1. [15 marks] This question asks you to perform competitive analysis of transpose (TR) and frequency count (FC) (i) 5 marks] Suppose that you are maintaining a list of n elements under access operation only. The cost of access to the i-th element in the list is i. Let S be a request sequence of m access operations over this list. For any sufficiently large m, construct a request sequence S such that for this request sequence, the total cost of TR divided by the total cost of MTF is w(1) (ii) [5 marks] Use the result of (i) to argue that TR is not competitive. Hint: You just have to use the definition of competitiveness. Therefore, You can solve this subquestion without having to solve (i) first i 5 marks] Further prove that FC is not competitive, either 1. [15 marks] This question asks you to perform competitive analysis of transpose (TR) and frequency count (FC) (i) 5 marks] Suppose that you are maintaining a list of n elements under access operation only. The cost of access to the i-th element in the list is i. Let S be a request sequence of m access operations over this list. For any sufficiently large m, construct a request sequence S such that for this request sequence, the total cost of TR divided by the total cost of MTF is w(1) (ii) [5 marks] Use the result of (i) to argue that TR is not competitive. Hint: You just have to use the definition of competitiveness. Therefore, You can solve this subquestion without having to solve (i) first i 5 marks] Further prove that FC is not competitive, either