The usual $$\Theta ({n^2})$$ implementation of Insertion Sort to sort an array uses linear search to identify the position where an element is to be inserted into the already sorted part of the array. If, instead, we use binary search to identify the position, the worst case running time will

The cube root of a natural number n is defined as the largest natural number m such that $${m^3} \le n$$. The complexity of computing the cube root of n (n is represented in binary notation) is

In a heap with n elements with the smallest element at the root, the 7^th smallest element can be found in time

Consider the grammar shown below

$$\eqalign{ & S \to iEtSS'\,|\,\,a \cr & S' \to eS\,|\,\,\varepsilon \cr & E \to b \cr} $$

In the predictive parse table, $$M$$, of this grammar, the entries $$M\left[ {S',e} \right]$$ and $$M\left[ {S',\phi } \right]$$ respectively are