Q4: Consider a stack of size 5. Consider the senesce of operations performed on the stack. Push (10), Push (20), Pop (), Push (30), Push(40), Pop(), Push(50), Push (60). For each operation draw stack and show how stack look like after each operation. (4 Marks)
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- 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.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.2. Given the following stack A = { 29,18,10,15,20,9,5,13,2,4,15} Create a queue by taking the elements from the top of the stack and adding them to a queue
- 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 complexityGiven 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.stack permutation of the numbers 0, 1, ..., n-1 is a permutation obtained as the sequence of numbers output by a stack after the original numbers have been processed left-to-right through a stack (via legal push and pop operations). For example, 0, 3, 2, 1 is a stack permutation of 0, 1, 2, 3 obtained by the sequence of operations: push, pop, push, push, push, pop, pop, pop. However, the permutation 1, 3, 0, 2 is not a stack permutation of 0, 1, 2, 3 Which of the following sequences are not stack permutations of 0,1,2,3,4,5,6,7,8,9? There could be more than one answer: select all those that you think are correct. There is a penalty for incorrect choices. Group of answer choices 4, 6, 8, 7, 5, 3, 2, 9, 0, 1 4, 3, 2, 1, 0, 9, 8, 7, 6, 5 2, 5, 6, 7, 4, 8, 9, 3, 1, 0 0, 4, 6, 5, 3, 8, 1, 7, 2, 9
- 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.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?
- 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.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.Problem 2 (Stacks): Consider the fundamental theorem of arithmetic, which is stated as follows:Every positive integer greater than 1 can be written uniquely as a prime or as the product of twoor more primes, where the prime factors are written in order of nondecreasing size. We want touse a stack to read a number and print all of its prime divisors in descending order. For example,with the integer 2100, the output should be:7 5 5 3 2 21. Write an algorithm, called Prime_Factorization, which accepts a positive integer greaterthan 1, and generates its prime factorization according to the above-mentioned theorem.[Hint: The smallest divisor greater than 1 of any integer is guaranteed to be a prime.]2. Propose a stack class to accommodate this prime decomposition. It should have at leasttwo member functions: One to compute the prime factorization of an integer, and one toprint all corresponding prime divisors in descending order.3. Give an implementation of all member functions defined in…