10. Sets & Maps

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ADSA: Sets&Maps/10 1

241-423 Advanced Data Structures

and Algorithms

Objectives implement sets and maps

Semester 2, 2010-2011

10. Sets and Maps

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Contents1. Set and Map Interfaces

2. The TreeSet Collection

3. A Spell Checker

4. Four Set Operators5. Ordered Set Operators

6. Maps

7. The TreeMap Collection8. Map Collection Views

9. Create a Concordance

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1. Set and Map Interfaces

The dashed lines indicate that the class implementsthe interface.

The Map interface is separate, since if defines

methods not relevant to general collections.

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The Set Interface

Set implements the Collection interface,

requiring each element to be unique.

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The Map Interface

A map stores an element as a key-value pair

the first field is a key which uniquely identifies the

pair

the second field is a value (an object)

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A map of String-Integer pairs to denote the

number of students in each of department:

Uses the key to access the value field of a pair.

e.g. deptMap.get("English") returns 117

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2. The TreeSet Collection

TreeSet is implemented by a Binary Search

Tree (BST).

Since BSTs store elements in order, it

implements the OrderedSet interface

it extends the Set interface, adding first() and

last().

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class TreeSet implements OrderedSet ds.util

Constructor

TreeSet()

Creates an empty ordered set whose elements have a specified type that

must implement the Comparable interface

Methods

T first()

Returns the minimum value of the elements in the set

T last()

Returns the maximum value of the elements in the set

String toString()

Returns a string containing a comma separated ordered list of elementsenclosed in brackets.

and others from the

Set interface

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3. A Spell Checker

A set is an ideal data structure for the

implementation of a simple spelling checker.

a dictionary setis constructed from the file

"dict.txt" which contains about 25,000 words

Each word in the input is checked against the

dictionary set. If the word is not in the set, then

the word is assumed to be misspelled.

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public static void spellChecker(String filename, Scanner keyIn)

{

// sets for the dictionary and misspelled words

TreeSet dictionary = new TreeSet();

TreeSet misspelledWords = new TreeSet();

Scanner dictFile=null, docFile=null;

try

{

// dictionary, document, input streams

dictFile = new Scanner(new FileReader("dict.txt"));docFile = new Scanner(new FileReader(filename));

}

catch(FileNotFoundException e){

System.err.println(e);

System.exit(1);

}

// insert each word from file "dict.txt" into set

while(dictFile.hasNext()) {

String word = dictFile.next();

dictionary.add(word);

}

:

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while(docFile.hasNext()) {

String word = docFile.next(); // get word from input

if (!dictionary.contains(word)) { // lookup word

System.out.println(word);

System.out.print(" 'a'(add) 'i'(ignore) " +

"'m'(misspelled) ");

String response = keyIn.next();

if (response.charAt(0) == 'a') // add to dict

dictionary.add(word);

else if (response.charAt(0) == 'm') // add to misspells

misspelledWords.add(word);

}}

System.out.println("\nMisspelled words: " +

misspelledWords);

} // end of spellChecker()

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UseSpellCheckerimport java.io.FileReader;

import java.io.FileNotFoundException;

import java.util.Scanner;

import ds.util.TreeSet;

public class UseSpellChecker{

public static void main(String[] args)

{

Scanner keyIn = new Scanner( System.in);

System.out.print("Enter file to spell check: ");

String fileName = keyIn.next();

spellChecker(fileName, keyIn);

}

// spellchecker() method goes here

} // end of UseSpellChecker class

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Files

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Execution

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4. Four Set Operators

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Implementation of Set Ops

public static Set setOp(Set setA, Set setB)

{

Set returnSet;

/* allocate concrete collection for returnSet:a TreeSet or HashSet object (see slide 3)

depending on the input argument type */

if (setA instanceof OrderedSet)

returnSet = new TreeSet();

elsereturnSet = new HashSet();

. . .

return returnSet;

}

General code, required

by all the set operators

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public static Set union(Set setA, Set setB)

{

Set setUnion;

// allocate concrete collection object for setUnion

. . .

// use iterator to add elements from setA

Iterator iterA = setA.iterator();

while (iterA.hasNext())

setUnion.add(iterA.next());

// use iterator to add non-duplicate elems from setB

Iterator iterB = setB.iterator();

while (iterB.hasNext())setUnion.add(iterB.next());

return setUnion;

} // end of union()

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public static Set intersection(Set setA, Set setB)

{

Set setIntersection;

T item;

// allocate concrete collection object for setIntersection

. . .

