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Stacks and Queues

Stacks and Queues 11
Stacks and Queues Chris Kiekintveld CS 2401 (Fall 2010) Elementary Data Structures and Algorithms Two New ADTs   Define two new abstract data types   Both are restricted lists   Can be implemented using arrays or linked lists   Stacks   “Last In First Out” (LIFO)   Queues   “First In First Out” (FIFO) Java Programming: Program Design Including Data Structures 2 Stacks   List of the same kind of elements   Addition and deletion of elements occur only at one end, called the top of the stack   Computers use stacks to implement method calls   Stacks are also used to convert recursive algorithms into nonrecursive algorithms Java Programming: Program Design Including Data Structures 3 Conceptual Stacks Figure 171 Various types of stacks Java Programming: Program Design Including Data Structures 4 Stacks (continued)   Stacks are also called Last Input First Output (LIFO) data structures   Operations performed on stacks   Push: adds an element to the stack   Pop: removes an element from the stack   Peek: looks at the top element of the stack Java Programming: Program Design Including Data Structures 5 Stacks (continued) Figure 173 Stack operations Java Programming: Program Design Including Data Structures 6 Stacks (continued) Figure 174 UML diagram of the interface StackADT Java Programming: Program Design Including Data Structures 7 StackException Class   Adding an element to a full stack and removing an element from an empty stack would generate errors or exceptions   Stack overflow exception   Stack underflow exception   Classes that handle these exceptions   StackException extends RunTimeException   StackOverflowException extends StackException   StackUnderflowException extends StackException Java Programming: Program Design Including Data Structures 8 Implementation of Stacks as Arrays   The array implementing a stack is an array of reference variables   Each element of the stack can be assigned to an array slot   The top of the stack is the index of the last element added to the stack   To keep track of the top position, declare a variable called stackTop Java Programming: Program Design Including Data Structures 9 Implementation of Stacks as Arrays (continued) Figure 176 Example of a stack Java Programming: Program Design Including Data Structures 10 Constructors   Default constructor public StackClass() maxStackSize = 100; stackTop = 0; //set stackTop to 0 list = (T) new ObjectmaxStackSize; //create the array //end default constructor Java Programming: Program Design Including Data Structures 11 Initialize Stack   Method initializeStack public void initializeStack() for (int i = 0; i stackTop; i++) listi = null; stackTop = 0; //end initializeStack Java Programming: Program Design Including Data Structures 12 Empty Stack   Method isEmptyStack public boolean isEmptyStack() return (stackTop == 0); //end isEmptyStack Java Programming: Program Design Including Data Structures 13 Full Stack   Method isFullStack public boolean isFullStack() return (stackTop == maxStackSize); //end isFullStack Java Programming: Program Design Including Data Structures 14 Push   Method push public void push(T newItem) throws StackOverflowException if (isFullStack()) throw new StackOverflowException(); liststackTop = newItem; //add newItem at the //top of the stack stackTop++; //increment stackTop //end push Java Programming: Program Design Including Data Structures 15 Peek   Method peek public T peek() throws StackUnderflowException if (isEmptyStack()) throw new StackUnderflowException(); return (T) liststackTop 1; //end peek Java Programming: Program Design Including Data Structures 16 Pop   Method pop public void pop() throws StackUnderflowException if (isEmptyStack()) throw new StackUnderflowException(); stackTop; //decrement stackTop liststackTop = null; //end pop Java Programming: Program Design Including Data Structures 17 Linked Implementation of Stacks   Arrays have fixed sizes   Only a fixed number of elements can be pushed onto the stack   Dynamically allocate memory using reference variables   Implement a stack dynamically   Similar to the array representation, stackTop is used to locate the top element  stackTop is now a reference variable Java Programming: Program Design Including Data Structures 18 Linked Implementation of Stacks (continued) Figure 1713 Nonempty linked stack Java Programming: Program Design Including Data Structures 19 Default Constructor   Default constructor public LinkedStackClass() stackTop = null; //end constructor Java Programming: Program Design Including Data Structures 20 Initialize Stack   Method initializeStack public void initializeStack() stackTop = null; //end initializeStack Java Programming: Program Design Including Data Structures 21 Empty Stack and Full Stack   Methods isEmptyStack and isFullStack public boolean isEmptyStack() return (stackTop == null); //end isEmptyStack public boolean isFullStack() return false; //end isFullStack Java Programming: Program Design Including Data Structures 22 Push   Method push public