berkeDet: A Dual Iterative Algorithm for Exact Determinant Computation via Block Copy-Paste Operations

We introduce berkeDet, a dual iterative algorithm that computes the determinant of an n×n matrix via the Leibniz formula using two independent subroutines: meryemSign, which generates the complete list of permutation signs in lexicographic order, and meryemPer, which generates the corresponding permutations. Both subroutines operate by block copy-paste and index-mapping operations, avoiding the per-permutation overhead inherent in classical approaches. In the standard lexicographic implementation of the Leibniz formula, computing the sign of each permutation via inversion counting costs O(n²) per permutation, yielding a total complexity of O(n²·n!). By contrast, meryemSign generates all n! signs in Θ(n!) total time — an amortized cost of O(1) per sign — and meryemPer generates all permutations in O(n·n!) total time. The combined berkeDet algorithm therefore runs in O(n·n!) time, improving the per-permutation cost by a factor of n over the classical lexicographic approach. We prove correctness by induction and verify the algorithm computationally for matrices up to order 8.