This lecture. Abstract Data Types (ADTs) The Stack ADT ( 4.2) Stacks. Stack Interface in Java. Exceptions. Abstract data types Stacks Queues

Size: px

Start display at page:

Download "This lecture. Abstract Data Types (ADTs) The Stack ADT ( 4.2) Stacks. Stack Interface in Java. Exceptions. Abstract data types Stacks Queues"

Daniel Riley
5 years ago
Views:

1 This lectue Abstact data types Stacks ueues Abstact Data Types (ADTs) An abstact data type (ADT) is an abstaction o a data stuctue An ADT speciies: Data stoed Opeations on the data Eo conditions associated with opeations Example: ADT modeling a simple stock tading system The data stoed ae buy/sell odes The opeations suppoted ae ode buy(stock, shaes, pice) ode sell(stock, shaes, pice) void cancel(ode) Eo conditions: Buy/sell a nonexistent stock Cancel a nonexistent ode ADTs, Stacks, ueues 1 ADTs, Stacks, ueues 2 The Stack ADT ( 4.2) Stacks The Stack ADT stoes abitay objects Insetions and deletions ollow the last-in ist-out scheme Think o a sping-loaded plate dispense Main stack opeations: push(object): insets an element object pop(): emoves and etuns the last inseted element Auxiliay stack opeations: object top(): etuns the last inseted element without emoving it intege size(): etuns the numbe o elements stoed boolean isempty(): indicates whethe no elements ae stoed ADTs, Stacks, ueues 3 ADTs, Stacks, ueues 4 Stack Inteace in Java Exceptions Java inteace coesponding to ou Stack ADT Requies the deinition o class EmptyStackException Dieent om the built-in Java class java.util.stack public inteace Stack { public int size(); public boolean isempty(); public Object top() thows EmptyStackException; public void push(object o); public Object pop() thows EmptyStackException; Attempting the execution o an opeation o ADT may sometimes cause an eo condition, called an exception Exceptions ae said to be thown by an opeation that cannot be executed In the Stack ADT, opeations pop and top cannot be peomed i the stack is empty Attempting the execution o pop o top on an empty stack thows an EmptyStackException ADTs, Stacks, ueues 5 ADTs, Stacks, ueues 6 1

2 Applications o Stacks Diect applications Page-visited histoy in a Web bowse Undo sequence in a text edito Chain o method calls in the Java Vitual Machine Indiect applications Auxiliay data stuctue o algoithms Component o othe data stuctues ADTs, Stacks, ueues 7 Method Stack in the JVM The Java Vitual Machine (JVM) keeps tack o the chain o active methods with a stack When a method is called, the JVM pushes on the stack a ame containing Local vaiables and etun value Pogam counte, keeping tack o the statement being executed When a method ends, its ame is popped om the stack and contol is passed to the method on top o the stack Allows o ecusion main() { int i = 5; oo(i); oo(int j) { int k; k = j+1; ba(k); ba(int m) { ba PC = 1 m = 6 oo PC = 3 j = 5 k = 6 main PC = 2 i = 5 ADTs, Stacks, ueues 8 Aay-based Stack Aay-based Stack (cont.) A simple way o implementing the Stack ADT uses an aay We add elements om let to ight A vaiable keeps tack o the index o the top element Algoithm size() etun t +1 Algoithm pop() i isempty() then thow EmptyStackException t t 1 etun S[t +1] The aay stoing the stack elements may become ull A push opeation will then thow a FullStackException Limitation o the aaybased implementation Not intinsic to the Stack ADT Algoithm push(o) i t = S.length 1 then thow FullStackException t t +1 S[t] o S t ADTs, Stacks, ueues 9 S t ADTs, Stacks, ueues 10 Peomance and Limitations Aay-based Stack in Java Peomance Let n be the numbe o elements in the stack The space used is O(n) Each opeation uns in time O(1) Limitations The maximum size o the stack must be deined a pioi and cannot be changed Tying to push a new element into a ull stack causes an implementation-speciic exception public class AayStack implements Stack { // holds the stack elements pivate Object S[ ]; // index to top element pivate int top = -1; // constucto public AayStack(int capacity) { S = new Object[capacity]); public Object pop() thows EmptyStackException { i isempty() thow new EmptyStackException ( Empty stack: cannot pop ); Object temp = S[top]; // acilitates gabage collection S[top] = null; top = top 1; etun temp; ADTs, Stacks, ueues 11 ADTs, Stacks, ueues 12 2

