Which one of the following in place sorting algorithms needs the minimum number of swaps?

The tightest lower bound on the number of comparisons, in the worst case, for comparison-based sorting is of the order of

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

Consider any array representation of an n element binary heap where the elements are stored from index 1 to index n of the array. For the element stored at index i of the array $$\left( {i \le n} \right)$$, the index of the parent is