Sortieren durch Zählen

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

Algorithm C (Comparison counting). This algorithm sorts R₁, ···, R_N on the keys K₁, ···, K_N by maintaining an auxiliary table COUNT[1], ···, COUNT[N ] to count the number of keys less than a given key. After the conclusion of the algorithm, COUNT[j] + 1 will specify the final position of record R_j.

[Clear COUNTs.] Set COUNT[1] through COUNT[N ] to zero.

[Loop on i.] Perform step C3, for i = N, N-1, ···, 2; then terminate the algorithm.

[Loop on j.] Perform step C4, for j = i-1, i-2, ···, 1.

[Compare K_i : K_j.] If K_i < K_j, increase COUNT[j] by 1; otherwise increase COUNT[i] by 1.