Stacks and Queues

1. Stacks and Queues Chapter 3

2. Templates in C++ • Template function in C++ makes it easier to reuse classes and functions. • A template can be viewed as a variable that can be instantiated to any data type, irrespective of whether this data type is a fundamental C++ type or a user-defined type.

3. Selection sort using templates

4. Code fragment illustration template instantiation

5. Stack • Last-In-First-Out (LIFO) list • Push • Add an element into a stack • Pop • Get and delete an element from a stack push pop

6. System stack after function call

7. Abstract data type Stack

8. Implementation • private: inttop; T *stack; int capacity; • template<class T> Stack<T>::Stack(intstackCapacity): MaxSize(stackCapacity) { stack=new T[capacity]; top=-1; }

9. template<classsT> inline Boolean Stack<T>::IsFull() { if (top==capacity-1) return TRUE; else return FALSE; } • template<classs T> inline Boolean Stack<T>::IsEmpty() { if (top==-1) return TRUE; else return FALSE; }

10. Adding to a stack

11. Deleting from a stack

12. Queue • First-In-First-Out (FIFO) list • Add an element into a queue • Get and delete an element from a queue • Variation • Priority queue

13. Abstract data type Queue

14. Implementation • private: intfront,rear; T *queue; int capacity; • template<class T> Queue<T>::Queue(intqueueCapacity):capacity(queueCapacity) { queue=new T[capacity]; front=rear= 0; }

15. template<classsT> inline Boolean Queue<T>::IsFull() { if (rear==capacity-1) return TRUE; else return FALSE; } • template<classs T> inline Boolean Stack<T>::IsEmpty() { if (front==rear) return TRUE; else return FALSE; }

16. Circular queue • Two indices • front: one position clockwise from the first element • rear: current end

17. Adding to a queue

18. Deleting from a queue

19. Problem: if front=rear? Increase the capacity of a queue just before it become full

20. A mazing problem 0: path 1: block

21. Allowable moves

22. Data type move • struct offsets { inta,b; }; enum directions{ N, NE, E, SE, S, SW, W, NW}; offsets move[8];

23. Table of moves

24. Implementation with a stack • A maze is represented by a two dimensional array maze[m][p] • struct Items{ int x, y, dir; };

25. Example

26. Example

27. First pass at finding a path through a maze

28. Finding a path through a maze

30. Evaluation of expressions • X = a / b - c + d * e - a * c • Suppose that a = 4, b = 2, c = 2, d =3, e = 3 • Interpretation 1: • ((4/2)-2)+(3*3)-(4*2)=0 + 8+9=1 • Interpretation 2: • (4/(2-2+3))*(3-4)*2=(4/3)*(-1)*2= -2.66666… • How to generate the machine instructions corresponding to a given expression? • Precedence rule + associative rule

31. Priority of operators in C++

32. Evaluation of expressions • Infix • Each operator comes in-between the operands • Eg. 2+3 • Postfix • Each operator appears after its operands • Eg. 23+ • Prefix • Each operator appears before its operands • Eg. +23

33. Example

34. Example: 6/2-3+4*2  62/3-42*+

35. Evaluating postfix expressions voidEval(Expression e) {// Assume that the last token in e is‘#’ // NextTokenis used to get the next token frome Stack<Token>stack; // initialize stack for (Token x = NextToken(e); x!= ‘#’;x=NextToken(e)) if (xis an operand) stack.Push(x) // add to stack else {// operator remove the correct number of operands for operatorx fromstack; perform the operationxand store the result onto the stack; } }

36. Infix to postfix • (1) Fully parenthesize expression • a / b - c + d * e - a * c  • ((((a / b) - c) + (d * e)) – (a * c)) • (2) All operators replace their corresponding right parentheses. • ((((a / b)- c)+ (d * e)) - a * c)) • (3) Delete all parentheses. • ab/c-de*+ac*-

37. Example: a+b*c

38. Example: a*b+c

39. Example: a*(b+c)*d