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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. -Suppose you have a stack with a maximum size of 1000 elements and you want to perform the following operations: Push 500 elements onto the stack. Pop 200 elements from the stack. Push 800 elements onto the stack. Pop all remaining elements from the stack. What is the final size of the stack after performing all these operations?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
- 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.Write a program to implement a Stack using array. In order to implement the stack, programfor following stack operations has to be written: • void push(int): to insert data onto the stack.• Int pop(): to remove and return the last inserted element from the stack.• Int top(): Returns the last inserted element without removing it.• int Size(): Returns the number of elements stored in the stack.• int IsEmptyStack(): Indicates whether any elements are stored in the stack or not.• int IsFullStack(): Indicates whether the stack is full or not.Can you explain in detail, line by line, what the attached algorithm is doing? I need further understanding. For further clarification the prompt asks the following: Write an algorithm Replace that takes a stack and two items. If the first item is in the stack, replace it with the second item, leaving the rest of the stack unchanged.
- Pseudocodes can be written using the operations PUSH(S,X), POP(S,X), PRINT(X), EMPTY STACK(S), and TOP OF STACK(S), which returns the top element of stack S. i) assign X to the bottom element of stack S, leaving the stack empty;ii) assign X to the bottom element of the stack, leaving the stack unchanged;iii) assign X to the nth element in the stack (from the top), leaving the stack unchanged.Consider the following statements: stackType<int> stack; int x; Suppose that the input is: 14 53 34 32 13 5 -999 Show what is output by the following segment of code: cin >> x; while (x != -999) { if (x % 2 == 0) { if (!stack.isFullStack()) stack.push(x); } else cout << "x = " << x << endl; cin >> x; } cout << "Stack Elements: "; while (!stack.isEmptyStack()) { cout << " " << stack.top(); stack.pop(); } cout << endl;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.
- Create a stack S of ten elements. Take a number x from the user and delete the elements smaller than or equal to X from the stack.Example: Suppose your initial stack is S where you pushed 10 elements as below- Top {9, 3, 4, 15, 20, 1, 6, 4, 9, 10} Bottom4. X is taken as input and X= 6. Then pop out and remove the elements smaller than or equal to X. Finally, the stack will look like-Top {9, 15, 20, 9, 10} BottomYou can use only one additional queue to solve this problem.In c++ pleaseWrite a program in c or c++ to implement a Stack using array. In order to implement the stack, programfor following stack operations has to be written: • void push(int): to insert data onto the stack.• Int pop(): to remove and return the last inserted element from the stack.• Int top(): Returns the last inserted element without removing it.• int Size(): Returns the number of elements stored in the stack.• int IsEmptyStack(): Indicates whether any elements are stored in the stack or not.• int IsFullStack(): Indicates whether the stack is full or not.Code in C One of the applications of a stack is to backtrack - that is, to retrace its steps. As an example, imagine we want to read a list of items, and each time we read a negative number we must backtrack and print the five numbers that come before the negative number and then discard the negative number. Use a stack to solve this problem. Use a stack and push them into the stack (without printing them) until a negative number is read. At this time, stop reading and pop five items from the stack and print them. If there are fewer than five items in the stack, print an error message and stop the program. After printing the five items, resume reading data and placing them in the stack. When the end of the file is detected, print the message and the items remaining in the stack. Sample Output 1 2 3 4 5 6 7 -1 7 6 5 4 3 9 6 4 3 -2 3 4 6 9 2 -3 Number of items left is less than five! Program is terminating! Project name : Backtrack Filenames: backtrack.h, backtrack.c,…