1. Stack Implementation Using 1D Array
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1 Lecture 5 Stacks 1
2 Lecture Content 1. Stack Implementation Using 1D Array 2. Stack Implementation Using Singly Linked List 3. Applications of Stack 3.1 Infix and Postfix Arithmetic Expressions 3.2 Evaluate a Valid Postfix Expression 3.3 Delimiter Matching 2
3 Stack A stack is a data structure which insertion (push, add) and deletion (pop, remove) take place at one end called the top. Other name for the stack is LIFO (last-in firstout). 3
4 Stack The intuitive model of a stack is a pile of coins, books on a table. 4
5 Stack Applications of stack - the implementation of recursive methods (or functions) in programming languages. - operating systems (store parameters and local variables of functions/methods) - computer graphics (used for transformations) - Implement Depth-First Search (DFS) 5
6 push, pop, peek, isempty, isfull Operations push() operation 6
7 push, pop, peek, isempty, isfull Operations pop() operation 7
8 1. Array-Based Stack class Stack { private int maxsize; // size of stack private int[] astack; // array-based stack private int top; // top of stack public Stack(int s); // constructor // push, pop, peek, isempty, isfull // end class Stack 8
9 1. Array-Based Stack public Stack(int s) { // constructor maxsize = s; // set array size astack = new int[maxsize]; // create array top = -1; // empty, no items yet 9
10 isfull and isempty Operations public boolean isfull() { // returns true if stack is full return (top == maxsize - 1); public boolean isempty() { // returns true if stack is empty return (top == -1); 10
11 Push Operation public void push(int x) { // put item on top of stack astack[++top] = x; // increment top, insert item 11
12 Pop Operation public int pop() { // take item from top of stack // access item, decrement top return astack[top--]; 12
13 peek Operation public int peek() { // peek at top of stack return astack[top]; 13
14 Display Stack Data public void stackdisplay() { // display stack content on screen int temp = top, x = 0; while (temp!= -1) { x = astack[temp--]; System.out.println(x); System.out.println(); 14
15 Java Stack Class import java.util.stack;... Stack<Integer> S = new Stack<Integer>(); Stack<Character> S = new Stack<Character>(); 15
16 Java Stack Class push() adds a new element to the top of the stack pop() returns and removes the top element in the stack peek() returns the top element in the stack empty() returns true if the stack is empty search(object o): returns the 1-based position where an object is on the stack. 16
17 Lecture Content 2. Stack Implementation Using Singly Linked List 17
18 2. SLL-Based Stack - Node Definition class Node { public int data; // data item public Node next; // next node in list public Node(int d) { // constructor data = d; 18
19 Node Definition public void displaynode() { // display node data System.out.println(data + " "); // end class Node 19
20 List Definition class NodeList { private Node first; // ref to first item public NodeList() { // constructor first = null; // no items on list yet public boolean isempty() { // returns true if list is empty return (first == null);... // end class NodeList 20
21 List Definition public void insertfirst(int d) { // insert at start of list Node newnode = new Node(d); // make new node newnode.next = first; // newnode --> old first first = newnode; // first --> newnode 21
22 List Definition public int deletefirst() { // delete first item // (assumes list not empty) Node temp = first; // save reference to node first = first.next; // delete it: first-->old next return temp.data; // return deleted node 22
23 List Definition public int First() { // return data member of first item return first.data; 23
24 List Definition public void displaylist() { // start at beginning of list Node current = first; while (current!= null) { // until end of list, current.displaynode(); // print data current = current.next; // move to next node System.out.println(); 24
25 Stack Definition class SLLStack { private NodeList List; public SLLStack() { // constructor List = new NodeList();... // end class SLLStack 25
