SUBSET_SUM is a C++ library 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.
I don't care what you do with this code.
SUBSET_SUM is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.
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.
SUBSET_SUM, a dataset directory which contains examples of the subset sum problem, in which a set of numbers is given, and is desired to find at least one subset that sums to a given target value.
TSP_BRUTE, a C++ program which reads a file of city-to-city distances and solves the traveling salesperson problem, using brute force.
- Donald Kreher, Douglas Simpson,
Combinatorial Algorithms,
CRC Press, 1998,
ISBN: 0-8493-3988-X,
LC: QA164.K73. - Silvano Martello, Paolo Toth,
Knapsack Problems: Algorithms and Computer Implementations,
Wiley, 1990,
ISBN: 0-471-92420-2,
LC: QA267.7.M37.
- subset_sum.cpp, the source code.
- subset_sum.hpp, the include file.
- subset_sum_prb.cpp, a sample calling program.
- subset_sum_prb.txt, the output file.
- BACKUP_ONE seeks the last 1 in the subarray U[0:TOLD-1].
- I4_MAX returns the maximum of two I4's.
- I4_MIN returns the minimum of two I4's.
- I4_POWER returns the value of I^J.
- I4_TO_DIGITS_BINARY produces the binary digits of an I4.
- I4VEC_COPY_NEW copies an I4VEC to a "new" I4VEC.
- I4VEC_DOT_PRODUCT computes the dot product of two I4VEC's.
- I4VEC_PRINT prints an I4VEC.
- SUBSET_SUM_COUNT counts solutions to the subset sum problem in a range.
- SUBSET_SUM_COUNT_TEST tests SUBSET_SUM_COUNT.
- SUBSET_SUM_COUNT_TESTS tests SUBSET_SUM_COUNT_TEST.
- SUBSET_SUM seeks a subset of a set that has a given sum.
- SUBSET_SUM_FIND_TEST tests SUBSET_SUM_FIND.
- SUBSET_SUM_FIND_TESTS tests SUBSET_SUM_FIND_TEST.
- SUBSET_SUM_NEXT seeks, one at a time, subsets of V that sum to S.
- SUBSET_SUM_NEXT_TEST tests the SUBSET_SUM_NEXT library.
- SUBSET_SUM_NEXT_TESTS calls SUBSET_SUM_NEXT_TEST with various values.
- SUBSET_SUM_TABLE sets a subset sum table.
- SUBSET_SUM_TABLE_TEST tests SUBSET_SUM_TABLE.
- SUBSET_SUM_TABLE_TESTS tests SUBSET_SUM_TABLE_TEST.
- SUBSET_SUM_TABLE_TO_LIST converts a subset sum table to a list.
- SUBSET_SUM_TABLE_TO_LIST_LENGTH returns the length of a table list.
- TIMESTAMP prints the current YMDHMS date as a time stamp.
You can go up one level to the C++ source codes.
Last revised on 15 July 2017.