3. Fill in the blanks: Amortized Analysis is used for algorithms where an occasional operation is very slow, but most of the other operations are faster. In Amortized Analysis, we analyze a sequence of operations and guarantee a worst case average time which is lower than the worst case time of a particular expensive operation. In computer science, amortized analysis is a method for analyzing a given algorithm's time complexity, or how much of a resource, especially time or memorv, it takes to execute. 50 100 25 75 Asymptotic analysis is input bound i.e., if there's no input to the algorithm, it is concluded to work in a constant time. Other than the "input" all other factors are considered constant. Asymptotic analysis refers to computing the running time of any operation in mathematical units of computation. a. In the worst case, a red-black tree insertion requires b. In the worst case a red-black tree deletion requires c. Walking a red-black tree with n nodes in pre-order takes d. Given a red-black tree with n elements, how fast can you sort them using the tree? rotations? node re-colorings? e. How fast can we build a red-black tree with n elements? f. If a data structure supports an operation X such that a sequence of n X's operations take: O (n log n) time in the worst case, then the amortized time of an X operation is 6( ) while the actual time of a single X operation could be as low as ( ) and as high as O 0