Sortieren durch Zählen von Häufigkeiten

Folgendes Sortierverfahren findet sich im Band 3 des Werks ``The Art of Computer Programming'' von D. Knuth:

Algorithm D (Distribution counting). Assuming that all keys are integers in the range u <= Kj <= v for 1 <= j <= N, this algorithm sorts the records R1, ..., RN by making use of an auxiliary table COUNT[u ], ..., COUNT[v ]. At the conclusion of the algorithm the records are moved to an output area S1, ..., SN in the desired order. [Clear COUNTs.] Set COUNT[u ] through COUNT[v ] all to zero.   [Loop on j.] Perform step D3, for 1 <= j <= N; then go to step D4.   [Increase COUNT[Kj].] Increase the value of COUNT[Kj] by 1.   [Accumulate.] (At this point COUNT[i] is the number of keys that are equal to i.) Set COUNT[i ] <- COUNT[i ] + COUNT[i-1 ], for i = u + 1, u + 2, ..., v.   [Loop on j.] (At this point COUNT[i] is the number of keys that are less than or equal to i; in particular, COUNT[v ] = N.) Perform step D6 for j = N, N-1, ..., 1; then terminate the algorithm.   [Output Rj.] Set i <- COUNT[Kj ], Si <- Rj, and COUNT[Kj ] <- i-1.

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