algorithm - Average number of swaps performed in Bubble Sort -


i came across problem right now: http://uva.onlinejudge.org/index.php?option=com_onlinejudge&itemid=8&category=24&page=show_problem&problem=3155 problems asks calculate average number of swaps performed bubble sort algorithm when given data shuffled order of first n (1 n listed randomly) natural numbers.

so, thought that:

  1. max no of swaps possible=n(n-1)/2. (when in descending order.)
  2. min no of swaps possible=0. (when in ascending order.)

so, mode of distribution (0+n(n-1)/2)/2 =n(n-1)/4. but, turned out answer. don't understand why did mode coincide mean.

since inputs sorted can random number equal probability of occurrence, distribution symmetrical.

it property of symmetrical distributions mean, median , modes coincide why mean , mode same.


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