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

Sample sequence of operations, using mergesort (the merge function below will merge two sorted sublists into a single sorted combined list):

elements[1..2] <- merge(elements[1..1], elements[2..2]) # 1 comparison
elements[3..4] <- merge(elements[3..3], elements[4..4]) # 1 comparison
elements[3..5] <- merge(elements[3..4], elements[5..5]) # 1-2 comparisons
elements[1..5] <- merge(elements[1..2], elements[3..5]) # 2-4 comparisons