Abstract Data Types (ADTs) Stacks. The Stack ADT ( 4.2) Stack Interface in Java

Transcription

1 Abstract Data Types (ADTs) tacks A abstract data type (ADT) is a abstractio of a data structure A ADT specifies: Data stored Operatios o the data Error coditios associated with operatios Example: ADT modelig a simple stock tradig system The data stored are buy/sell orders The operatios supported are order buy(stock, shares, price) order sell(stock, shares, price) void cacel(order) Error coditios: Buy/sell a oexistet stock Cacel a oexistet order tacks The tack ADT (.) tack Iterface i Java The tack ADT stores arbitrary objects Isertios ad deletios follow the last- i first- out scheme Thik of a sprig- loaded plate dispeser Mai stack operatios: push(object): iserts a elemet object pop(): removes ad returs the last iserted elemet Auxiliary stack operatios: object top(): returs the last iserted elemet without removig it iteger size(): returs the umber of elemets stored boolea isempty(): idicates whether o elemets are stored Java iterface correspodig to our tack ADT Requires the defiitio of class EmptytackExceptio Differet from the built-i Java class java.util.tack public iterface tack { public it size(); public boolea isempty(); public Object top() throws EmptytackExceptio; public void push(object o); public Object pop() throws EmptytackExceptio; tacks tacks

2 Exceptios Attemptig the executio of a operatio of ADT may sometimes cause a error coditio, called a exceptio Exceptios are said to be throw by a operatio that caot be executed I the tack ADT, operatios pop ad top caot be performed if the stack is empty Attemptig the executio of pop or top o a empty stack throws a EmptytackExceptio Applicatios of tacks Direct applicatios Page-visited history i a Web browser Udo sequece i a text editor Chai of method calls i the Java Virtual Machie Idirect applicatios Auxiliary data structure for algorithms Compoet of other data structures tacks tacks Method tack i the JVM The Java Virtual Machie (JVM) keeps track of the chai of active methods with a stack Whe a method is called, the JVM pushes o the stack a frame cotaiig Local variables ad retur value Program couter, keepig track of the statemet beig executed Whe a method eds, its frame is popped from the stack ad cotrol is passed to the method o top of the stack Allows for recursio mai() { it i = ; foo(i); foo(it j) { it k; k = j+; bar(k); bar(it m) { bar PC = m = foo PC = j = k = mai PC = i = tacks 7 Array-based tack A simple way of implemetig the tack ADT uses a array We add elemets from left to right A variable keeps track of the idex of the top elemet Algorithm size() retur t + Algorithm pop() if isempty() the throw EmptytackExceptio t t retur [t +] 0 t tacks 8

3 Array-based tack (cot.) The array storig the stack elemets may become full A push operatio will the throw a FulltackExceptio Limitatio of the arraybased implemetatio Not itrisic to the tack ADT Algorithm push(o) if t =.legth the throw FulltackExceptio t t + [t] o 0 t Performace ad Limitatios Performace Let be the umber of elemets i the stack The space used is O() Each operatio rus i time O() Limitatios The maximum size of the stack must be defied a priori ad caot be chaged Tryig to push a ew elemet ito a full stack causes a implemetatio- specific exceptio tacks 9 tacks 0 Array-based tack i Java Paretheses Matchig public class Arraytack implemets tack { // holds the stack elemets private Object [ ]; // idex to top elemet private it top = -; // costructor public Arraytack(it capacity) { = ew Object[capacity]); public Object pop() throws EmptytackExceptio { if isempty() throw ew EmptytackExceptio ( Empty stack: caot pop ); Object temp = [top]; // facilitates garbage collectio [top] = ull; top = top ; retur temp; Each (, {, or [ must be paired with a matchig ),, or [ correct: ( )(( )){([( )]) correct: ((( )(( )){([( )]) icorrect: )(( )){([( )]) icorrect: ({[ ]) icorrect: ( tacks tacks

