4. (20 points) Suppose T(n) 1.3.5 (2n 1). Derive the asymptotics of log(T(n using Stirling's formula we learned in class. 5. (20 points) Recall the "hare and tortoise" (or pointer chasing) algorithm we learned in class for cycle-detection in singly linked list: in each iteration, the tortoise pointer moves one step ahead and the hare pointer moves two steps ahead. (a) Suppose there are 100 nodes before entering the cycle, and the cycle consists of 17 nodes. (b) If there are L nodes before entering the cycle, which consists of C nodes. Express the number Determine the number of iterations it takes the tortoise and the hare to meet. of iterations it takes the tortoise and the hare to meet in terms of L and C