1) Consider a Sorted Doubly-Linked List, which means that keys are kept always sorted and stored in a doubly linked list:

a) Implement an operation SD-LIST-INSERT(L,k) that inserts an integer key k into list L. What is the running time (.) of your implementation?

b) Implement an operation SD-LIST-DELETE(L,k) that removes a key k from the list. What is the running time (.) of your implementation?

c) Implement operations SD-LIST-SUCCESSOR(L,k) and SD-LIST-PREDECESSOR(L,k) that returns the successor and predecessor of a key k, respectively. What is the running time (.) of your implementation?

d) Implement an operation SD-LIST-SEARCH(L,k) that searches for a key k in list L and returns its node position (e.g., 1 if first, 2 if second, etc). What is the running time (.) of your implementation?

e) Implement an operation SD-LIST-REVERSE(L) that reverses the order of the keys in place (i.e., (n) space complexity). What is the running time (.) of your implementation?