Abstract Data Types (ADT) Collection –An object that can hold a list of other objects Homogeneous Collection –Contains elements all of the same type –Example: Array of integers Heterogeneous Collection –Contains elements of differing types –Example: The Java Stack Abstract Data Type –A data structure with a well-defined interface –Examples: stack, queue, list, tree, graph

Stacks/Queues/Dynamic lists Stack Operations –push, pop, isEmpty(), isFull(), look(), reset() –look() is sometimes called peek() Queue Operations –add(), remove(), isFull(), isEmpty(), reset() Tree Operations –insert(), remove(), find(), traverse(), bfs(), dfs() Key: a well defined interface to abstract the data structure Key: We can change the data structure without effecting users

Implementation Possibilities Use generic built-in methods –Advantage: standard data type supported by Java –Disadvantage: lose flexibility Using Arrays –Advantages: fast, native Java data structure –Disadvantage: The size must be known in advance Dynamic storage –Advantage: The structure can grow and shrink –Disadvantage: Executes more slowly

A Stack Example public static void main( String args[] ) { Stack stack = new Stack(); String string = "Hello this is a test string"; System.out.println("String: " + string); for (int k = 0; k < string.length(); k++) stack.push(new Character( string.charAt(k))); Object obj = null; String reversed = ""; while (!stack.isEmpty()) { obj = stack.pop(); reversed = reversed + o.toString(); } System.out.println("Reversed: " + reversed); } Reverse a String

Java Generic Classes Vector Vector vec = new Vector (); vec.addElement("alpha"); rec.addElement("beta"); System.out.println(vec.elementAt(0)); Stack Stack stk = new Stack (); stk.push("alpha"); stk.push("beta"); System.out.println(stk.pop()); LinkedList List link = new LinkedList (); link.add(new PhoneRecord("Roger", "(541) ")); for (PhoneRecord pr : theList) System.out.println(pr); Java has many other generic interfaces and classes –Examples: Set, Map, Hashtable

Stack of doubles with Arrays public class Stack { int top; double[] data; public Stack(int size) { data = new double[size]; top = -1; } public void push(double x) throws Exception { if (!isFull() { data[++top] = value; } else throw new Exception(); } public double pop() { if (!isEmpty()) return data[top--]; else throw new StackException(); } public boolean isEmpty() {return (top==-1); } public boolean isFull() {return (top==data.length-1);} public double peek() throws Exception() { if (!isEmpty()) {return data[top];} else throw new StackException(); } }

Algorithm: Evaluating InfixExpressions Instantiate two stacks: operator, operand Remove white space from the string expression Break string expression into tokens (delimeters = "+-/*()") WHILE more tokens exist, get nextToken SWITCH nextToken Left paren: push '(' on operator stack ): WHILE top of operator stack !='(' THEN CALL Eval() Pop the matching ( + or –: WHILE top of operator stack is '+', '-', '*', or '/' THEN CALL eval() push nextToken to operator stack * or /: WHILE top of operator() stack is '*' or '/' THEN CALL eval() push nextToken to operator stack DEFAULT: Convert to double & push nextToken to operand stack WHILE operator stack is not empty THEN CALL eval() Result is on top of operand stack Note: eval() method pop two operands and one operator, calculate, and push result to operand stack

Example Expression Algorithm push 1 to operand push '+' to operator push 2 to operand push '*' to operator push 16 to operand Call Eval: pop 16, pop 2, pop '*', 2*16->32, push 32 to operand push '/' to operator push 4 to operand Call Eval: pop 4, pop 32, pop '/,' 32/4->8, push 8 to operand Call Eval: pop 8, pop 1, pop '+,' 1+8->9, push 9 to operand Result is at top of operand stack (9) Evaluate: "1+2*16/4"

Example Expression Algorithm push 3 to operand, push '+' to operator, push '(' to operator push 5 to operand, push '+' to operator, push 6 to operand push '/' to operator, push 2 to operand Call Eval: pop 2, pop 6, pop '/', 6/2->3, push 3 to operand Call Eval: pop 3, pop 5, pop '+', 5+3->8, push 8 to operand pop '(' push '*' to operator, push 3 to operand Call Eval: pop 3 pop 8, 8*3->24, push 24 to operand push '/' to operator, push 2 to operand Call Eval: pop 2, pop 24, 24/2->12, push 12 to operand push '-' to operator, push 4 to operand Call Eval: pop 4, pop 12, 12-4->8, push 8 to operand Call Eval: pop 8, pop 3, 3+8->11, push 11to operand Result is at top of operand stack (11) Evaluate: "3+(5+6/2)*3/2-4"

Queue Concepts using Arrays A circular array –We store data in consecutive locations –When we reach the bottom, we then wrap around to the top Example –Goal: Store x at next location in an array, data –Assume: we stored the last element at offset j –Java Code: j = (j+1)%data.length; data[j] = x; data j Question: if x=3.5, where is it stored? What if j=2?

Queues with an array implementation Instance variables –int head, int tail, double data[] –We add to the tail and remove from the head –We update the tail on insertion, and update the head on removal. How do we check if the queue is full? –Answer: Check if the next tail location equals the head How do we remove an item –Answer: Extract from the head and increment the pointer. If the head and tail pointers become equal, we set both to minus one.

Using dynamic storage Class Node { Object info; Node next; public Node(Object data) { info=data; next=null; } } node1 = new Node("alpha"); node1.next = new Node("beta"); node1.next.next = new Node("gamma"); "alpha""beta""gamma" X

Doubly linked Doubly linked node class Node { String info; Node next; Node previous; } Tree nodes class Node {int info; Node[] next; }

Doubly Linked Class Node { Object info; Node next; public Node(Object data) { info=data; next = prev =null; } } Node node1 = new Node("alpha"); Node node2 = new Node("gamma"); Node node3 = "new Node("gamma"); node1.next = node2; node2.next = node3; node3.prev = node2; node2.prev = node1; "alpha""beta" "gamma" X X X