5.Asymptotic Notations and Basic Efficiency Classes

"What is the time complexity of fun()? int fun(int n) { int count = 0; for (int i = 0; i < n; i++) for (int j = i; j > 0; j--) count = count + 1; return count; } "

Theta (n)

Theta (n^2)

Theta (n*logN)

Theta (nLognLogn)

"What is time complexity of fun()? int fun(int n) { int count = 0; for (int i = n; i > 0; i /= 2) for (int j = 0; j < i; j++) count += 1; return count; }"

O(n^2)

O(nLogn)

O(n)

O(nLognLogn)

What is the asymptotic runtime for traversing all nodes in a binary search tree with n nodes and printing them in order?

O(n^2)

O(nLogn)

O(n)

O(nLognLogn)

Suppose we have a O(n) time algorithm that finds median of an unsorted array. Now consider a QuickSort implementation where we first find median using the above algorithm, then use median as pivot. What will be the worst case time complexity of this modified QuickSort.

O(n^2)

O(n^2 Logn)

O(n Logn Logn)

O(nLogn)

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