3 Paentheses Matching Each (, {, o [ must be paied with a matching ),, o [ coect: ( )(( )){([( )]) coect: ((( )(( )){([( )]) incoect: )(( )){([( )]) incoect: ({[ ]) incoect: ( Paentheses Matching Algoithm Algoithm PaenMatch(X,n): Input: An aay X o n tokens, each o which is eithe a gouping symbol, a vaiable, an aithmetic opeato, o a numbe Output: tue i and only i all the gouping symbols in X match ADTs, Stacks, ueues 13 ADTs, Stacks, ueues 14 Paentheses Matching Algoithm Let S be an empty stack o i=0 to n-1 do i X[i] is an opening gouping symbol then S.push(X[i]) i X[i] is a closing gouping symbol then i S.isEmpty() then etun alse {nothing to match with i S.pop() does not match the type o X[i] then etun alse {wong type i S.isEmpty() then etun tue {evey symbol matched etun alse {some symbols wee neve matched ADTs, Stacks, ueues 15 ueues ADTs, Stacks, ueues 16 The ueue ADT ( 4.3) The ueue ADT stoes abitay objects Insetions and deletions ollow the ist-in ist-out scheme Insetions ae at the ea o the queue and emovals ae at the ont o the queue Main queue opeations: enqueue(object): insets an element at the end o the queue object dequeue(): emoves and etuns the element at the ont o the queue Auxiliay queue opeations: object ont(): etuns the element at the ont without emoving it intege size(): etuns the numbe o elements stoed boolean isempty(): indicates whethe no elements ae stoed Exceptions Attempting the execution o dequeue o ont on an empty queue thows an EmptyueueException ueue Example Opeation Output enqueue(5) (5) enqueue(3) (5, 3) dequeue() 5 (3) enqueue(7) (3, 7) dequeue() 3 (7) ont() 7 (7) dequeue() 7 () dequeue() eo () ADTs, Stacks, ueues 17 ADTs, Stacks, ueues 18 3

4 ueue Example Opeation Output isempty() tue () enqueue(9) (9) enqueue(7) (9, 7) size() 2 (9, 7) enqueue(3) (9, 7, 3) enqueue(5) (9, 7, 3, 5) dequeue() 9 (7, 3, 5) Applications o ueues Diect applications Waiting lists, bueaucacy Access to shaed esouces (e.g., pinte) Multipogamming Indiect applications Auxiliay data stuctue o algoithms Component o othe data stuctues ADTs, Stacks, ueues 19 ADTs, Stacks, ueues 20 Aay-based ueue Use an aay o size N in a cicula ashion Two vaiables keep tack o the ont and ea index o the ont element index immediately past the ea element Aay location is kept empty nomal coniguation wapped-aound coniguation 012 ADTs, Stacks, ueues 21 ueue Opeations We use the modulo opeato (emainde o division) Algoithm size() etun (N + ) mod N Algoithm isempty() etun ( = ) 012 ADTs, Stacks, ueues 22 ueue Opeations (cont.) Opeation enqueue thows an exception i the aay is ull This exception is implementationdependent 012 Algoithm enqueue(o) i size() = N 1 then thow FullueueException [] o ( + 1) mod N ueue Opeations (cont.) Opeation dequeue thows an exception i the queue is empty This exception is speciied in the queue ADT 012 Algoithm dequeue() i isempty() then thow EmptyueueException o [] ( + 1) mod N etun o ADTs, Stacks, ueues 23 ADTs, Stacks, ueues 24 4

5 ueue Inteace in Java Aay-based ueue in Java Java inteace coesponding to ou ueue ADT Requies the deinition o class EmptyueueException No coesponding built-in Java class public inteace ueue { public int size(); public boolean isempty(); public Object ont() thows EmptyueueException; public void enqueue(object o); public Object dequeue() thows EmptyueueException; public class Aayueue implements ueue { // holds the queue elements pivate Object [ ]; // ont, end+1, size pivate int,, s; // constucto public Aayueue(int capacity) { = new Object[capacity+1]); public void enqueue(object o) thows FullueueException { i (s ==.length - 1) thow new FullueueException ( The queue is ull ); [] = o; = ( + 1)%(.length); s++; // add othe methods yousel ADTs, Stacks, ueues 25 ADTs, Stacks, ueues 26 Application: Round Robin Schedules We can implement a ound obin schedule using a queue,, by epeatedly peoming the ollowing steps: 1. e =.dequeue() 2. Sevice element e 3..enqueue(e) 1. Deque the next element The ueue 2. Sevice the next element 3. Enqueue the seviced element Summay Stacks and ueues ae abstact data types Stack is LIFO, ueue is FIFO Useul data stuctues, oten auxiliay Can be implemented eiciently using an aay, but this implementation has disadvantages (stack o queue may get ull) We ll see othe implementations (using lists) late in the couse Shaed Sevice ADTs, Stacks, ueues 27 ADTs, Stacks, ueues 28 5

How many times is the loop executed? middle = (left+right)/2; if (value == arr[middle]) return true;

How many times is the loop executed? middle = (left+right)/2; if (value == arr[middle]) return true; This lectue Complexity o binay seach Answes to inomal execise Abstact data types Stacks ueues ADTs, Stacks, ueues 1 binayseach(int[] a, int value) { while (ight >= let) { { i (value < a[middle]) ight =