A complete binary min-heap is made by including each integer in $$[1,1023]$$ exactly once. The depth of a node in the heap is the length of the path from the root of the heap to that node. Thus, the root is at depth $$0.$$ The maximum depth at which integer $$9$$ can appear is ___________.

The Floyd-Warshall algorithm for all-pair shortest paths computation is based on

Assume that the algorithms considered here sort the input sequences in ascending order. If the input is already in ascending order, which of the following are TRUE?

$$\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,$$ Quicksort runs in $$\Theta \left( {{n^2}} \right)$$ time
$$\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,\,\,$$ Bubblesort runs in $$\Theta \left( {{n^2}} \right)$$ time
$$\,\,\,{\rm I}{\rm I}{\rm I}.\,\,\,\,\,\,\,$$ Mergesort runs in $$\Theta \left( n \right)$$ time
$$\,\,\,{\rm I}V.\,\,\,\,\,\,\,$$ Insertion sort runs in $$\Theta \left( n \right)$$ time

Which one of the following grammars is free from $$left$$ $$recursion$$?