The document discusses implementing a stack using a linked list as an alternative to an array. It explains that a linked list avoids size limitations of an array implementation. Elements can be inserted and removed from the start of the list in constant time, making it suitable for a stack. The four basic stack operations - push, pop, top, and isEmpty - can all be performed in constant time on this linked list implementation.

1. Class No.06 Data Structures http://ecomputernotes.com

2. Stack Using Linked List We can avoid the size limitation of a stack implemented with an array by using a linked list to hold the stack elements. As with array, however, we need to decide where to insert elements in the list and where to delete them so that push and pop will run the fastest. http://ecomputernotes.com

3. Stack Using Linked List For a singly-linked list, insert at start or end takes constant time using the head and current pointers respectively. Removing an element at the start is constant time but removal at the end required traversing the list to the node one before the last. Make sense to place stack elements at the start of the list because insert and removal are constant time. http://ecomputernotes.com

4. Stack Using Linked List No need for the current pointer; head is enough. top 2 5 7 1 1 7 5 2 head http://ecomputernotes.com

5. Stack Operation: List int pop() { int x = head->get(); Node* p = head; head = head->getNext(); delete p; return x; } top 2 5 7 1 7 5 2 head http://ecomputernotes.com

6. Stack Operation: List void push(int x) { Node* newNode = new Node(); newNode->set(x); newNode->setNext(head); head = newNode; } top 2 5 7 9 7 5 2 head push(9) 9 newNode http://ecomputernotes.com

7. Stack Operation: List int top() { return head->get(); } int IsEmpty() { return ( head == NULL ); } All four operations take constant time. http://ecomputernotes.com

8. Stack: Array or List Since both implementations support stack operations in constant time, any reason to choose one over the other? Allocating and deallocating memory for list nodes does take more time than preallocated array. List uses only as much memory as required by the nodes; array requires allocation ahead of time. List pointers (head, next) require extra memory. Array has an upper limit; List is limited by dynamic memory allocation. http://ecomputernotes.com

9. Use of Stack Example of use: prefix, infix, postfix expressions. Consider the expression A+B: we think of applying the operator “+” to the operands A and B. “ +” is termed a binary operator : it takes two operands. Writing the sum as A+B is called the infix form of the expression. http://ecomputernotes.com

10. Prefix, Infix, Postfix Two other ways of writing the expression are + A B prefix A B + postfix The prefixes “pre” and “post” refer to the position of the operator with respect to the two operands. http://ecomputernotes.com

11. Prefix, Infix, Postfix Consider the infix expression A + B * C We “know” that multiplication is done before addition. The expression is interpreted as A + ( B * C ) Multiplication has precedence over addition. http://ecomputernotes.com

12. Prefix, Infix, Postfix Conversion to postfix A + ( B * C ) infix form http://ecomputernotes.com

13. Prefix, Infix, Postfix Conversion to postfix A + ( B * C ) infix form A + ( B C * ) convert multiplication http://ecomputernotes.com

14. Prefix, Infix, Postfix Conversion to postfix A + ( B * C ) infix form A + ( B C * ) convert multiplication A ( B C * ) + convert addition http://ecomputernotes.com

15. Prefix, Infix, Postfix Conversion to postfix A + ( B * C ) infix form A + ( B C * ) convert multiplication A ( B C * ) + convert addition A B C * + postfix form http://ecomputernotes.com

16. Prefix, Infix, Postfix Conversion to postfix (A + B ) * C infix form http://ecomputernotes.com

17. Prefix, Infix, Postfix Conversion to postfix (A + B ) * C infix form ( A B + ) * C convert addition http://ecomputernotes.com

18. Prefix, Infix, Postfix Conversion to postfix (A + B ) * C infix form ( A B + ) * C convert addition ( A B + ) C * convert multiplication http://ecomputernotes.com

19. Prefix, Infix, Postfix Conversion to postfix (A + B ) * C infix form ( A B + ) * C convert addition ( A B + ) C * convert multiplication A B + C * postfix form http://ecomputernotes.com

20. Precedence of Operators The five binary operators are: addition, subtraction, multiplication, division and exponentiation. The order of precedence is (highest to lowest) Exponentiation  Multiplication/division *, / Addition/subtraction +, - http://ecomputernotes.com

21. Precedence of Operators For operators of same precedence, the left-to-right rule applies: A+B+C means (A+B)+C. For exponentiation, the right-to-left rule applies A  B  C means A  ( B  C ) http://ecomputernotes.com

22. Infix to Postfix Infix Postfix A + B A B + 12 + 60 – 23 12 60 + 23 – (A + B)*(C – D ) A B + C D – * A  B * C – D + E/F A B  C*D – E F/+ http://ecomputernotes.com