Answer the following question and show how to do

22. The smallest worst-case complexity of a comparison-based sorting algorithm is: a) (log n) b) e (n) c) (n log n) d) (m) e) e (n) 23. Assuming a uniform distribution the worst case and average complexities of Insertion sort are: a) n/2 and -1/4 b) -nlogan and-logan/2 c) -4n and 2n d)-/2 and -1/4 e) -4/2 and -21 24. The worst-case complexity of Quicksort occurs when: a) The list is already sorted b) The largest element occurs in the first position c) The input list satisfies a uniform distribution d) The input list has large size e) None of the above 25. Which of the following sorting algorithms is not in-place: a) Bubble sort b) Insertion sort c) Mergesort d) Quicksort e) They are all in-place 26. The depth of a complete binary tree on n nodes is approximately equal to: a) 2" b) n logan c) logan d) e) 27. The depth of a complete binary tree having n leaf nodes is approximately equal to a) 2 b) n logan c) logan 28. Consider the array implementation of a complete binary tree in C++. For a node indexed by the indices the parent, left child and right child are respectively given by: a) I, 2*1, 31 b) (I-1)2,21+1,21 + 2 c) 1-1,2*1,2*1+1 d) (1-1)/2,2*1.31 e) I-1,1+1 1+2 29. The total number of nodes of a 2-tree with 40 leaf nodes is: a) 40 b) 70 c) 79 d) 80 e) 89