/* scan elements in setA and check whetherthey are also elements in setB */


while (iterA.hasNext()) {

item = iterA.next();

if (setB.contains(item)) // is item in both sets?

setIntersection.add(item);}

return setIntersection;

} // end of intersection()

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public static Set difference(Set setA, Set setB)

{

Set setDifference;

T item;

// allocate concrete collection object for setDifference

. . .

/* scan elements in setA and check whether

they are not in setB */


while (iterA.hasNext()) {

item = iterA.next();

if (!setB.contains(item)) // is A item not in B?setDifference.add(item);

}

return setDifference;

} // end of difference()

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public static boolean subset(Set setA, Set setB)

// is setA a subset of setB?

{

return ( intersection(setA, setB).size() == setA.size() );

// is all of setA in the intersection with setB?

}

setBsetA

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4.1. UsingSets

import java.io.*;import java.util.Scanner;

import ds.util.Sets;


import ds.util.Set;

public class UsingSets

{


{

// declare ordered sets for current and new accountsSet oldAcct = new TreeSet();

Set currAcct = new TreeSet();

:

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// input names from file into the set

try{

readAccounts("oldAcct.txt", oldAcct);

readAccounts("currAcct.txt", currAcct);

}

catch(IOException e)

{ System.err.println("Cannot open account files");System.exit(1);

}

// use set union to determine all accounts to update

Set processAcct = Sets.union(currAcct, oldAcct);

:

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// determine carryover accounts using intersectionSet carryOverAcct =

Sets.intersection(currAcct, oldAcct);

// find new and obsolete accounts using difference

Set newAcct = Sets.difference(currAcct, oldAcct);

Set obsoleteAcct = Sets.difference(oldAcct, currAcct);

// list elements in sets

System.out.println("Old Accounts: " + oldAcct);

System.out.println("Current Accounts: " + currAcct);

System.out.println("Process Accounts: " +processAcct);

System.out.println("New Accounts: " + newAcct);System.out.println("Carryover Accounts: " +carryOverAcct);

System.out.println("Obsolete Accounts: " +obsoleteAcct);

} // end of main()

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public static void readAccounts(String filename,Set t) throws IOException

{

Scanner sc = new Scanner(new FileReader(filename));

// input the set of current accounts

while(sc.hasNext())t.add( sc.next() ); // add an account name

} // end of readAccounts()

} // end of UseSets class

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Execution

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5. Ordered Set Operators

If a set is ordered, the set operators can be

implemented by using an iterator that scans the

set faster.

TreeSet uses ordered sets because it

implements the OrderedSet interface

see slide 3

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Ordered Set Intersection

Ordered set intersection uses iterators to make

apairwise scan of the elements in the two sets.

at each step, a comparison is made between twoelements in the two sets

if a match is found, then the element is copied to

the intersection set

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advance()

private static T advance(Iterator iter)

/* if more elements remain, return the

next value; otherwise return null */

{

T value = null;

if (iter.hasNext())

value = iter.next();

return value;

}

A support method for

orderedIntersection()

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orderedIntersection()

public static

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// move forward as long as we have not

// reached the end of either set

while (lhsValue != null && rhsValue != null) {

if (lhsValue.compareTo(rhsValue) < 0)

lhsValue = advance(lhsIter); // next value in lhs

else if (rhsValue.compareTo(lhsValue) < 0)

rhsValue = advance(rhsIter); // next value in rhs

else { // lhsValue == rhsValue

setIntersection.add(lhsValue); // add to inter

lhsValue = advance(lhsIter); // next lhs

rhsValue = advance(rhsIter); // next rhs

}

}

return setIntersection;

} // end oforderedIntersection()

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Complexity of orderdIntersection()

Assume that nlhs and nrhs are the number of

elements in setA and setB.

Each iteration of the loop makes one or two

comparisons

assume these occur in O(1) running time

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We must make at most nlhs + nrhs

comparisons, so the algorithm has

worst-case running time O(nlhs + nrhs).

So the algorithm is linearwith respect to

the total number of elements in the two sets.

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6. Maps

A map stores data in key-value pairs. A key acts like an index to locate the

corresponding value in the map

a map is also called an associative array

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interface MAP (partial) ds.utilvoid clear()

Removes all mappings from this map.

boole

an

containsKey(Object key)

Returns true if this map contains a mapping for the specified key.

boole

an

isEmpty()

Returns true if this map contains no key-value mappings.V remove(Object key)

Removes the mapping for this key from this map if present. Returns the previous

value associated with specified key, or null if there was no mapping for key.

int size()

Returns the number of key-value mappings in this map.

