Suppose the numbers 0, 1, 2, .9 were pushed onto a stack in that order, but that pops occurred at random points between the various pushes. The following is a valid sequence in which the values in the stack could have been popped: 3, 2, 6, 5, 7, 4, 1, 0, 9, 8 Explain why it is not possible that 3, 2, 6, 4, 7, 5, 1, 0, 9, 8 is a valid sequence in which the values could have been popped off the stack.
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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.Question 16. The following operations are applied to an empty stack s: s. push (1) s. push (2) s. push (3) s.pop() s. push (4) s.pop() The result of a further s.pop () is ... a) a number b) undefined c) 4 d) 2Consider a (literal) plate stack. If the stack becomes too tall, it may collapse.In practise, we would most likely create a new stack when the preceding stack reaches a certain threshold. Create a data structure SetOfStacks that is similar to this. SetOfStacks should be made up of many stacks and should build a new stack when the preceding one reaches its capacity.SetOfStacks. Push() and SetOfStacks are both functions. pop() should operate exactly like a single stack (that is, it should return the same values as if there were just one stack).COMPLETE THE FORMULACreate a popAt(int index) method that executes a pop operation on a given substack.
- 1: Consider the fundamental theorem of arithmetic, which is stated as P follows: Every positive integer greater than 1 can be written uniquely as a prime or as the product of two or more primes, where the prime factors are written in order of nondecreasing size. We want to use 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 2 1. Write an algorithm, called Prime_Factorization, which accepts a positive integer greater than 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 structure based algorithm to accommodate this prime decomposition. First, you should compute the prime factorization of an integer. Second, you need to print all corresponding prime divisors in descending order.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 the above stack…Given two stacks of textbooksof the following subjects {“Chemistry”, “Mathematics”, “Biology”,“English”}and {“Biology”, “English”, “Geography”, “Physics”},find the subjects that are (1) only present in the first stack; (2) only present inthe second stack; (3) present in both stacks.
- 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?Stack A has the entries a, b, c (with a on top). Stack B is empty. An entry popped out of stack A can be printed immediately or pushed to stack B. An entry popped out of the stack B can only be printed. In this arrangement, which of the following permutations of a, b, c are not possible?The puzzle includes various sizes of coins. It starts with an order of size, taking the top one the least. The puzzle needs to be constructed to have a conical shape and consider these laws: In every step, you can push one coin; every move includes taking the upper coin from the stack and putting it on top of other stack or starting a new stack. None of the coins can be put on top of the smaller coin; finally, at any moment, at most L, various stacks can be in use. Make PDDL in a way it will not rely on A and L.
- Two stacks of positive integers are needed, one containing elements withvalues less than or equal to 1,000 and the other containing elements with values larger than 1,000.The total number of elements in the small-value stack and the large-value stack combined are notmore than 200 at any time, but we cannot predict how many are in each stack. (All of the elements2could be in the small-value stack, they could be evenly divided, both stacks could be empty, andso on.).1. Can you think of a way to implement both stacks in one array?Given a stack myData: 34, 56, 78, 12, 66 (top is 34) what is the output after the following operations? Push(myData 43) Pop(myData) Pop(myData) print(Peek(myData) Pop(myData) print(Peek(myData)) 43 34 O 34 56 O 56 78 O 12 668. Consider the following operation performed on a stack of size 5. Push (1); Pop (); Push (2) Push (3); Pop (); Push (4) Pop (); Push (5); After the completion of all operations, the number of elements present in the stack is? A. 1 B. 2 C. 3 D.4 how do you increment the rear end of the queue?