Using Figure 8.3 as a model, illustrate the operation of \(\textsc{Radix-Sort}\) on the following list of English words: COW, DOG, SEA, RUG, ROW, MOB, BOX, TAB, BAR, EAR, TAR, DIG, BIG, TEA, NOW, FOX.
Each word has 3 letters, so we sort on 3 positions, starting from the least significant (rightmost).
Initial list:
\[\text{COW, DOG, SEA, RUG, ROW, MOB, BOX, TAB, BAR, EAR, TAR, DIG, BIG, TEA, NOW, FOX}\]After sorting on position 3 (last letter):
\[\text{SEA, TEA, MOB, TAB, DOG, RUG, DIG, BIG, BAR, EAR, TAR, COW, ROW, NOW, BOX, FOX}\]
After sorting on position 2 (middle letter):
\[\text{TAB, BAR, EAR, TAR, SEA, TEA, DIG, BIG, MOB, DOG, COW, ROW, NOW, BOX, FOX, RUG}\]After sorting on position 1 (first letter):
\[\text{BAR, BIG, BOX, COW, DIG, DOG, EAR, FOX, MOB, NOW, ROW, RUG, SEA, TAB, TAR, TEA}\]The words are now sorted alphabetically! The stability of the intermediate sorts ensures that words with the same leading characters maintain the correct relative order based on their later characters.