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Decision Tree question: Among all comparison-based algorithms for sorting, determine the minimum number of comparisons in...

Decision Tree question: Among all comparison-based algorithms for sorting, determine the minimum number of comparisons in the worst case AND best case needed for the following number of elements:

2

3

4 (the answer to this is 5)

5

6

Some explanation would be great! I'm reviewing for my final. Thank you

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Answer #1

In the case of the Best case and Worst Case " Bubble sort and Insertion sort" are determine the minimum number of comparison. because this array is already sorted.so no more sort of number requires so it easily sorts this array.

Best time complexity:

  1. Bubble sort and Insertion sort : n because array isalready sorted.
  2. Selection Sort: n^2 this is independent of distributed data.
  3. Merge Sort and Heap Sort: nlogn this is also independent of distributed data.
  4. Quick Sort: nlogn

Worst-case time complexity:

  1. Bubble sort and Insertion sort: n^2
  2. Selection Sort: n^2 this is independent of distributed data.
  3. Merge Sort and Heap Sort: nlogn this is also independent of distributed data
  4. Quick sort : n^2
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