void push(T newElement) StackNodeT newNode; //reference variable to create //the new node newNode = new StackNodeT(newElement, stackTop); //create //newNode and insert //before stackTop stackTop = newNode; //set stackTop to point to //the top element //end push Java Programming: Program Design Including Data Structures 23 Peek   Method peek public T peek() throws StackUnderflowException if (stackTop == null) throw new StackUnderflowException(); return stackTop.info; //end top Java Programming: Program Design Including Data Structures 24 Pop   Method pop public void pop() throws StackUnderflowException if (stackTop == null) throw new StackUnderflowException(); stackTop = stackTop.link; //advance stackTop to the //next node //end pop Java Programming: Program Design Including Data Structures 25 Applications of Stacks: Postfix Expression Calculator   Infix notation   The operator is written between the operands   Prefix or Polish notation   Operators are written before the operands   Does not require parentheses   Reverse Polish or postfix notation   Operators follow the operands   Has the advantage that the operators appear in the order required for computation Java Programming: Program Design Including Data Structures 26 Applications of Stacks: Postfix Expression Calculator (continued) Table 171 Infix expressions and their equivalent postfix expressions Java Programming: Program Design Including Data Structures 27 Applications of Stacks: Postfix Expression Calculator (continued)   Algorithm to evaluate postfix expressions   Scan the expression from left to right   When an operator is found, back up to get the required number of operands   Perform the operation   Continue processing the expression Java Programming: Program Design Including Data Structures 28 Main Algorithm   Main algorithm in pseudocode for processing a postfix expression Get the next expression while more data to process a. initialize the stack b. process the expression c. output result d. get the next expression Java Programming: Program Design Including Data Structures 29 Method evaluateExpression   General algorithm for evaluateExpression get the next token while (token = '=') if (token is a number) output number push number into stack else token is an operation call method evaluateOpr to evaluate the operation if (no error in the expression) get next token else discard the expression Java Programming: Program Design Including Data Structures 30 Method evaluateOpr   This method evaluates an operation   Two operands are needed to evaluate an operation   Operands are stored in the stack   The stack must contain at least two operands   Otherwise, the operation cannot be evaluated Java Programming: Program Design Including Data Structures 31 Removing Recursion: Nonrecursive Algorithm to Print a Linked List Backward   Naïve approach   Get the last node of the list and print it   Traverse the link starting at the first node   Repeat this process for every node   Traverse the link starting at the first node until you reach the desired node   Very inefficient Java Programming: Program Design Including Data Structures 32 Removing Recursion: Nonrecursive Algorithm to Print a Linked List Backward (continued) current = first; //Line 1 while (current = null) //Line 2 stack.push(current); //Line 3 current = current.link; //Line 4 Java Programming: Program Design Including Data Structures 33 Removing Recursion: Nonrecursive Algorithm to Print a Linked List Backward (continued) Figure 1736 List and stack after the staments stack.push(current); and current = current.link; executes Java Programming: Program Design Including Data Structures 34 The class Stack Table 172 Members of the class Stack Java Programming: Program Design Including Data Structures 35 Queues   Data structure in which the elements are added at one end, called the rear, and deleted from the other end, called the front   A queue is a First In First Out data structure   As in a stack, the middle elements of the queue are inaccessible Java Programming: Program Design Including Data Structures 36 Queue Operations   Queue operations  initializeQueue  isEmptyQueue  isFullQueue  front  back  addQueue  deleteQueue Java Programming: Program Design Including Data Structures 37 QueueException Class   Adding an element to a full queue and removing an element from an empty queue would generate errors or exceptions   Queue overflow exception   Queue underflow exception   Classes that handle these exceptions   QueueException extends RunTimeException   QueueOverflowException extends QueueException   QueueUnderflowException extends QueueException Java Programming: Program Design Including Data Structures 38 Implementation of Queues as Arrays   Instance variables   An array to store the queue elements  queueFront: keeps track of the first element  queueRear: keeps track of the last element  maxQueueSize: specifies the maximum size of the queues Java Programming: Program Design Including Data Structures 39 Implementation of Queues as Arrays (continued) Figure 1742 Queue after two more addQueue operations Java Programming: Program