Bareiss algorithm (Determinant of Matrices with Integer Entries Determinant of Matrices with Integer Entries)
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Time Complexity
$O(n^{5} L^{2} (\log(n)$^{2} + L^{2}))
Space Complexity
$O(n^{2}(n*log(n)$+nL)) bits
(Keeps track of $O(n^2)$ entries that have absolute value at most $O(n^{(n/2)}2^{(nL)})$)
Description
Approximate?
Exact
Randomized?
No, deterministic
Model of Computation
Word RAM? (without O(1) multiplication)
Year
1968