Data Structures.list Implementation

8/9/2019 Data Structures.list Implementation

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CSE 326: Data Structures

Part Two: Lists

Henry KautzAutumn Quarter 2002


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Today

Abstract versus Concrete Data Types

List ADT

Iterators

Comparing implementations

Sparse vectors

Nested lists Sparse arrays

Expressions


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Abstract vs. Concrete Data Types

Abstract Data Type (ADT) Mathematical description of an object and the set of

operations on the object List, Stack, Tree, Heap, Graph,

One ADT may specialize another ADT

One ADT may implement another ADT

Concrete Data Type Implementation of an ADT using some set ofprimitive

data types and operations of known complexity Primitives: integers, arrays, pointers or references

Object-oriented programming languages (Java, C++) letyou explicitly define new concrete data types thatcorrespond to ADTs.


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List ADT

Mathematical description: asequence of items

Ai precedes Ai+1 for 1 i < n

Operations

First() = position

Value(position) = item

Next(position) = position

Length() = integer

Insert(item,position)

Delete(position)

( A1 A2 An-1 An )length = n

What other operations

might be useful?


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List ADT

Mathematical description: asequence of items

Ai precedes Ai+1 for 1 i < n

Operations

First() = position

Value(position) = item

Next(position) = position

Length() = integer

Insert(item,position)

Delete(position)

( A1 A2 An-1 An )length = n

What other operations

might be useful?

Kth(integer)=item

SetKth(item,integer)

Find(item)=position


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Specialization Hierarchy

ListProperty: Sequence

First()=pos Value(pos)=item Kth(integer)=item

Next(pos)=pos Length()=integer SetKth(item,integer)Insert(item,pos) Delete(pos) Find(item)=position

StackProperty: LIFO

Push(item)

Pop()=item

IsEmpty()=true/false

QueueProperty: FIFO

Enqueue(item)

Dequeue()=item

IsEmpty()=true/false

VectorProperty: randomaccess

Kth(int) = item

SetKth(item,integer)


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Implementation Hierarchy

ListComplexity: Unspecified

First()=pos Value(pos)=item Kth(integer)=item

Next(pos)=pos Length()=integer SetKth(item,integer)

Insert(item,pos) Delete(pos) Find(item)=position

Linked List

(1) for:

(n) for:

Array

(1) for:

(n) for:


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Specialization and Implementation

HierarchiesList

Stack Queue Vector

Linked List

Sorted Vector


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Concrete Data Types

List

Linked List

Linked List using

References

Whats an alternative

implementation?

nodeB.value = b;

nodeC.value = c;

list = nodeB;

nodeB.next = nodeC

b c


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Concrete Data Types

List

Linked List

Linked List using

References

nodeB.value = b;

nodeC.value = c;

list = nodeB;

nodeB.next = nodeC

b c

Linked List using

Arrays

c b

0 2

list = 4;

1 2 3 4 5


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Linked Lists in C

struct node{Object element;

struct node * next; }

Everything else is a pointer to a node!

typedef stuct node * List;

typedef struct node * Position;

a b c L


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Linked Lists in Java version 1

References to objects are implicitpointers

class ListNode{

Object element;

ListNode next; }

class List{

Listnode head;

Listnode find(Object item) {

Listnode n = head;

while (n != null) {

if (n.element == item)

return n; }

return null; }


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Data Hiding

Good programming style hides internal details of an objectfrom the rest of the program

Guarantees that data structure always works as expected cannot

easily be corrupted

Here, must make details of ListNode and List public

Type returned by find

For iterating through a list:

ListNode n;

for (n = mylist.head; n!= null; n = n.next){

v = n.element;

do something on each v

}


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Iterators Introduce a new public class to explicitly represent a position in a list

public class LinkedListItr {

ListNode current;

public Object retrieve() {

return current.element; }

public void advance() {

current = current.next; }

Then:

LinkedListItr i;

for (i = mylist.first(); !i.pastEnd(); i.advance){

do something on each v.retrieve()

}


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Abstract Iterators

Iterators can also be defined for an arrayimplementation of lists:

public class ArrayListItr {

Object [] data;

integer current;

public Object retrieve() {

return data[current]; }

public void advance() {

current = current+1; }

We can create an abstractiterator that works forboth

linked list and array implements of List


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Abstract Iterator

abstract class ListItr {

abstract Object retrieve();

abstract void advance();

}

class LinkedListItr extends ListItr { }

class ArrayListItr extends ListItr { }

Why do this?


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Array Implementation of Linked Lists

How do we implement

Delete(position) ?

Insert(element, position)?

F O A R N R T

3 8 6 4 -1 10 5

Data

Next

1 7 92 3 4 5 6 8 10

First = 2


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Free Cell Management

When an item is removed from the list, mustreclaim the unused cell for later use

Can use same array to manage a second list of

unused cells

F O A R N R T

7 9 03 8 6 4 -1 10 5

Data

Next

1 7 92 3 4 5 6 8 10

First = 2 Free = 1


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Memory Management

Keeping a free cell list is an example of a memory

management strategy

How is memory managed in C?

C++?

Java?


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Summary: ComplexityLinked list Array Sorted

array

Kth(int)

Find(e)

Insert(e,pos)

Next(pos)

InsertAnywhere(e)


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To ADT or NOT to ADT?

