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16 April, 20101

Recursion

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Recursion

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By: S. Hassan Adelyar

16 April, 20102 Recursion

RecursionThere are two kinds of repetitive technique:

i

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Recursive

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l IterationIteration use loops (for, while, or do).

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ct Iteration often provide a straightforward and efficientway to implement a repetitive process.

Da Iterative solution is complex. Discovering or verifying

such solution is not simple task. In these cases recursionis an elegant alternativeis an elegant alternative.


16 April, 20103

RecursionRecursion

i i i l i

gorit

hms Recursion is an important problem solving strategy.

Simple solution to difficult problems.

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l Programming technique in which a method call itself. In each call the argument become smaller so the

b

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ct problem become simpler.Recursive method calls itself. When it calls itself, it d t l ll blD

a does so to solve a smaller problem.


16 April, 20104 Decimal To Binary

RecursionClass dectobin{static int a = 2;

gorit

hms ;

static int b =65;public static void main(String [] args){performop(b a);

ures

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l performop(b,a); }public static void performop(int n, int s) {

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ct if (n > 0 ) {performop (n/s, s);System.out.print(n % s);

Da y p ( );

}}}}


16 April, 20105 Factorial

RecursionN! = n*(n-1)*(n-2)*……3*2*1Public static int recursivefactorial(int n)

gorit

hms Public static int recursivefactorial(int n)

{if (n == 0) return 1;

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l if (n == 0) return 1;else return n*recursivefactorial(n-1);

}

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ct }

Da


16 April, 20106

Recursionclass factofN {static int a;

gorit

hms static int a;

static int b =7;public static void main(String [] args){

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a= recursivefactorial(b);System.out.println(a);

}

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ct } public static int recursivefactorial(int n) {

if (n == 0) return 1;

Da

else return n*recursivefactorial(n-1);}}}


16 April, 20107 Counting the sum of 1+2+3………..+n:

Recursionclass sumofnum {static int a;

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hms static int b =10;

public static void main(String [] args){a= sumof(b);System out println(a);

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l System.out.println(a);} public static int sumof(int n) {int sum;

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ct if (n == 1)sum = 1;else

Da sum = sumof(n-1) + n;

return sum;}}}


16 April, 20108 Write each digit vertically

Recursionclass vertnum {static int n =3652;

gorit

hms public static void main(String [] args){

writevertical(n); }

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public static void writevertical(int n) {if (n<10)System.out.println(n);

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ct else{writevertical(n/10);

Da ( )

System.out.println(n % 10);}}}}


16 April, 20109 Fibonacci Sequence

RecursionThe fibonacci sequence is: 1,1,2,3,5,8,13,21 …..Long fib( int n) {

gorit

hms g ( ) {

{If (n<2) return n;Return fib(n 1) + fib(n 2);

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l Return fib(n-1) + fib(n-2);}

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16 April, 201010

Recursionpublic class FibonacciNumber {public static void main (String [] args) {

gorit

hms public static void main (String [] args) {

int firstFibNum =3;int secondFibNum =5;

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l int secondFibNum 5;int nth =6;System.out.println("The Fibonacci number at position" + nth + "is:

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ct "+ rFibNum(firstFibNum, secondFibNum, nth));

}Da }


16 April, 201011

Recursionpublic static int rFibNum(int a, int b, int n){

if(n == 1)

gorit

hms if(n == 1)

return a;else if(n==2)

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l else if(n 2)return b;

else

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ct return rFibNum(a, b, n-1) + rFibNum(a, b, n-2);}

Da }


16 April, 201012

Recursionimport java.io.*;public class FibonacciNumber {

gorit

hms p {

static BufferedReader keyboard = newBufferedReader (new InputStreamReader (System.in));

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

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l public static void main (String [] args) throws IOException {int firstFibNum;int secondFibNum;

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ct int nth;System.out.print("Enter the first Fibonacci Number: ");firstFibNum = Integer.parseInt(keyboard.readLine());

Da g p ( y ());

System.out.println();

