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8 4 2 Explain why the worst case running time for bucket sort is ‚

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8. 4-2 Explain why the worst-case running time for bucket
sort is .n2/. What simple change to the algorithm
preserves its linear average-case running time and makes
its worst-case running time O.n lg n/?
Solution
The worst case for bucket sort occurs when the all inputs
falls into single bucket,
Example
>Since we use insertion sort for sorting buckets and
insertion sort has a worst case of O(n2), the worst case
runtime for bucket sort is O(n2).
>By using an algorithm with worst case runtime of O(nlgn)
instead of insertion sort for sorting buckets, we can ensure
that worst case is O(nlgn) without affecting the average
case behavior
>To see that the worst case is still O(nlgn), lets consider a
case where n data are distributed among two buckets, a
elements in one bucket and n a in the other. Since we use
O(nlgn sorting algorithm in each bucket, the run time for
each sort is, kalg(a) + c2 and k(n a)lg(n a) + c2, where k,
c2 are positive constants.

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8. 4-2 Explain why the worst-case running time for bucket sort is ‚.n2/. What simple change to the algorithm preserves its linear average-case running time and makes its worst-case running time O.n lg n/? Solution The worst case for bucket sort occurs when the all inputs falls into single bucket, Example >Since we use insertion sort for sorting buckets and insertion sort has a worst case of O(n2), the worst case runtime for bucket sort is O(n2). >By using an algorithm with worst case runtime of O(nlgn) instead of insertion sort for sorting buckets, we can ensure that worst case is O(nlgn) ...
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