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

FWIW, here's a compact and easy to follow Python version with tests to make sure it works:

def sort5(a, b, c, d, e):
    'Sort 5 values with 7 Comparisons'
    if a < b:      a, b = b, a
    if c < d:      c, d = d, c
    if a < c:      a, b, c, d = c, d, a, b
    if e < c:
        if e < d:  pass
        else:      d, e = e, d
    else:
        if e < a:  c, d, e = e, c, d
        else:      a, c, d, e = e, a, c, d
    if b < d:
        if b < e:  return b, e, d, c, a
        else:      return e, b, d, c, a
    else:
        if b < c:  return e, d, b, c, a
        else:      return e, d, c, b, a

if __name__ == '__main__':
    from itertools import permutations

    assert all(list(sort5(*p)) == sorted(p) for p in permutations(range(5)))