26 isempty and peek Operations public boolean isempty() { // returns true if stack is empty return (List.isEmpty()); public int peek() { // peek at top of stack return List.First(); 26
27 push and pop Operations public void push(int data) { // put item on top of stack List.insertFirst(data); public int pop() { // take item from top of stack return List.deleteFirst(); 27
28 Display Stack Data public void stackdisplay() { if (isempty()) System.out.println( "Stack is empty"); else { System.out.println( "Stack (top-->bottom): "); List.displayList(); 28
29 3. Applications of Stack 3.1 Infix and Postfix Arithmetic Expressions 3.2 Evaluate a Valid Postfix Expression 3.3 Delimiter Matching 29
30 3.1 Infix and Postfix Arithmetic Expressions Infix and postfix conversion Infix = 3 * (4 + 5) - 6 / (1 + 2) is converted to Postfix = * / - Infix = ((2 + 4) * 7) + 3 * (9-5) is converted to Postfix = * * + 30
31 3.1 Convert from Infix to Postfix Algorithm [Noel Kalicharan] 1. Initialize a stack S to empty. 2. Get the next item, x, from the infix expression; if none, go to step 8 (x is either an operand, a left bracket, a right bracket, or an operator). 3. If x is an operand, output x. 4. If x is a left bracket, push it onto S. 31
32 3.1 Convert from Infix to Postfix 5. If x is a right bracket, pop items off S and output popped items until a left bracket appears on top of S; pop the left bracket and discard. 6. If x is an operator, then do the following. while (S is not empty) and (precedence of the operator on top of S is equal to or higher than that of x) pop S and output popped item push x onto S 32
33 3.1 Convert from Infix to Postfix 7. Repeat from step Pop S and output the popped item until S is empty. 33
34 3.2 Evaluate a Valid Postfix Expression Postfix = * / - is evaluated to 25 (Infix = 3 * (4 + 5) - 6 / (1 + 2) = 25) Postfix = * * + is evaluated to 54 (Infix = ((2 + 4) * 7) + 3 * (9-5) = 54) 34
35 3.2 Evaluate a Valid Postfix Expression Algorithm [Noel Kalicharan] 1. Initialize a stack S to empty 2. While we have not reached the end of the expression 2.1 Get the next item, x, from the expression 2.2 If x is an operand, push it onto S 2.3 Else (i.e., if x is an operator), Pop two operands from S Apply the operator to the two operands Push the result onto S 3. Pop S and store the popped item in y 4. Return y // this is the value of the expression 35
36 3.3 Delimiter Matching c[d] // correct a{b[c]de // correct a{b(c]de // not correct; ] doesn t match ( a[b{cd]e // not correct; nothing matches final a{b(c) // not correct; nothing matches opening { 36
37 3.3 Delimiter Matching Algorithm [Mark Allen Weiss - dsapsuj4e] 1. Make an empty stack. 2. Read symbols until the end of the expression If symbol is opening symbol, push it onto stack If symbol is closing symbol, do the following. 37
38 3.3 Delimiter Matching If the stack is empty, report an error Otherwise, pop the stack If popped symbol is not corresponding opening symbol, report an error. 3. At the end of the expression, if the stack is not empty, report an error. 38
39 Exercises 1. Write a Java program to convert a nonnegative integer n in decimal form into binary one using stack. For example: n = = Write a Java program to reverse a string using Java Stack class. For instance, part trap. import java.util.stack; Stack<Character> S = new Stack<Character>(); 39
40 Exercises 3. Write a Java program to evaluate a valid postfix expression using Java Stack class. For example, Postfix = * / - is evaluated to 25 (Infix = 3 * (4 + 5) - 6 / (1 + 2) = 25) Postfix = * * + is evaluated to 54 (Infix = ((2 + 4) * 7) + 3 * (9-5) = 54) 40
41 Exercises 4. Write a Java program to convert a valid infix expression to a postfix expression using Java Stack class. For example, Infix = 3 * (4 + 5) - 6 / (1 + 2) is converted to Postfix = * / - Infix = ((2 + 4) * 7) + 3 * (9-5) is converted to Postfix = * * + 41
42 Exercises 5. Write a Java program to check the delimiter matching of an arithmetic expression using Java Stack class. For example, c[d] // correct a{b[c]de // correct a{b(c]de // not correct; ] doesn t match ( a[b{cd]e // not correct; nothing matches final a{b(c) // not correct; nothing matches opening { 42
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