A SpecialStackTM is a stack modified to support the following two operations: PUSHCLEAR(v) successively pops consecutive items from the top of the stack that are less than u, then pushes v onto the stack. POP() deletes the item at the top of the stack. Assume these operations are implemented using a singly-linked list. PUSHCLEAR(v) iter- ates through the linked list to pop the applicable items and then adds v to the beginning. POP() deletes the first item. (a) Describe the ordering of values on the stack. (b) Explain how a single call to PUSHCLEAR(V) could take (n) time. (c) If we assume that every operation takes linear time, we get a naive bound of O(n²) on the total runtime. But this doesn't consider the fact that these expensive operations happen infrequently so let's analyze it more closely. Show that any sequence of n operations takes O(n) time.

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