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

A B C D E

A
| C D E     - 1 Comparison
B

A C
| | E       - 1 Comparison
B D

  A
 / \
B   C   E   - 1 Comparison
     \
      D

E needs 3 comparisons. It should be compared to A, C, D

Try A-C-D-E in that order.

Overall there will be nine comparisons -- not very performant.