Q6 (12 pts) This question tests your understanding of the time complexities of sorting algorithms. (a) In the decision tree for Quicksort on n elements, what is the length (i.e., the number of hops) of the longest root-to-leaf path? Check the corresponding box on the answer sheet. (b) In the decision tree for Quicksort on n elements, what is the length (i.e., the number of hops) of the shortest root-to-leaf path? Check the corresponding box on the answer sheet. (c) In the decision tree for Mergesort on n elements, what is the length (i.e., the number of hops) of the longest root-to-leaf path? Check the corresponding box on the answer sheet. (d) In the decision tree for Mergesort on n elements, what is the length (i.e., the number of hops) of the shortest root-to-leaf path? Check the corresponding box on the answer sheet. (e) In the decision tree for Insertion Sort on n elements, what is the length (i.e., the number of hops) of the longest root-to-leaf path? Check the corresponding box on the answer sheet. (f) In the decision tree for Insertion Sort on n elements, what is the length (i.e., the number of hops) of the shortest root-to-leaf path? Check the corresponding box on the answer sheet