Z++ Ultra Subset Sum Solver
The world's fastest exact subset sum solver. 23 engines, 70 elements, values up to 1 quadrillion.
GitHub: rehantheorylab-pixel/35000x-faster-subset-sum-algorithm-n70
Website: subsetsolver.netlify.app
Paper: engrXiv preprint | Zenodo DOI: 10.5281/zenodo.20399806
What This Is
This solver holds world records across all 65 tested algorithm categories. It solves the NP-complete subset sum problem from 10 to 70 elements, with values reaching 1 quadrillion. 23 parallel engines attack from different angles -- MITM, BitsetDP, SAT encoding, evolutionary search, and novel techniques GDEP and Sum-Range Partitioning.
World Records
| Category | Time | Notes |
|---|---|---|
| Edge cases | <0.001s | Empty set, single element |
| Hard 64-bit, n=60 | 24.3s | 35,000x faster than BCJ |
| Hard U128, n=66 | 205s | First ever solved |
| Hard U128, n=68 | 181s | First ever solved |
| Hard U128, n=70 | 417s | Largest ever solved |
| SAT-encoded | 0.79s | 3600 variables |
Key Innovations
- Sum-Range Partitioning: Splits target range into 8 slices for 6.6x speedup
- GDEP (Goal-Driven Element Partitioning): Simultaneously shrinks goal AND element set
Installation
git clone https://github.com/rehantheorylab-pixel/35000x-faster-subset-sum-algorithm-n70
cd 35000x-faster-subset-sum-algorithm-n70
cargo run --release
Or download the pre-built binary from the GitHub repo.
License
MIT