Á¶ÇÕ·Ð ÇÁ·ÎÁ§Æ®

"Java ¿Í Mathematica ¸¦ ÀÌ¿ëÇÑ Á¶ÇÕ·Ð ¾Ë°í¸®ÁòÀÇ ±¸Çö"

¼º±Õ°ü´ëÇб³ ¼öÇаú 4Çгâ 1992312068¹ø À¯º´Çõ


ÇÑ Çб⵿¾È Á¶ÇÕ·ÐÀ» ¹è¿ì¸é¼­ ´À³¤ °á·ÐÀº, Á¶ÇÕ·ÐÀº Çö½Ç¼¼°è¸¦ ¼öÇÐÀûÀ¸·Î ¸ðµ¨¸µÇϱ⿡ ÁÁÀº Çй®À̶ó´Â °ÍÀ̾ú½À´Ï´Ù. ÇÏÁö¸¸, Çö½Ç¼¼°èÀÇ º¹À⼺À¸·Î ÀÎÇÏ¿© ±×°ÍÀ» ¼º°øÀûÀ¸·Î ¸ðµ¨¸µÇÏ¿´´Ù°í ÇÏ´õ¶óµµ ¸ðµ¨¸µÇÑ ½ÄÀ» ¼ÕÀ¸·Î °è»êÇÑ´Ù´Â °ÍÀº °ÅÀÇ ºÒ°¡´ÉÇÑ ÀÏÀÓÀ» ¾Ë°Ô µÇ¾ú½À´Ï´Ù.

±âÁ¸ÀÇ ¼öÇÐ ÇÁ·Î±×·¡¹ÖÀº C ³ª PASCAL, ±×¸®°í FORTRAN µîÀ» ÀÌ¿ëÇÑ °ÍÀ̾úÀ¸³ª, ÀÌ°ÍÀº ÇÁ·Î±×·¡¹Ö¿¡ ¼Ò¿äµÇ´Â ½Ã°£ÀÌ ±æ°í, ¸ðµ¨¸µµÈ ³»¿ëÀ» È­¸é¿¡ ½Ã°¢ÀûÀ¸·Î ³ªÅ¸³»±â¿¡´Â ºÒÆíÇÑ Á¡ÀÌ ¸¹¾Ò½À´Ï´Ù. ¶ÇÇÑ ÇöÀç´Â ÀÎÅͳÝÀÇ World Wide Web(ÀÌÇÏ À¥) ȯ°æÀ» ÀÌ¿ëÇÑ Á¤º¸ÀÇ °øÀ¯°¡ ÁÖ°¡ µÇ´Âµ¥, ±âÁ¸ÀÇ ÇÁ·Î±×·¡¹Ö ¾ð¾î´Â °á°ú¸¦ °øÀ¯Çϱ⿡ ºÒÆíÇÑ Á¡ÀÌ ¸¹¾Ò½À´Ï´Ù.

±×·± ÀÌÀ¯·Î ¼öÇÐÀûÀÎ ¸ðµ¨¸µÀ» ÄÄÇ»Å͸¦ ÀÌ¿ëÇØ ºü¸£°Ô ½Ã°¢È­ÇÏ°í °á°ú°ªÀ» ±¸Çس¾ ¼ö ÀÖ´Â ¸Þ½îµå¸¦ ã´ø Áß, ¼­·Î ¼º°ÝÀÌ ´Ù¸¥ µµ±¸Áö¸¸, Java ¿Í Mathematica °¡ ±×°Í¿¡ ÀûÇÕÇÏ´Ù´Â °á·Ð¿¡ À̸£°Ô µÇ¾ú½À´Ï´Ù. ±×·¡¼­ ÀúÀÇ ÇÁ·ÎÁ§Æ®¿¡¼­´Â Java ¿Í Mathematica ¶ó´Â µµ±¸¸¦ ¼Ò°³ÇÏ°í, ±×°ÍÀ» °¡Áö°í Á¶ÇÕ·ÐÀÇ ¹®Á¦µéÀ» ½ÇÁ¦ÀûÀ¸·Î ±¸Çö / Ç®¾î³»´Â °úÁ¤À» ¹ßÇ¥Çϱâ·Î ÇÏ¿´½À´Ï´Ù. ÀÌ ÇÁ·ÎÁ§Æ®´Â ÇâÈÄ ¼öÇÐ ÇÁ·Î±×·¡¹ÖÀ» ÇÏ·Á´Â »ç¶÷µéÀ» À§ÇÑ °¡À̵尡 µÉ ¼ö ÀÖÀ¸¸®¶ó »ý°¢ÇÕ´Ï´Ù.

ÀúÀÇ ÇÁ·ÎÁ§Æ®´Â ´ÙÀ½°ú °°Àº ±¸Á¶·Î ÀÌ·ç¾îÁ®ÀÖ½À´Ï´Ù.

