trees.

SUBSET_SUM, a MATLAB library 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.

TSP_BRUTE, a MATLAB program which reads a file of city-to-city distances and solves the traveling salesperson problem, using brute force.

### 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.
• timestamp.m prints the current YMDHMS date as a time stamp.

### Examples and Tests:

You can go up one level to the MATLAB source codes.

Last revised on 21 August 2014.