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Problem 1 (10 points).
In the previous assignment, you wrote a program that takes an arithmetic expression in infix
notation and evaluates it. You used a Stack class in your program that was implemented
using an array. This imposed the restriction that the maximum size of the stack needed to
be fixed when an object of Stack type was created.
In this assignment, you need to change the implementation of the Stack class and use linked
lists instead of arrays. The only public members of the class should be corresponding to the
operations that a stack allows (push, pop, top, isEmpty). In particular, all the details related
to the linked list should be private to the class. Do not forget to provide suitable constructors
and a destructor.
Check that your program still evaluates an expression input in infix notation correctly.
Problem 2 (10 points).
Write a C++ program with the following functions:
• A function createList that inputs a sequence of integers from the users until the
number 0 is entered, and puts the numbers in a singly linked list in the order in which
the numbers arrive. The function should take no arguments and return a pointer to the
first element in the list (the start pointer).
• A function PrintList that takes a pointer to the first element (the start pointer) in a
linked list and prints the numbers in the list in the order in which they appear in the
list.
• A function Reverse that takes a reference to the start pointer of a linked list and
reverses the linked list. The function should update the start pointer appropriately.
The function should use the same nodes as in the original linked list i.e., you should not
create any new nodes.
Test these functions by creating a list, reversing it and then printing it in your main function.
You can use the following definition of a Node class:
class Node {
public:
int data;
Node *next;
};
Problem 3 (10 points). Write a C++ function whose declaration is “Node* mergeSort(Node
*start);”, where the class Node is as in the previous exercise. The function takes a pointer to
the first node in a linked list, sorts the linked list using the merge sort algorithm and returns
a pointer to the first node in the sorted list. Your algorithm should run in time O(n log n)
where n is number of nodes in the input linked list.
Problem 4 (10 points). Suppose that you are given the start pointer to a linked list that
some other programmer has created. As such a linked list is supposed to end with nullptr,
but you suspect that due to programming errors, the linked list may contain a cycle as shown
in the figure. Give an algorithm (pseudocode suffices) to check if this is the case. The
algorithm should take O(n) time where n is the number of distinct nodes in the list and it
should use only a constant amount of memory (apart from the storage used for the list).
Figure 1: Linked list with a cycle.
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