Bubble sort. The bubble sort algorithm is a popular method for sorting n numbers in nondecreasing…

Bubble sort. The bubble sort algorithm is a popular method for sorting n numbers in nondecreasing order of their magnitudes. The algorithm maintains an ordered set of the numbers {ai, a2, … , an} that it rearranges through a sequence of several passes over the set. In each pass, the algorithm examines every pair of elements (ak&#39; ak + I) for each k = 1, … ,(n.I), and if the pair is out of order (i.e., ak > ak + 1)&#39; it swaps the positions of these elements. The algorithm terminates when it makes no swap during one entire pass. Show that the algorithm performs at most n passes and runs in 0(n2) time. For every n, construct a sorting problem (Le., the initial ordered set of numbers {a., a2, … ,an} SO that the algorithm performs O(n2) operations. Conclude that the bubble sort is a 8(n 2 ) algorithm.

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