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<title>Problem 367 - Project Euler</title>
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<h2>bozo sort</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 367</h3><span style="width:300px;color:#666;">Published on Saturday, 14th January 2012, 10:00 pm; Solved by 257</span></div>
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<div class="problem_content" role="problem">
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<p>
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<b>Bozo sort</b>, not to be confused with the slightly less efficient <b>bogo sort</b>, 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.
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</p>
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<p>
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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.<br />
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The already sorted sequence takes 0 steps.
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</p>
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<p>
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In this problem we consider the following variant on bozo sort.<br />
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If the sequence is not in order we pick three elements at random and shuffle these three elements randomly.<br />
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All 3!=6 permutations of those three elements are equally likely. <br />
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The already sorted sequence will take 0 steps.<br />
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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. <br />
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Consider as input sequences the permutations of the first 11 natural numbers.<br />
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Averaged over all 11! input sequences, what is the expected number of shuffles this sorting algorithm will perform?
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Give your answer rounded to the nearest integer.
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