Access/Update MethodsK get(Object key)

Returns the value to which this map maps the specified key or null if the map

contains no mapping for this key.

Vput(K key, V value)

Associates the specified value with the specified key in this map. Returns the

previous value associated with key, or null if there was no mapping for key.

The Map Interface

V

K

K

K

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size(), isEmpty(), and clear() are like those in

the Collection interface.

A map does not have an iterator to scan its

elements

instead, keySet() and entrySet() return the keys and

the entries in a map as a set (see later)

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7. The TreeMap Collection

TreeMap is an ordered collection that

accesses elements in ascending order of its

keys.

The class implements the OrderedMap

interface (see slide 3) firstKey() and lastKey() return the values

corresponding to the minimum and maximum

keys

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Brief TreeMap Example

// arrays for class names and their enrollment (student nos)

String[] className = {"ECON 101","CS 173","ENGL 25"};

int[] enrollment = {85, 14, 30};

// create a TreeMap object

TreeMap tm = new TreeMap();for(int i = 0; i < 3; i++)

tm.put(className[i], enrollment[i]);

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7.1. Student Working Hours Map


import java.io.FileReader;


import ds.util.TreeMap;

import ds.time.Time24;

public class CalcHours

{


{

TreeMap workMap =new TreeMap();

:

the key-value pair is

student name and

hours worked

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/* access the student info file:

each line consists of a student name and

their work time in hours and mins

*/

Scanner fin = null;try { // load student info

fin = new Scanner(new FileReader("studwk.txt"));

}

catch (FileNotFoundException e) {

System.err.println("Cannot open "\"studwk.dat\"");

System.exit(1);}

:

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// input names and times

while (fin.hasNext()) {

String studName = fin.next();

// get hours and minutes from the input line

int hours = fin.nextInt();

int mins = fin.nextInt();

Time24 workTime = new Time24(hours,mins);

// access entry for the student name

Time24 timeValue = workMap.get(studName);

:

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if (timeValue == null) // add new entryworkMap.put(studName, workTime);

else { // update existing entry

timeValue.addTime(hours*60 + mins);

workMap.put(studName, timeValue);

}

}

// display the work Map

System.out.println("Student-Time: " + workMap);

} // end of main()

} // end of CalcHours class

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Execution

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7.2. A Software Map

import java.io.FileReader;



import ds.util.TreeMap;


public class MakeSoftMap

{


{TreeMap softwareMap =

new TreeMap();

:


company name and

a set of software names

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/* access the product info file:

each line consists of a company name and

software product name, separated by a tab

*/

Scanner fin = null;

try { // load product info

fin = new Scanner(new FileReader("product.txt"));

fin.useDelimiter("[\t\n\r]+");

}

catch (FileNotFoundException e){

System.err.println("Cannot open "\"product.txt\"");

System.exit(1);

}

:

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while(fin.hasNext()){

String company = fin.next();

String product = fin.next();

// look for software set for the company

TreeSet prodSet = softwareMap.get(company);

// if no entry found, then create empty software set

if (prodSet == null)prodSet = new TreeSet();

prodSet.add(product); // add product name to set

softwareMap.put(company, prodSet); // add entry

}

// display contents of software Map

System.out.println(softwareMap);

} // end of main()

} // end of MakeSoftMap class

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Execution

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8. Map Collection Views

A map does not have an iteratorfor accessing

its elements.

Instead we can use two collection views, which

are sets that act on the original map

the keySet collection view

the entrySet collection view

The original map is sometimes called the

backing collection.

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In Map, keySet() returns a set of map keys.

This set is a collection view for the map.

Set keys = peopleMap.keySet();

8.1. The keySet Collection View

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Deletion

Deleting a key from the set removes the

corresponding entry from the map.

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The Set interface defines an add() operation,

but this makes no sense for a keySet view:

add() would have to add a key-value pair to thebacking collection, but what value should be

added?

Instead add() throws an

UnsupportedOperationException in a keySetview

Insertion

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8.2. The entrySet Collection View

In Map, entrySet() returns a view called an

entry set, is a set of key-value entries.

The entries implement the Map.Entry interface

an interface inside the Map interface

Set< Map.Entry > entriesSet =peopleMap.entrySet();

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entriesSet is a set of Map.Entry objects from

the peopleMap.

Operations on the set affect the map.

interface MAP.ENTRY ds.util.Map

K getKey()

Returns the key corresponding to this entry..

V getValue()

Returns the value corresponding to this entry..

V setValue(V value)

Replaces the value corresponding to this entry with the specified value. Returns

the old value corresponding to the entry

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confTimeMap holds conference activities andtheir times.

