Pop Operation on Two Stacks Mack A Consider two stacks, Stack A and Stack B, each implemented using a singly linked list. In one stack, the top-of-stack is at the tail of the list and in the other stack the top-of-sta was recorded for both stacks on increasing stack sizes. The results are shown in the below plot Running Time Stack B Input Sen Which stack uses the head as teh top-of-stack? Stack A uses the head as the top-of-stack Stack B uses the head as the top-of-stack There is not enough information provided to tell which stack uses the head for the top-of-stack and which uses the tail
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- 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. -Imagine a (literal) stack of plates. If the stack gets too high, it might topple.Therefore, in real life, we would likely start a new stack when the previous stack exceeds somethreshold. Implement a data structure SetOfStacks that mimics this. SetOfStacks should becomposed of several stacks and should create a new stack once the previous one exceeds capacity.SetOfStacks. push() and SetOfStacks. pop() should behave identically to a single stack(that is, pop () should return the same values as it would if there were just a single stack).FOLLOW UPImplement a function popAt(int index) which performs a pop operation on a specific substack.Design a stack MAXSTACK, which functions like an ordinary linked stacksupporting the ADT operations of PUSH, POP and EMPTYSTACK, besidesGETMAX. GETMAX is an operation that records the maximum element in thestack. Can you design the stack in such a way that GETMAX merely consumes O(1) time complexity
- (2) Answer the following questions concerning lists, stacks, and queues Please be thorough with explanatio! (d) Suppose you are implementing a list of stacks. Let's say you decide to implement both the general list (the list of stacks) and each individual stack using a double linked list. Assume that there are currently N stacks in the list, and each stack has a maximum of K items, where N and K are both large. You are going to iterate through the general list and apply a single operation to each stack as you encounter it. Now answer the following four questions, using big-Theta notation: What is the average-case time complexity of pushing one additional item into each stack? What is the worst-case time complexity of pushing one additional item into each stack? What is the average-case time complexity of popping one item from each stack? What is the worst-case time complexity of popping one additional item from each stack? (For pops, if the stack is empty, you can assume that the pop…S1 and S2 are two sorted stacks of n and m numbers, with the top elements of each stack pointing to the smallest number in their list. To ensure that all of the components in stacks S1 and S2 are available in MERGE in decreasing order, with the largest element at the top, create a stack MERGE that combines the items in stacks S1 and S2.Remember that there are (n + m) components in the stack MERGE.Given the following sequence of characters: DA&T!A ST*R&U!CT!&UR*ES. Consider the stack data structure, supporting two operations push and pop. Suppose that for the above sequence, each letter (such as DATA STRUCTURES) corresponds to a push of that letter onto the stack, each exclamation mark(!) corresponds one pop operation on the stack, each ampersand (&) corresponds one peep operation on the stack and each asterisk (*) corresponds two pop operations on the stack. Show the sequence of values returned by the pop operations. Also, display the remaining elements in the stack after all the push and pop operations.
- Imagine a stack of dishes, literally. The stack may collapse if it becomes too tall.Therefore, when the prior stack above a certain threshold in real life, we probably start a new stack. Create a data structure called SetOfStacks to resemble this. When a stack's capacity is reached, a new stack should be created and added to the SetOfStacks. SetOfStacks. SetOfStacks with push(). In other words, pop() should return the same values as it would if there were only one stack. It should operate exactly like a single stack.TAKE ACTIONCreate a function called popAt(int index) that does a pop operation on a certain substack.A CapnStackSparrow is an extended stack that supports four main operations: the standard Stack operations push(x) and pop() and the following non-standard operations:• max(): returns the maximum value stored on the Stack.• ksum(k): returns the sum of the top k elements on the Stack.The zip file gives an implementation SlowSparrow that implements these operations so that push(x) and pop() each run in ?(1) time, but max() and ksum(k) run in ?(?) time. For this question, you should complete the implementation of FastSparrow that implements all four operations in ?(1) (amortized) time per operation. As part of your implementation, you may use any of the classes in the Java Collections Framework and you may use any of the source code provided with the Java version of the textbook. Don't forget to also implement the size() and iterator() methods. Think carefully about your solution before you start coding. Here are two hints:1. don't use any kind of SortedSet or SortedMap, these all require…Short answer: Answer the following in your own words: 1) Your friend says they implemented a stack as a linked list with reference pointers to both a head and the tail node (i.e. they implemented a stack as a double endedlinked list). They said this significantly improved the performance for all functions (push, pop, search, and update). Are they correct? Why or why not?
- Implementing a Stack ADT using a linked solution. The implementations are linked Nodes. class Node: def __init__(self, data, node=None): # Initialize this node, insert data, and set the next node if any self.data = data self.chain = node class SubSetStack: def __init__(self, data=None): # Initialize this stack, and store data if it exists def push(self, data): # Add data to the beginning of the stack def pop(self): # Remove the element at the beginning of the stack. # Return the data in the element at the beginning of the stack, or None if the stack is empty def top(self): # Return the data in the element at the beginning but does not remove it. # Return None if stack is empty. def __len__(self): # Return the number of elements in the stack def subset_sum(target, sub_list): # Returns True if Target can be formed from sub_list repeated # some arbitrary number of times. In the above function a Node…2. An ordered stack is a data structure that stores a sequence of items and supports the following operations. • OrderedPush(x): removes all items smaller than x from the beginning of the sequence and then adds x to the beginning of the sequence. • Pop: deletes and returns the first item in the sequence (or Null if the sequence is empty). Suppose we implement an ordered stack with a simple linked list, using the obvious OrderedPush and Pop algorithms. Prove that if we start with an empty data structure, the amortized cost of each OrderedPush or Pop operation is O(1).The queues that function as a stack together work on X) and POP(S, Y), where S is purportedly a stack, X is the element to be added to S, and Y is the element discarded from S. Assume that only queues are accessible to ADT's ENQUEUE, DEQUEUE, and EMPTYQUEUE operations.Show how your function operates on a list of items (a, b, and c) that will be used as a stack by the queues Q1 and Q2.