Radix sort ($T(n,d,R)=O(d(n+R))$)

Radix sort sorts encoded sort keys a digit at a time. Its least-significant-digit version uses stable sorting on each successive digit, often by counting sort. For $d$ digits with $R$ possible values each, it takes $O(d(n+R))$ time complexity in Big O notation, assuming constant-cost digit extraction and indexing. Stable sorting retains the ordering established by earlier digits when a later digit ties. Both digit access and the direct indexing in counting sort lie outside the comparison sort model, so these bounds do not contradict the comparison sorting lower bound.^[ref]