1. C++ Programming: Program Design Including Data Structures, Fourth Edition Chapter 18: Stacks and Queues (part 2)

2. C++ Programming: Program Design Including Data Structures, Fourth Edition 2 Linked Implementation of Stacks Array only allows fixed number of elements If number of elements to be pushed exceeds array size −Program may terminate Linked lists can dynamically organize data In a linked representation, stackTop is pointer to top element in stack

7. C++ Programming: Program Design Including Data Structures, Fourth Edition 7 Default Constructor Initializes the stack to an empty state when a stack object is declared −Sets stackTop to NULL

8. C++ Programming: Program Design Including Data Structures, Fourth Edition 8 Empty Stack and Full Stack In the linked implementation of stacks, the function isFullStack does not apply −Logically, the stack is never full

9. C++ Programming: Program Design Including Data Structures, Fourth Edition 9 Initialize Stack

10. C++ Programming: Program Design Including Data Structures, Fourth Edition 10 Push The newElement is added at the beginning of the linked list pointed to by stackTop

11. C++ Programming: Program Design Including Data Structures, Fourth Edition 11 Push (continued)

12. C++ Programming: Program Design Including Data Structures, Fourth Edition 12 Push (continued)

13. C++ Programming: Program Design Including Data Structures, Fourth Edition 13 Push (continued)

14. C++ Programming: Program Design Including Data Structures, Fourth Edition 14 Push (continued) We do not need to check whether the stack is full before we push an element onto the stack

15. C++ Programming: Program Design Including Data Structures, Fourth Edition 15 Return the Top Element

16. C++ Programming: Program Design Including Data Structures, Fourth Edition 16. Pop Node pointed to by stackTop is removed

18. C++ Programming: Program Design Including Data Structures, Fourth Edition 18 Pop (continued)

19. C++ Programming: Program Design Including Data Structures, Fourth Edition 19 Copy Stack

20. C++ Programming: Program Design Including Data Structures, Fourth Edition 20 Copy Stack (continued) Notice that this function is similar to the definition of copyList for linked lists

21. C++ Programming: Program Design Including Data Structures, Fourth Edition 21 Constructors and Destructors

22. C++ Programming: Program Design Including Data Structures, Fourth Edition 22 Overloading the Assignment Operator (=)

23. C++ Programming: Program Design Including Data Structures, Fourth Edition 23 Application of Stacks: Postfix Expressions Calculator Infix notation: usual notation for writing arithmetic expressions −The operator is written between the operands −Example: a + b −The operators have precedence Parentheses can be used to override precedence

24. C++ Programming: Program Design Including Data Structures, Fourth Edition 24 Application of Stacks: Postfix Expressions Calculator (continued) Prefix (Polish) notation: the operators are written before the operands −Introduced by the Polish mathematician Jan Lukasiewicz Early 1920s −The parentheses can be omitted −Example: + a b

25. C++ Programming: Program Design Including Data Structures, Fourth Edition 25 Application of Stacks: Postfix Expressions Calculator (continued) Reverse Polish notation: the operators follow the operands (postfix operators) −Proposed by the Australian philosopher and early computer scientist Charles L. Hamblin Late 1950's −Advantage: the operators appear in the order required for computation −Example: a + b * c In a postfix expression: a b c * +

26. C++ Programming: Program Design Including Data Structures, Fourth Edition 26 Application of Stacks: Postfix Expressions Calculator (continued)

27. C++ Programming: Program Design Including Data Structures, Fourth Edition 27 Application of Stacks: Postfix Expressions Calculator (continued) Postfix notation has important applications in computer science −Many compilers first translate arithmetic expressions into postfix notation and then translate this expression into machine code Evaluation algorithm: −Scan expression from left to right −When an operator is found, back up to get the operands, perform the operation, and continue

28. C++ Programming: Program Design Including Data Structures, Fourth Edition 28 Application of Stacks: Postfix Expressions Calculator (continued) Example: 6 3 + 2 * = −Read first symbol 6 is a number  push it onto the stack −Read next symbol 3 is a number  push it onto the stack

29. C++ Programming: Program Design Including Data Structures, Fourth Edition 29 Application of Stacks: Postfix Expressions Calculator (continued) Example: 6 3 + 2 * = −Read next symbol + is an operator (two operands)  pop stack twice, perform operation, put result back onto stack

30. C++ Programming: Program Design Including Data Structures, Fourth Edition 30 Example: 6 3 + 2 * = −Read next symbol 2 is a number  push it onto the stack Application of Stacks: Postfix Expressions Calculator (continued)

31. C++ Programming: Program Design Including Data Structures, Fourth Edition 31 Example: 6 3 + 2 * = −Read next symbol * is an operator  pop stack twice, perform operation, put result back onto stack Application of Stacks: Postfix Expressions Calculator (continued)

32. C++ Programming: Program Design Including Data Structures, Fourth Edition 32 Example: 6 3 + 2 * = −Read next symbol = is an operator  indicates end of expression Print the result (pop stack first) Application of Stacks: Postfix Expressions Calculator (continued)

33. C++ Programming: Program Design Including Data Structures, Fourth Edition 33 Application of Stacks: Postfix Expressions Calculator (continued) Symbols can be numbers or anything else: −+, -, *, and / are operators Pop stack twice and evaluate expression If stack has less than two elements  error −If symbol is =, the expression ends Pop and print answer from stack If stack has more than one element  error −If symbol is anything else Expression contains an illegal operator

34. C++ Programming: Program Design Including Data Structures, Fourth Edition 34 Application of Stacks: Postfix Expressions Calculator (continued) Examples: 7 6 + 3 ; 6 - = ; is an illegal operator 14 + 2 3 * = Does not have enough operands for + 14 2 3 + = Error: stack will have two elements when we encounter equal ( = ) sign

35. C++ Programming: Program Design Including Data Structures, Fourth Edition 35 Application of Stacks: Postfix Expressions Calculator (continued) We assume that the postfix expressions are in the following form: #6 #3 + #2 * = −If symbol scanned is #, next input is a number −If the symbol scanned is not #, then it is: An operator (may be illegal) or An equal sign (end of expression) We assume expressions contain only +, -, *, and / operators

36. C++ Programming: Program Design Including Data Structures, Fourth Edition 36 Main Algorithm Pseudocode: We will write four functions: − evaluateExpression, evaluateOpr, discardExp, and printResult

37. C++ Programming: Program Design Including Data Structures, Fourth Edition 37 Function evaluateExpression

38. C++ Programming: Program Design Including Data Structures, Fourth Edition 38 Function evaluateOpr

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40. C++ Programming: Program Design Including Data Structures, Fourth Edition 40 Function discardExp This function is called whenever an error is discovered in the expression

41. C++ Programming: Program Design Including Data Structures, Fourth Edition 41 Function printResult If the postfix expression contains no errors, the function printResult prints the result −Otherwise, it outputs an appropriate message The result of the expression is in the stack and the output is sent to a file

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43. C++ Programming: Program Design Including Data Structures, Fourth Edition 43 Removing Recursion: Nonrecursive Algorithm to Print a Linked List Backward To print the list backward, first we need to get to the last node of the list −Problem: how do we get back to previous node? Links go in only one direction −Solution: save a pointer to each of the nodes with info 5, 10, and 15 Use a stack (LIFO)

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46. C++ Programming: Program Design Including Data Structures, Fourth Edition 46 Let us now execute the following statements: Output: 20 15 10 5 Removing Recursion (continued)