sorting - Design an efficient algorithm to sort 5 distinct keys in fewer than 8 comparisons

Question

Design an efficient algorithm to sort 5 distinct - very large - keys less than 8 comparisons in the worst case. You can't use radix sort.

Answer 1

Compare A to B and C to D. WLOG, suppose A>B and C>D. Compare A to C. WLOG, suppose A>C. Sort E into A-C-D. This can be done with two comparisons. Sort B into {E,C,D}. This can be done with two comparisons, for a total of seven.