  1. Java & Mathematica ¿¡ ´ëÇÑ ¼Ò°³
  2. Java Applet À» ÀÌ¿ëÇÑ ±¸Çö
  3. Mathematica À» ÀÌ¿ëÇÑ ±¸Çö
  4. È°¿ë ¿¹

1. Java & Mathematica ¿¡ ´ëÇÑ ¼Ò°³.

1.1 Java

Java ´Â Sun Microsystems¿¡¼­ °³¹ß, ÇöÀç ¹«·á·Î ¹èÆ÷ÇÏ°í ÀÖ´Â ÇÁ·Î±×·¡¹Ö ¾ð¾î·Î½á 1999³â 11¿ù ÇöÀç ¹öÁ¯ 1.2 ±îÁö ¹èÆ÷µÇ¾î ÀÖ´Â »óÅÂÀÔ´Ï´Ù. Sun Microsystems ÀÇ À¥»çÀÌÆ® http://www.javasoft.com ¿¡¼­ ÀÚ¹Ù°³¹ßÀÚ Å°Æ®(JDK: Java Developement Kit) Àüü¸¦ ÀÎÅͳݿ¡¼­ ´Ù¿î ¹ÞÀ» ¼ö ÀÖ½À´Ï´Ù. ÀÌ »çÀÌÆ®´Â À©µµ¿ìÁî 95/98, À©µµ¿ìÁî NT, ¼Ö¶ó¸®½º ¹× ¸ÅŲÅä½Ã¿¡ ´ëÇÑ JDK ¹öÁ¯À» Á¦°øÇÕ´Ï´Ù.

( Microsoft ÀÇ Java °³¹ß µµ±¸, Visual J++ ÀÇ È­¸é ¿¹ )

Java ´Â C ³ª PASCAL °ú´Â ´Þ¸® °´Ã¼ÁöÇâÀûÀÎ °³³äÀ» ³»Æ÷ÇÏ°í ÀÖÀ¸¸ç, ¿©·¯ Ư¡À» °¡Áö°í Àִµ¥, ƯÈ÷ Java ´Â Java Applet À» Á¦ÀÛÇÒ ¼ö ÀÖ´Â ±â´ÉÀ» °¡Áø´Ù´Â Á¡¿¡ ÁÖ¸ñÇÒ¸¸ ÇÕ´Ï´Ù. ÀÌ°ÍÀº ÀÚ½ÅÀÌ Á¦ÀÛÇÑ ÇÁ·Î±×·¥À» º°µµÀÇ ÀúÀå°ú ÄÄÆÄÀÏ °úÁ¤ ÇÊ¿ä¾øÀÌ ³Ý½ºÄÉÀÌÇÁ³ª ÀÎÅÍ³Ý ÀͽºÇ÷η¯ µîÀÇ À¥ ºê¶ó¿ìÀú¿¡¼­ ¹Ù·Î ½ÇÇàÇÒ ¼ö ÀÖµµ·Ï Çϴ Ư¡ÀÔ´Ï´Ù..

Java ¿¡ ´ëÇÑ ´õ ¸¹Àº Á¤º¸´Â, SunÞäÀÇ Java ȨÆäÀÌÁö(http://java.sun.com)¿¡¼­ ãÀ» ¼ö ÀÖ½À´Ï´Ù.

1.2. Mathematica

Mathematica ´Â Wolfram Research¿¡¼­ °³¹ß, ÇöÀç ¹öÁ¯ 4.0 ±îÁö Ãâ½ÃµÇ¾î ÀÖ½À´Ï´Ù. Mathematica ´Â ¹æ´ëÇÑ ¾çÀÇ ¼öÇÐ ÆÐÅ°Áö¸¦ º¸À¯ÇÏ°í ÀÖÀ¸¸ç ƯÈ÷ ±×·¡ÇÈ°ú ¼öÇÐ½Ä Ç¥Çö¿¡ ÇÊ¿äÇÑ ÇÔ¼öµéÀ» ¸¹ÀÌ Æ÷ÇÔÇÏ°í Àֱ⠶§¹®¿¡ ¼öÇÐÀûÀÎ ¸ðµ¨¸µÀ» ½±°Ô ½Ã°¢È­ ÇÒ ¼ö ÀÖ´Â µµ±¸ÀÔ´Ï´Ù.

( Mathematica ÀÇ È­¸é ¿¹ )

Mathematica ¸¦ ÀÌ¿ëÇϸé ƯÁ¤ÇÑ ÇÔ¼ö¸¦ Á¦°øÇÏ´Â ÆÐÅ°Áö¸¦ ¸¸µé ¼ö ÀÖÀ¸¸ç ±×°ÍÀ» »ç¿ëÇÏ¿© ÀÛ¾÷ÀÇ »ý»ê¼ºÀ» ³ôÀÏ ¼ö ÀÖ½À´Ï´Ù.

Mathematica ¿¡ ´ëÇÑ ´õ ¸¹Àº Á¤º¸´Â, Wolfram ResearchÀÇ È¨ÆäÀÌÁö(http://www.wolfram.com)¿¡¼­ ¾òÀ» ¼ö ÀÖ½À´Ï´Ù.


