Suppose we have an O(n) time algorithm that finds the median of an unsorted array. Now consider a QuickSort implementation where we first find the median using the above algorithm, then use the median as a pivot. What will be the worst-case time complexity of this modified QuickSort?
What is recurrence for worst case of QuickSort and what is the time complexity in Worst case?
Recurrence is T(n) = T(n-2) + O(n) and time complexity is O(n^2)
Recurrence is T(n) = T(n-1) + O(n) and time complexity is O(n^2)
Recurrence is T(n) = 2T(n/2) + O(n) and time complexity is O(nLogn)
Recurrence is T(n) = T(n/10) + T(9n/10) + O(n) and time complexity is O(nLogn)
Quicksort is run on two inputs shown below to sort in ascending order taking the first element as pivot,
(i) 1, 2, 3,......., n (ii) n, n-1, n-2,......, 2, 1
Let C1 and C2 be the number of comparisons made for the inputs (i) and (ii) respectively. Then,
We cannot say anything for arbitrary n
If we use Radix Sort to sort n integers in the range (nk/2,nk], for some k>0 which is independent of n, the time taken would be?
What is the best time complexity of bubble sort(optimised)?
In a modified merge sort, the input array is splitted at a position one-third of the length(N) of the array. Which of the following is the tightest upper bound on time complexity of this modified Merge Sort.
Which of the following sorting algorithms has the lowest worst-case complexity?
Which of the following is not true about comparison-based sorting algorithms?
The minimum possible time complexity of a comparison-based sorting algorithm is O(n(log(n)) for a random input array
Any comparison based sorting algorithm can be made stable by using position as a criteria when two elements are compared
Counting Sort is not a comparison based sorting algorithm
Heap Sort is not a comparison based sorting algorithm.
In a permutation a1.....an of n distinct integers, an inversion is a pair (ai, aj) such that i < j and ai > aj. What would be the worst-case time complexity of the Insertion Sort algorithm, if the inputs are restricted to permutations of 1.....n with at most n inversions?
You have an array of n elements. Suppose you implement quick sort by always choosing the central element of the array as the pivot. Then the tightest upper bound for the worst case performance is
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