# KNAPSACK_01 Maximal Packing of a Knapsack with Given Items

KNAPSACK_01, a FORTRAN90 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 FORTRAN90 library which considers the change making problem, in which a given sum is to be formed using coins of various denominations.

COMBINATION_LOCK, a FORTRAN90 program which simulates the process of determining the secret combination of a lock.

COMBO, a FORTRAN90 library which includes many combinatorial routines.

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

PARTITION_PROBLEM, a FORTRAN90 library which seeks solutions of the partition problem, splitting a set of integers into two subsets with equal sum.

SATISFY, a FORTRAN90 program which demonstrates, for a particular circuit, an exhaustive search for solutions of the circuit satisfiability problem.

SUBSET, a FORTRAN90 library which enumerates, generates, ranks and unranks combinatorial objects including combinations, partitions, subsets, index sets, and trees.

SUBSET_SUM, a FORTRAN90 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 FORTRAN90 program which reads a file of city-to-city distances and solves the traveling salesperson problem, using brute force.

### List of Routines:

• KNAPSACK_01 seeks a solution of the 0/1 Knapsack problem.
• SUBSET_GRAY_NEXT generates all subsets of a set of order N, one at a time.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the FORTRAN90 source codes.

Last revised on 21 August 2014.