Issue: when to bypass / expand List ADT?

Using general list (stack) operations:

List reverse(List x) {

y = new List;

while (! x.isEmpty())

y.Push( x.Pop() )return y; }

Disadvantages?


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Destructive Method

Reverse() {

ListNode x, last, tmp;

x = head;

last = null;

while (x.next != null){tmp = x.next;

x.next = last;

last = x;

x = tmp;}

head = x; }

a b c x

a b c x

Faster in practice?

Asymptotically faster?


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Slow Reverse

List reverse(List x) {

y = new List;

for (i=1; i


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Polynomial ADT

Possible linked list implementation:

Aiis the coefficient of the xi-1 term:

5 + 2x + 3x2 ( 5 2 3 )

7 + 8x ( 7 8 )

3 + x2 ( 3 0 2 )

Problem?

List ADT


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4 + 3x2001

( 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 )


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Sparse Vector Data Structure:

4 + 3x2001

4

0

3

2001

( )

class Term { int coeff, power; }

class PolyNode extends ListNode {Term data; }

class Polynomial extends List {

Polynode header;

}


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Addition of Two Polynomials?

Complexity?

1050 31200

15+10x50 +3x1200

150p

30

50

4

100

5+30x50 +4x100

5

0

q


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Addition of Two Polynomials

One pass down each list: (n+m)

1050 31200

15+10x50 +3x1200

150p

30

50

4

100

5+30x50 +4x100

5

0

q

4

100

3

1200

40

50

20

0

r


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Sparse Matrices

How could we represent this compactly?

1 8 0 3 3 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 9 9 0 0

0 0 0 0 0 00 0 0 0 0 2 7


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Sparse Matrices

How could we represent this compactly?

( (row (column data) (column data) )

(row ( (column data) (column data) ) )

( (1 (1 18) (2 33)(4 (4 99))

(5 (5 27)) )

1 8 0 3 3 0 0 0

0 0 0 0 0 0

0 0 0 0 0 0

0 0 0 9 9 0 0

0 0 0 0 0 00 0 0 0 0 2 7


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Nested Polymorphic Lists

Polymorphic elements in list may be of different

types

Trivial in Java, doable butpainful in C++ Nested elements of a list is are lists

Nested polymorphic list elements of list may be

of non-list types (e.g. int) or lists


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Universal Data Structure

NPLs can be used to implement any of the other

linked data structures well cover in the course

Trees, heaps, graphs, disjoint sets LISP programming language that uses NPLs to

representboth data and programs

LISP pioneered (in the 1950s!) many ideas that are the

basis of modern programming languages Recursion, garbage collection, interactive programming

environments

JAVA combines the best features of LISP with the best features of

C++ (strict type checking, objects and inheritance)
http://www.hypermeta.com/graphics/powered-by-lisp.gifhttp://www.hypermeta.com/graphics/powered-by-lisp.gifhttp://www.hypermeta.com/graphics/powered-by-lisp.gifhttp://www.hypermeta.com/graphics/powered-by-lisp.gif


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Programs As Lists

(progn

(setq x 10)

(setq y 1)

(while (greater-than x 1)

(progn

(setq y (times y x))(setq x (minus x 1)))))


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-Lisp

Lets see how easy it is to build our ownprogramming language interpreter

(plus (times (minus 6 2) 14) 8)

Grammar for an expression:

expression :: = integer

| ( symbol {expression}* )

symbol ::= [a-z]+

repeat 0 ormore times

repeat 1 or

more times


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Lists

For these slides: convention that head field of list

points directly to first node of list (no dummy node)

class Node {

Object element;

Node next; }

class List {

Node head;

}


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Read/Eval/Print Loop

The top level program:

While (not EOF)

Print( Eval( ReadExpression()))


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Reading Expressions

ReadExpression() {

t = GetToken();

if (t is numeric)

return new Integer(t);

if (t is ())

return ReadList();

if (t is )) return null;

else return new Symbol(t);

}

see Weiss

for

tokenizer


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ReadList

ReadList() {

e = ReadExpression();

if (e == null)

return a new empty List;

else return

Push( e, ReadList() );}

Why is the recursive call inside the Push?


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EvalList

EvalList(Node n){

if (n == null)

return a new empty list;

else return

Push( Eval(n.element),

EvalList(n.next) );}


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Apply

Apply(f, params){

if (f is plus)

return sum of params

else if (f is minus)

return difference of params

else } params is always a list

of ints it has been

fully evaluated!


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Thats It!

33 lines of pseudo-code

About 100 lines of Java

What about variables? If statements? Loops?


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Adding Variables

Keep an symbol table list of variable/value pairs

( (a 15) (b 22) (c 2) )

Add to Eval: to evaluate a variable, find it in the symbol table and

return its value if it is not the table, error.

to set a variable, check for the special form

(set symbol expression)


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Eval with VariablesEval( e ){

if (e is an Integer)

return its value;

if (e is a List)

f = e.head.element;

if (f is set){

var = e.head.next.element;

val = e.head.next.next.element;

Put (var,val) in symbol table; }else return Apply(f,

EvalList(e.head.next))

else return es value in symbol table;

}


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Coming Up

Sorting

Weiss Chapter 7

Know how the following work: Bubble Sort (selection sort)

Merge Sort

Quicksort

Documents

Data Structures.list Implementation