Problem 367Published on Saturday, 14th January 2012, 10:00 pm;
Solved by 247 Bozo sort, not to be confused with the slightly
less efficient bogo sort, consists out of checking if the input
sequence is sorted and if not swapping randomly two elements.
This is repeated until eventually the sequence is sorted. If we
consider all permutations of the first 4 natural numbers as
input the expectation value of the number of swaps, averaged
over all 4! input sequences is 24.75. The already sorted
sequence takes 0 steps. In this problem we consider the
following variant on bozo sort. If the sequence is not in order
we pick three elements at random and shuffle these three
elements randomly. All 3!=6 permutations of those three elements
are equally likely. The already sorted sequence will take 0
steps. If we consider all permutations of the first 4 natural
numbers as input the expectation value of the number of
shuffles, averaged over all 4! input sequences is 27.5. Consider
as input sequences the permutations of the fir