Advanced Subset Sum Calculator

Calculator Inputs

Set Values

Use commas, spaces, or line breaks. Decimals and negatives are allowed.

Target Sum Minimum Subset Size Maximum Subset Size

Stored Solutions Per Sum

Higher limits store more subsets but increase memory and runtime.

Subset Display Order

Allow empty subset when valid

Show closest sums when no exact match exists

Example Data Table

Case	Set Values	Target	Size Range	One Valid Subset	Subset Sum
Budget Mix	5, 8, 12, 14, 20	32	1 to 4	12, 20	32
Score Target	3, 7, 12, 19, 25, 31	38	1 to 6	7, 31	38
Mixed Signs	-4, 6, 9, 13, 17	15	1 to 5	-4, 6, 13	15

Formula Used

The calculator solves the subset sum problem with dynamic programming. For a set S = {a₁, a₂, ..., aₙ} and target T, it checks whether some subset produces:

Σ aᵢ = T for selected indices only.

Each new value extends existing reachable sums. The recurrence is:

DP[k][x] = DP[k-1][x] OR DP[k-1][x - aₖ]

This implementation stores reconstructed subsets, applies subset-size limits, supports decimals by scaling values, and reports exact plus closest sums.

How to Use This Calculator

Enter the available numbers using commas, spaces, or line breaks.
Type the target sum you want to match exactly.
Set minimum and maximum subset sizes for tighter filtering.
Choose how many solutions per reachable sum should be stored.
Enable closest-sum output if you want near matches.
Click Calculate Subset Sum to show the result above the form.
Download the exact result table as CSV or PDF if needed.

Frequently Asked Questions

1. What does this calculator actually solve?

It tests whether selected values from your list can add to an exact target. It also shows matching subsets, closest sums, and useful search statistics.

2. Can I use decimals and negative numbers?

Yes. The tool scales decimal values before processing, then converts them back for display. Negative numbers are also supported in the search.

3. Why is there a limit on how many numbers I enter?

Subset sum grows quickly as list size increases. A practical cap keeps the page responsive and reduces memory use on standard hosting environments.

4. What does stored solutions per sum mean?

Multiple subsets can produce the same intermediate sum. This setting limits how many examples are saved for each reachable total during reconstruction.

5. Will it always return every possible matching subset?

Not always. If many combinations exist, the saved-solution limit may trim some alternatives. Increase the limit when you need broader coverage.

6. What happens if no exact subset exists?

The calculator reports that no exact match was found. If enabled, it also lists subsets whose sums are closest to your target.

7. Where is this calculator useful?

It is helpful for budgeting, score combinations, inventory bundling, classroom exercises, test-case design, and algorithm studies involving constrained selections.