7/25/2019 Java Lect 24

1/19

Java Lecture

Recursion29thfeb 2005

AshishFA@cse.iitb.ac.in

7/25/2019 Java Lect 24

2/19

Saturday, January16, 2016

CFILT java

Recursion

solve(problem){

If problem is simple

Return the answerElse

{

Break the problem as p1,p2,p3 pn

or ea!h problem "

solve(")#

$

$

7/25/2019 Java Lect 24

3/19

Saturday, January16, 2016

CFILT java

Properties

Cas t!e sa"e #unction $it! s"aer i%p&

'ivide and con(uer strate)y

7/25/2019 Java Lect 24

4/19

Saturday, January16, 2016

CFILT java

*+a"pe

Litte tricy

7/25/2019 Java Lect 24

5/19

Saturday, January16, 2016

CFILT java

-ppication o# recursion

?

7/25/2019 Java Lect 24

6/19

Saturday, January16, 2016

CFILT java

To$ers o# .anoi

Let/s try t!is

%anoi

Rues

Input

utputSoution #or 1, 2, , , 3 n

http://hanoi/Sample.htmlhttp://hanoi/Sample.html

7/25/2019 Java Lect 24

7/19

Saturday, January16, 2016

CFILT java

'e#ine t!e pro4e"

5rap!ica inter#ace 7

8!at is input 9

:7u"4er o# discs; 8!at is output9

:Fina state 9

7/25/2019 Java Lect 24

8/19

Saturday, January16, 2016

CFILT java

-nao)y $it! recursion

Soution #or discs

Can t!e soution #or 4e 4roen9

=roen pro4e" "ust 4e s"a& It s!oud 4e sa"e as t!e "ain pro4e"&

8!en to stop 9

Soution #orxdiscs is very si"pe& Sove itdirecty

7/25/2019 Java Lect 24

9/19

Saturday, January16, 2016

CFILT java

Steps

Pro4e" de#inition

Input representation

utput representation

-)orit!"

I"pe"entation

7/25/2019 Java Lect 24

10/19

Saturday, January16, 2016

CFILT java

'esi)n

8e no$

Recursive condition

Ter"inatin) condition

Let/s try t!e a)orit!" #or n

7/25/2019 Java Lect 24

11/19

Saturday, January16, 2016

CFILT java

Input%utput

7a"e t!e #unction solve_hanoi

Input ~ argument ~ (integer n)

Output

Assume 3 towers three names.. 3 variables t !t"! t3

t # $le%t&

t" # $mi''le& t3 # $right&

Are the t! t"! t3 also arguments

7/25/2019 Java Lect 24

12/19

Saturday, January16, 2016

CFILT java

Seeton code

Sove>!anoi?inte)er n, to$ers t1, t2, t@A

o something.

o somethingsove>!anoi?so"e s"a n, t1, t2, t@

'o so"et!in)3&

'o so"et!in)3

B

7/25/2019 Java Lect 24

13/19

Saturday, January16, 2016

CFILT java

Te"ination

Sove>!anoi?inte)er n, to$ers t1, t2, t@

AI% (n ## ) then

move the 'iscn %rom t to t3

o something

sove>!anoi?so"e s"a n@

'o so"et!in)3&'o so"et!in)3

B

7/25/2019 Java Lect 24

14/19

Saturday, January16, 2016

CFILT java

Su4divsion

Start?@ *nd?

7/25/2019 Java Lect 24

15/19

Saturday, January16, 2016

CFILT java

3Contd&

Sove>!anoi?inte)er n, to$ers t1, t2, t@

A1& Dove t!e n:1 discs #ro" t1to t2usin) t

2& 7o$ "ove ony re"ainin) disc #ro" t1 to t

& Dove t!e n:1 discs #ro" t2to tusin) t1

B

8!ic! steps are recursive 9

7/25/2019 Java Lect 24

16/19

7/25/2019 Java Lect 24

17/19

Saturday, January16, 2016

CFILT java

Co"pete java #unction

Pu4ic static void sove>!anoi?int n, Strin) t1, t2, t@

A

i# ?n 1@ t!en

Syste"&out&printn?G"ove t!e discHnH #ro" Gt1H to G t@

ese

A

sove>!anoi?n:1, t1, t, t2@

Syste"&out&printn?G"ove t!e discHnH #ro" Gt1H to G t@

sove>!anoi?n:1, t2, t1, t@B

B

7/25/2019 Java Lect 24

18/19

Saturday, January16, 2016

CFILT java

Re#erence

Pay t!e )a"e or see t!e soutions !ere !ttpK%%$$$&"ae$ors&co"%!anoi%

RecursionK!ttpK%%$$$&cs&uca&edu%Min)er%dorene%"at!&!t"

.istory o# t!e )a"e K!ttpK%%$$$&a$rence!ao#science&or)%Java%To$er%to$er!i

story&!t"

http://www.mazeworks.com/hanoi/http://www.cs.ucla.edu/~klinger/dorene/math4.htmhttp://www.lawrencehallofscience.org/Java/Tower/towerhistory.htmlhttp://www.lawrencehallofscience.org/Java/Tower/towerhistory.htmlhttp://www.lawrencehallofscience.org/Java/Tower/towerhistory.htmlhttp://www.lawrencehallofscience.org/Java/Tower/towerhistory.htmlhttp://www.cs.ucla.edu/~klinger/dorene/math4.htmhttp://www.mazeworks.com/hanoi/

7/25/2019 Java Lect 24

19/19

Saturday, January16 2016

CFILT java