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A Deterministic π-Driven Hybrid Algorithm for the Partition Problem Worst-Case Polynomiality and Digit Bounds
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Description: This project introduces a fully deterministic, polynomial-time algorithm for the classic Partition Problem, replacing the pseudorandom component of a hybrid heuristic with a sequential read of decimal digits from pi. The algorithm alternates up to K Fisher–Yates permutations with greedy selection, followed, if necessary, by a monotonic balancing routine. The method guarantees determinism, bounded runtime, and limited digit consumption, formally achieving worst-case O(n²) complexity. Empirical evaluation confirms 100% success on all tested partitionable instances, including adversarial inputs like powers of ten. The project includes the article PDF, source code, and formal proofs, contributing to the study of deterministic approaches to NP-complete problems.
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