System out print("Enter the second Fibonacci Number: ");System.out.print("Enter the second Fibonacci Number: ");secondFibNum = Integer.parseInt(keyboard.readLine());System.out.println(); By: S. Hassan Adelyar

16 April, 201013

RecursionSystem.out.print("Enter the position of the desired" + "Fibonacci number: ");

nth = Integer.parseInt(keyboard.readLine());

gorit

hms g p ( y ());

System.out.println();System.out.println("The Fibonacci number at position" + nth + "is: "

+ rFibNum(firstFibNum secondFibNum nth));

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l + rFibNum(firstFibNum, secondFibNum, nth));}

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16 April, 201014

Recursionpublic static int rFibNum(int a, int b, int n){

if(n == 1)

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hms ( )

return a;else if(n==2)

return b;

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l return b;else

return rFibNum(a, b, n-1) + rFibNum(a, b, n-2);

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ct }}

Da


16 April, 201015 Fractals

Recursionimport java.applet.Applet;i j *

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hms import java.awt.*;

public class Fractal extends Applet {

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l private Image display;private Graphics drawingArea;

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16 April, 201016

Recursionpublic void init() {

int height = getSize().height;

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hms g g () g ;

int width = getSize().width;display = createImage(width, height);drawingArea display getGraphics();

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l drawingArea = display.getGraphics();randomFractal(0, height/2, width, height/2, drawingArea);

}

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ct public void paint(Graphics g) {g.drawImage(display, 0, 0, null);

}

Da }


16 April, 201017

Recursionpublic static void randomFractal

(

gorit

hms (

int leftX,

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l int leftY,int rightX,

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ct int rightY,Graphics drawingArea

Da

)


16 April, 201018

Recursion{

final int STOP =4;

gorit

hms int midX, midY;

int delta;if(( rightX - leftX) <= STOP)

drawingArea drawLine(leftX leftY rightX rightY);

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l drawingArea.drawLine(leftX, leftY, rightX, rightY);else {

midX = (leftX + rightX) /2;midY = (leftY + rightY) / 2;

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( g )delta = (int) (( Math.random() - 0.5) * (rightX - leftX));midY += delta;randomFractal(leftX, leftY, midX, midY, drawingArea);

Da randomFractal(midX, midY, rightX, rightY, drawingArea);

}}

}}


16 April, 201019 The Towers of Hanoi

RecursionAn ancient puzzle. There are 3 towers and there are 7 disks on tower A The disks have different diameter

gorit

hms A. The disks have different diameter.

The goal is to transfer all the disks from tower A to tower Caccording to the following rules:

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Carry only one disk at a time.Never put a big disk on the small disk.

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ct You can use tower B temporary.If the sub-tree has an odd number of disks, start by moving the topmost disk directly to the tower where you want the sub-tree to go

Da topmost disk directly to the tower where you want the sub tree to go.

Tower of HanoiBy: S. Hassan Adelyar

16 April, 201020

Recursionclass towerapp {

static int ndisks =3;

gorit

hms static int ndisks =3;

public static void main (String[] args){

dotowers(ndisks, 'A', 'B', 'C');

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}public static void dotowers(int topn, char from, char inter, char to){

if(topn == 1)

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ct if(topn == 1)System.out.println("Disk 1 from " + from + " to " + to);

else{

Da dotowers(topn-1, from, to, inter);

System.out.println("Disk " + topn + "from " + from + "to " + to);dotowers(topn-1, inter, from, to);

}}}

}By: S. Hassan Adelyar

16 April, 201021

Recursion

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16 April, 201022 Traversing a Maze

RecursionSuppose the following two facts about a maze:Somewhere is a panel which contain the secret of the universe

gorit

hms Somewhere is a panel which contain the secret of the universe.

You can keep this panel if you can enter the maze, find the panel, and return to the maze’s entrance.

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The maze is built on a rectangular grid. At each point of the grid, there are four directions to move: north, east, south, or west. Some directions may be blocked by an impenetrable wall

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ct directions may be blocked by an impenetrable wall. You accept to enter the maze but only with the help of your portablecomputer and a method that we will write to guide you into the maze

Da p g y

and back out.


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