4 Paretheses Matchig Algorithm Algorithm PareMatch(X,): Iput: A array X of tokes, each of which is either a groupig symbol, a variable, a arithmetic operator, or a umber Output: true if ad oly if all the groupig symbols i X match Let be a empty stack for i=0 to - do if X[i] is a opeig groupig symbol the.push(x[i]) if X[i] is a closig groupig symbol the if.isempty() the retur false {othig to match with if.pop() does ot match the type of X[i] the retur false {wrog type if.isempty() the retur true {every symbol matched retur false {some symbols were ever matched HTML Tag Matchig For fully-correct HTML, each <ame> should pair with a matchig </ame> <body> <ceter> <h> The Little Boat </h> </ceter> <p> The storm tossed the little boat like a cheap seaker i a old washig machie. The three druke fisherme were used to such treatmet, of course, but ot the tree salesma, who eve as a stowaway ow felt that he had overpaid for the voyage. </p> <ol> <li> Will the salesma die? </li> <li> What color is the boat? </li> <li> Ad what about Naomi? </li> </ol> </body> The Little Boat The storm tossed the little boat like a cheap seaker i a old washig machie. The three druke fisherme were used to such treatmet, of course, but ot the tree salesma, who eve as a stowaway ow felt that he had overpaid for the voyage.. Will the salesma die?. What color is the boat?. Ad what about Naomi? tacks tacks Tag Matchig Algorithm Is similar to paretheses matchig: import java.util.trigtokeizer; import datastructures.tack; import datastructures.nodetack; import java.io.*; /** impli.ed test of matchig tags i a HTML documet. */ public class HTML { /** Nested class to store simple HTML tags */ public static class Tag { trig ame; // The ame of this tag boolea opeig; // Is true i. this is a opeig tag public Tag() { // Default costructor ame = ""; opeig = false; public Tag(trig m, boolea op) { // Preferred costructor ame = m; opeig = op; /** Is this a opeig tag? */ public boolea isopeig() { retur opeig; /** Retur the ame of this tag */ public trig getname() {retur ame; /** Test if every opeig tag has a matchig closig tag. */ public boolea ishtmlmatched(tag[ ] tag) { tack = ew Nodetack(); // tack for matchig tags for (it i=0; (i<tag.legth) && (tag[i]!= ull); i++) { if (tag[i].isopeig()).push(tag[i].getname()); // opeig tag; push its ame o the stack { if (.isempty()) // othig to match retur false; if (!((trig).pop()).equals(tag[i].getname())) // wrog match retur false; if (.isempty()) retur true; // we matched everythig retur false; // we have some tags that ever were matched tacks Tag Matchig Algorithm, cot. public fial static it CAPACITY = 000; // Tag array size upper boud /* Parse a HTML documet ito a array of html tags */ public Tag[ ] parsehtml(bufferedreader r) throws IOExceptio { trig lie; // a lie of text boolea itag = false ; // true iff we are i a tag Tag[ ] tag = ew Tag[CAPACITY]; // our tag array (iitially all ull) it cout = 0 ; // tag couter while ((lie = r.readlie())!= ull) { // Create a strig tokeizer for HTML tags (use < ad > as delimiters) trigtokeizer st = ew trigtokeizer(lie,"<> \t",true); while (st.hasmoretokes()) { trig toke = (trig) st.exttoke(); if (toke.equals("<")) // opeig a ew HTML tag itag = true; if (toke.equals(">")) // edig a HTML tag itag = false; if (itag) { // we have a opeig or closig HTML tag if ( (toke.legth() == 0) (toke.charat(0)!= / ) ) tag[cout++] = ew Tag(toke, true); // opeig tag // edig tag tag[cout++] = ew Tag(toke.substrig(), false); // skip the // Note: we igore aythig ot i a HTML tag retur tag; // our array of tags /** Tester method */ public static void mai(trig[ ] args) throws IOExceptio { BufferedReader stdr; // tadard Iput Reader stdr = ew BufferedReader(ew IputtreamReader(ystem.i)); HTML tagchecker = ew HTML(); if (tagchecker.ishtmlmatched(tagchecker.parsehtml(stdr))) ystem.out.pritl("the iput file is a matched HTML documet."); ystem.out.pritl("the iput file is ot a matched HTML documet."); tacks

5 Computig pas (ot i book) We show how to use a stack as a auxiliary data structure i a algorithm Give a a array X, the spa [i] of X[i] is the maximum umber of cosecutive elemets X[j] immediately precedig X[i] ad such that X[j] X[i] pas have applicatios to fiacial aalysis E.g., stock at -week high 7 0 X 0 Quadratic Algorithm Algorithm spas(x, ) Iput array X of itegers Output array of spas of X # ew array of itegers for i 0 to do s while s i X[i s] X[i] ( ) s s ( ) [i] s retur Algorithm spas rus i O( ) time tacks 7 tacks 8 Computig pas with a tack Liear Algorithm We keep i a stack the idices of the elemets visible whe lookig back We sca the array from left to right Let i be the curret idex We pop idices from the stack util we fid idex j such that X[i] < X[j] We set [i] i j We push x oto the stack Each idex of the array Is pushed ito the stack exactly oe Is popped from the stack at most oce The statemets i the while- loop are executed at most times Algorithm spas rus i O() time Algorithm spas(x, ) # ew array of itegers A ew empty stack for i 0 to do while ( A.isEmpty() X[top()] X[i] ) do j A.pop() if A.isEmpty() the [i] i + [i] i j A.push(i) retur tacks 9 tacks 0