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consider the following algorithm for sorting a list of n distinct numbers into increasing order. initially they are in a random order, with all orders equally likely. the algorithm compares the numbers in positions 1 and 2, and swaps them if needed, then it compares the new numbers in positions 2 and 3, and swaps them if needed, etc., until it has gone through the whole list. call this one "sweep" through the list. after the first sweep, the largest number is at the end, so the second sweep (if needed) only needs to work with the first n − 1 positions. similarly, the third sweep (if needed) only needs to work with the first n − 2 positions, etc. sweeps are performed until n − 1 sweeps have been completed or there is a swapless sweep. for example, if the initi

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