TreeMap confTimeMap =

new TreeMap();

confTimeMap.put("Session 1", new Time24(9,30));

confTimeMap.put("Session 2", new Time24(14,00));

confTimeMap.put("Lunch", new Time24(12,0));

confTimeMap.put("Dinner", new Time24(17,30));

Entry Set View Example

confTimeMap

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// create an entry set for confTimeMap

Set< Map.Entry > entries =

confTimeMap.entrySet();

entries set

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8.3. Scanning a Map's Entries

A Map.Entry set can be used to define an

iteratorfor scanning the map entries.

The iterator can access an entry's key and

access/update an entry's value.

The iterator remove() method removes anentry from the map

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Entry Set Iterators

An entry set iterator provides a way to scan the

entries in a map.

The iterator references a Map.Entry element in

the map

the programmer can use Map.Entry methods to

access the map components

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// create an entry set for confTimeMap

Set< Map.Entry > entries =

confTimeMap.entrySet();

// create an iterator for the entry set

Iterator< Map.Entry > iter =entries.iterator();

Examples

entries set

iter

iterator

continued

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map entriesset

entriesiterator

changes will affect

original map

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Delay all activities by 30 minutes.

// scan map entries

while (iter.hasNext()) {

Map.Entry me = iter.next();// get next Map.Entry object

Time24 t = me.getValue();

t.addTime(30); // add 30 mins

me.setValue(t); // update map entry

}

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for (Map.Entry i : entries) {

String activity = (String)i.getKey();

if (activity.indexOf("Session") != -1) //is activity a session?

System.out.println("Activity " + activity +" Starting time " + i.getValue());

}

Activity Session 1 Starting time 10:00

Activity Session 2 Starting time 14:30

List session starting time.

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9. Create a Concordance

A concordance is a list of all the unique

words from a file along with the line

numbers where the words appear.

We implement the concordance as a

TreeMap.

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Input File

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import java.io.*;

import java.util.regex.*;

import java.util.StringTokenizer;

import java.util.Scanner;import ds.util.*;

public class CreateConcordance

{

private static Pattern identifierPattern =

Pattern.compile("[a-zA-Z][a-zA-Z0-9]*");

public static void main(String[] args) throws IOException

{

System.out.print("Enter the file name: ");

Scanner keyIn = new Scanner(System.in);

String filename = keyIn.nextLine();

System.out.println();

concordance(filename); // create concordance

} // end of main()

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public static void concordance(String filename)

throws IOException

{

// create the concordance treemap

TreeMap concordanceMap =

new TreeMap();

// create scanner to input from document file

Scanner fin = new Scanner(new FileReader(filename));:


identifier name and

a set of line numbers

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// read the file a line at a timeint lineNumber = 0;

while(fin.hasNext()) {

String inputLine = fin.nextLine(); // read a line

lineNumber++;

// create matcher to find identifiers in line

Matcher matcher = identifierPattern.matcher(inputLine);

// extract identifiers until end of line

while (matcher.find()) {

String ident = inputLine.substring(

matcher.start(), matcher.end());

:

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// find line number set for the identifier

TreeSet lineNums =

concordanceMap.get(ident);

if (lineNums == null) // no set; make one

lineNums = new TreeSet();

// add line number to set

lineNums.add(lineNumber);concordanceMap.put(ident, lineNums);

}

}

// output the concordance

writeConcordance(concordanceMap);

} // end of concordance()

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public static void writeConcordance(

TreeMap map){

// create entry view for the map

Set entries =

map.entrySet();

// create iterator over the entry view

Iterator iter =entries.iterator();

while (iter.hasNext()) {

Map.Entry e = iter.next();

System.out.print( e.getKey() ); // output key

// pad output to 12 characters using blanks

if (e.getKey().length() < 12)

for (int i=0;i < 12 - (e.getKey().length()); i++)

System.out.print(' ');

:

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// extract map value as a TreeSetTreeSet lineNumberSet = e.getValue();

// display identifier and line numbers

System.out.print(formatInt(4, lineNumberSet.size()) +

": ");

// iterate over TreeSet of line numbers

Iterator setIter = lineNumberSet.iterator();

while (setIter.hasNext())

System.out.print( setIter.next() + " ");

System.out.println();

}System.out.println();

}

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private static String formatInt(int w, int n)

/* returns a formatted string with integer n

right-justified in a field of w spaces;

used to line up output in concordance

*/{ . . . }

} // end of CreateConcordance class

Documents

10. Sets & Maps