# SUBSET_SUM The Subset Sum Problem

SUBSET_SUM, a C++ code which seeks solutions of the subset sum problem.

SUBSET_SUM_NEXT works by backtracking, returning all possible solutions one at a time, keeping track of the selected weights using a 0/1 mask vector of size N.

SUBSET_SUM_TABLE works by a kind of dynamic programming approach, constructing a table of all possible sums from 1 to S. The storage required is N * S, so for large S this can be an issue.

SUBSET_SUM_FIND works by brute force, trying every possible subset to see if it sums to the desired value. It uses the bits of a 32 bit integer to keep track of the possibilities, and hence cannot work with more N = 31 weights.

### Languages:

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

### Related Data and Programs:

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

COMBO, a C++ library which includes many combinatorial routines.

KNAPSACK_01, a C++ library which uses brute force to solve small versions of the 0/1 knapsack problem;

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

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

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

### Reference:

1. Donald Kreher, Douglas Simpson,
Combinatorial Algorithms,
CRC Press, 1998,
ISBN: 0-8493-3988-X,
LC: QA164.K73.
2. Silvano Martello, Paolo Toth,
Knapsack Problems: Algorithms and Computer Implementations,
Wiley, 1990,
ISBN: 0-471-92420-2,
LC: QA267.7.M37.

### Source Code:

Last revised on 20 April 2020.