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Fundamental Data Types: String, Math, Casting 1

Struktur Data & Algoritme(Data Structures & Algorithms)

Fa k u l t a s I l m u K o m p u t e r

Un i v e r s i t a s I n d o n e s i a

S em e s t e r Ge na p - 2 0 0 0 / 2 0 0 1V e r s i o n 1 .0 - I n t e r n a l U s e O n l y

Denny

[email protected]

Stacks & Queues

SDA/STACK-QUEUE/D N/V1.0/2

Reviewn Abstract data type (ADT)

n Kumpulan obyek dan metoda operasi yang

mempresentasikan sifat-sifat abstraks bagi "user"

dengan menyembunyikan bagaimana semua itu

direpresentasikan dalam representasi data level yang

lebih rendah

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Objectives

n Memahami cara kerja dan kegunaan Stack & Queuen Dapat mengimplementasi stack dan queue


Outlinen ADT Stacks

n Basic operations

n Examples of use

n Implementations

Array-based and linked list-based

n ADT Queues

n Basic operations

n Examples of use

n Implementations

Array-based and linked list-based

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Struktur data linear

n kumpulan komponen-komponen yang tersusunmembentuk satu garis linear

n Stack: struktur data linear dimana penambahan ataupengurangan komponen dilakukan di satu ujung saja.

n Queue: struktur data linear dimana penambahankomponen dilakukan di satu ujung, sementarapengurangan dilakukan di ujung lain (yang satu lagi).

n Kedua struktur tersebut merupakan struktur data

abstraks dimana implementasi pada tingkat lebihrendah dapat menggunakan struktur sikuensial (array)

atau struktur berkait (linear linked-list).


Stack

n All access is restricted to the most recently insertedelements

n Basic operations arepush,pop, top.

n Constant time basic operations

Stack

push pop, top

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Non-Computer Examples

n Stack of papersn Stack of bills

n Stack of plates

n Expect O( 1 ) time per stack operation. (In otherwords, constant time per operation, no matter howmany items are actually in the stack).


Application

n Stack can be used to check a program for balancedsymbols (such as {}, (), []).

n Example: {()} is legal, {(}) is not (so simplycounting symbols does not work).

n When a closing symbol is seen, it matches the mostrecently seen unclosed opening symbol. Therefore, astack will be appropriate.

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Balanced Symbol Algorithm

n Make an empty stack.n Repeatedly read tokens; if the token is

n an opening symbol, push it onto the stack

n a closing symbol

and the stack is empty, then report an error;

otherwise pop the stack and verify that the poppedsymbol is a match (if not report an error)

n At the end of the file, if the stack is not empty, reportan error.


Example

n Input: {()}

n Push {

n Push (; stack has {(

n Pop; popped item is ( which matches ). Stack nowhas {.

n Pop; popped item is { which matches }.

n End of file; stack is empty, so all is good.

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Performance

n Running time is O( N), where Nis amount of data(that is, number of tokens).

n it processes the input sequentially, never needing tobacktrack.


Call Stack

n Matching symbols is similar to methodcall andmethod return, because when a method returns, itreturns to the most recently active method.

n Call stack can be used to keep track of this.

n Abstract idea: when method call is made, savecurrent state on a stack. On return, restore the stateby popping the stack.

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Activation Records

n Actual implementation is slightly different (note thattext describes the abstract implementation).

n The top of stack can store the current methodenvironment.

n When method is called, the new enviromment ispushed onto stack.

n On return, old enviroment is restored by pop


Other Applications

n Recursion removal can be done with stacks

n Operator precedence parsing (future lecture)

n Reversing things is easily done with stacks

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Array Implementations

n Stack can be implemented with an array and aninteger top that stores the array index of the top ofthe stack.

n Empty stack has top equal to -1.

n To push, increment the top counter, and write in thearray position.

n To pop, decrement the top counter.


Stages

top(-1)

A top(0) A

B top(1)

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Array Doubling

n If stack is full (because array size has been reached),we can extend the array, using array doubling.

n We allocate a new, double-sized array and copycontents over:

Object [] oldArray = array;

array = new Object [oldArray.length * 2 ];

for (int j = 0; j < oldArray.length; j++)

array[j] = oldArray[j];

n Amortization technique


Running Time

n Without array doubling, all operations are constanttime, and do not depend on number of items in thestack.

n With array, doubling, a push could occasionally beO(N). However, it is essentially O(1) because eacharray doubling that costs Nassignments is precededby N/2 non-doubling pushes.

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Linked-List Implementation

n first item in the list = top of stackn push:

n create a new node

n attach it as the new first element

n pop:

n advance tos to the second item in the list

d c b a

topOfStack


Queues

n All access is restricted to the least recently insertedelements

n Basic operations are enqueue, dequeue, getFront.

n Constant time basic operations

Queueenqueuedequeue

getFront

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Examples

n Line for 21 ticketsn Line printer queue

n Queue is a British word for line.

n Expect O(1) time per queue operation because it issimilar to stack.


Applications

n Queues are useful for storing pending work.

n We will see several examples later in the course:

n Shortest paths problem (minimize the number ofconnecting flights between two arbitrary airports)

n Topological ordering: given a sequence ofevents, andpairs (a,b) indicating that event aMUST occur prior tob, provide a schedule.

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Queues: Simple Idea

n Store items in an array with front item at index zeroand back item at index Back.

n Enqueue is easy: increment Back.

n Dequeue is inefficient: all elements have to beshifted.

n Result: Dequeue will be O( N).


Better Idea

n Keep a Front index.

n To Dequeue, increment Front.

a b c d

Front Back

a b c d

Front Back

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Circular Implementation

n Previous implementation is O(1) per operation.n However, afterArray.length enqueues, we are full,

even if queue is logically nearly empty.

n Solution: use wraparound to reuse the cells at thestart of the array. To increment, add one, but if thatgoes past end, reset to zero.


Circular Example

n Both Front and Back wraparound as needed.

b c d

Front Back

b c d

FrontBack

e f

e fg

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Java Implementation

n Mostly straightforward; maintainn Front

n Rear

n Current number of items in queue

n Only tricky part is array doubling because contiguityof wraparound must be maintained.


Linked-List Application

n front back

n enqueue:

n create a new node

n if empty, front = back

n else attach it as the new back

n dequeue:

n get node at the front

a b c d

front back

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Summary

n Both the array and linked-list versions run in O(1)n Linked-list has overhead one reference each node

n Especially for Queues, array-based implementation isharder to code

n Doubling space in array implementation need at leastthree times as much as the number of data items.


Further Readingn Chapter 6, 15

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Whats Next

n Application of stack & queue, orn Tree

11 12 stacks queue

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