Design Including Data Structures 40 Implementation of Queues as Arrays (continued) Figure 1743 Queue after the deleteQueue operation Java Programming: Program Design Including Data Structures 41 Implementation of Queues as Arrays (continued)   Problems with this implementation   Arrays have fixed sizes   After various insertion and deletion operations, queueRear will point to the last array position   Giving the impression that the queue is full   Solutions   Slide all of the queue elements toward the first array position   Use a circular array Java Programming: Program Design Including Data Structures 42 Implementation of Queues as Arrays (continued) Figure 1745 Circular queue Java Programming: Program Design Including Data Structures 43 Implementation of Queues as Arrays (continued) Figure 1746 Queue with two elements at positions 98 and 99 Java Programming: Program Design Including Data Structures 44 Implementation of Queues as Arrays (continued) Figure 1747 Queue after one more addQueue operation Java Programming: Program Design Including Data Structures 45 Constructors   Default constructor //Default constructor public QueueClass() maxQueueSize = 100; queueFront = 0; //initialize queueFront queueRear = maxQueueSize 1; //initialize queueRear count = 0; list = (T) new ObjectmaxQueueSize; //create the //array to implement the queue Java Programming: Program Design Including Data Structures 46 initializeQueue   Method initilializeQueue public void initializeQueue() for (int i = queueFront; i queueRear; i = (i + 1) maxQueueSize) listi = null; queueFront = 0; queueRear = maxQueueSize 1; count = 0; Java Programming: Program Design Including Data Structures 47 Empty Queue and Full Queue   Methods isEmptyQueue and isFullQueue public boolean isEmptyQueue() return (count == 0); public boolean isFullQueue() return (count == maxQueueSize); Java Programming: Program Design Including Data Structures 48 Front   Method front public T front() throws QueueUnderflowException if (isEmptyQueue()) throw new QueueUnderflowException(); return (T) listqueueFront; Java Programming: Program Design Including Data Structures 49 Back   Method back public T back() throws QueueUnderflowException if (isEmptyQueue()) throw new QueueUnderflowException(); return (T) listqueueRear; Java Programming: Program Design Including Data Structures 50 addQueue   Method addQueue public void addQueue(T queueElement) throws QueueOverflowException if (isFullQueue()) throw new QueueOverflowException(); queueRear = (queueRear + 1) maxQueueSize; //use the //mod operator to advance queueRear //because the array is circular count++; listqueueRear = queueElement; Java Programming: Program Design Including Data Structures 51 deleteQueue   Method deleteQueue public void deleteQueue() throws QueueUnderflowException if (isEmptyQueue()) throw new QueueUnderflowException(); count; listqueueFront = null; queueFront = (queueFront + 1) maxQueueSize; //use the //mod operator to advance queueFront //because the array is circular Java Programming: Program Design Including Data Structures 52 Linked Implementation of Queues   Simplifies many of the special cases of the array implementation   Because the memory to store a queue element is allocated dynamically, the queue is never full   Class LinkedQueueClass implements a queue as a linked data structure   It uses nodes of type QueueNode Java Programming: Program Design Including Data Structures 53 Linked Implementation of Queues (continued)   Method initializeQueue public void initializeQueue() queueFront = null; queueRear = null; Java Programming: Program Design Including Data Structures 54 Linked Implementation of Queues (continued)   Methods isEmptyQueue and isFullQueue public boolean isEmptyQueue() return (queueFront == null); public boolean isFullQueue() return false; Java Programming: Program Design Including Data Structures 55 addQueue   Method addQueue public void addQueue(T newElement) QueueNodeT newNode; newNode = new QueueNodeT(newElement, null); //create //newNode and assign newElement to newNode if (queueFront == null) //if initially the queue is empty queueFront = newNode; queueRear = newNode; else //add newNode at the end queueRear.link = newNode; queueRear = queueRear.link; //end addQueue Java Programming: Program Design Including Data Structures 56 front and back   Methods front and back public T front() throws QueueUnderflowException if (isEmptyQueue()) throw new QueueUnderflowException(); return queueFront.info; public T back() throws QueueUnderflowException if (isEmptyQueue()) throw new QueueUnderflowException(); return queueRear.info; Java Programming: Program Design Including Data Structures 57 deleteQueue   Method deleteQueue public void deleteQueue() throws QueueUnderflowException if (isEmptyQueue()) throw new QueueUnderflowException(); queueFront = queueFront.link; //advance queueFront if (queueFront == null) //if after deletion the queue queueRear = null; //is empty, set queueRear to null //end deleteQueue Java Programming: Program Design Including Data Structures 58
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