Consider the following array of elements.

$$\,\,\,\,\,\,\,\,$$$$〈89, 19, 50, 17, 12, 15, 2, 5, 7, 11, 6, 9, 100〉$$

The minimum number of interchanges needed to convert it into a max-heap is

Assume that a mergesort algorithm in the worst case takes $$30$$ seconds for an input of size $$64.$$ Which of the following most closely approximates the maximum input size of a problem that can be solved in $$6$$ minutes?

Let $$f\left( n \right) = n$$ and $$g\left( n \right) = {n^{\left( {1 + \sin \,\,n} \right)}},$$ where $$n$$ is a positive integer. Which of the following statements is/are correct?

$$\eqalign{ & \,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,f\left( n \right) = O\left( {g\left( n \right)} \right) \cr & \,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,\,\,f\left( n \right) = \Omega \left( {g\left( n \right)} \right) \cr} $$

Among simple $$LR (SLR) ,$$ canonical $$LR,$$ and look-ahead $$LR$$ $$(LALR),$$ which of the following pairs identify the method that is very easy to implement and the method that is the most powerful , in that order?