2. Java Applet À» ÀÌ¿ëÇÑ ±¸Çö

Java Applet À» ÀÌ¿ëÇÏ¿© (¼öÇÐ) ÇÁ·Î±×·¥À» Á¦ÀÛ ÇÏ´Â °ÍÀº ´ÙÀ½ÀÇ ´Ü°è¸¦ °ÅĨ´Ï´Ù.

  1. ¾Ë°í¸®Áò ºÐ¼®
  2. ¼Ò½ºÄÚµå ÀÛ¼º
  3. ÄÄÆÄÀÏ / µð¹ö±ë
  4. ¹ÙÀÌÆ®ÄÚµå ÀÛ¼º
  5. À¥ ¹®¼­¿Í ¿¬°á
  6. À¥ ¹®¼­ ³»¿¡¼­ ½ÇÇà

´ÙÀ½Àº ÁÖ¾îÁø ¼öÀÇ FactorialÀ» Ç¥½ÃÇÏ´Â Java Applet ÀÇ ÄÚµå¿Í ½ÇÁ¦ Applet ÀÔ´Ï´Ù.

(¡Ø À§ Applet Àº ÁÖ¾îÁø ¼ýÀÚ°¡ 21 ÀÌ»óÀ϶§ factorial °ªÀÌ Java ÀÇ Á¤¼öÇ¥Çö ÇѰ躸´Ù Ä¿Áö±â ¶§¹®¿¡ Á¦´ë·Î ÀÛµ¿ÇÏÁö ¾Ê½À´Ï´Ù. )

À§ Applet À» ±¸¼ºÇÏ´Â Source Code ´Â ´ÙÀ½°ú °°½À´Ï´Ù.

import java.awt.*;
import java.applet.*;
import java.awt.event.*;

/**
 * ÀÌ AppletÀº »ç¿ëÀڷκÎÅÍ ÇϳªÀÇ ÀÚ¿¬¼ö¸¦ ¹Þ¾Æ¼­, ±×°Í¿¡ ÇØ´çÇÏ´Â
 * Factorial °ªÀ» ¸®ÅÏÇÕ´Ï´Ù.
 */

public class Factorial extends Applet implements ActionListener {
    Label numLabel, resultLabel;
    TextField num, result;
    
    public void init()
    {
        numLabel = new Label("¼ýÀÚ¸¦ ÀÔ·ÂÇÏ°í Enter¸¦ ´©¸£¼¼¿ä");
        num = new TextField( 10 );
        num.addActionListener( this );
        resultLabel = new Label("Factrial °ª : ");
        result = new TextField( 20 );
        result.setEditable( false );
        
        add( numLabel );
        add( num );
        add( resultLabel );
        add( result );
    }
    
    public void actionPerformed( ActionEvent e )
    {
        long number, factorialValue;
        
        number = Long.parseLong( num.getText() );
        showStatus( "Calculating... " );
        factorialValue = factorial( number );
        showStatus( "Done." );
        result.setText( Long.toString(factorialValue) );
    }
    
    long factorial( long n )
    {
        if( n == 0 || n == 1 )
            return 1;
        else
            return n * factorial( n - 1 );
    }
    
}

¼Ò½ºÄڵ带 ÀÛ¼ºÇÑ ÈÄ, JDKÀÇ Java compiler ¸¦ ÀÌ¿ëÇÏ¿© ´ÙÀ½ÀÇ ¹®ÀåÀ» ½ÇÇàÇÏ¸é °á°ú·Î Factorial.class È­ÀÏÀ» ¾ò½À´Ï´Ù.

c:\work> javac Factorial.java

ÀÌ·¸°Ô ¸¸µé¾îÁø Factorial.class È­ÀÏÀ» À¥ ¹®¼­¿¡ »ðÀÔÇÏ´Â ÄÚµå´Â ´ÙÀ½°ú °°½À´Ï´Ù.

<html>
  <body>
    <applet code="Factorial.class" width="320" height="60">
    </applet>
  </body>
</html>

´ÙÀ½Àº °°Àº ¿ø¸®¿Í, ´ÙÀ½ÀÇ ÇÔ¼ö¸¦ ÀÌ¿ëÇÏ¿© Á¦ÀÛÇÑ fibonacci number »ý¼º¿ë Java Applet ÀÔ´Ï´Ù. ´ÙÀ½ Applet ÀÇ ¼Ò½ºÄÚµå´Â fibonacci.java ÀÔ´Ï´Ù. 1)

long fibonacci( long n )
{
    if( n == 0 || n == 1 )
        return n;
    else
        return fibonacci( n - 1 ) + fibonacci( n - 2 );
}

´õ À¯¿ëÇÑ Java Applet ÀÇ È°¿ëÀº 4ÀåÀÇ È°¿ë ¿¹¿¡¼­ »ìÆ캸±â·Î ÇÏ°Ú½À´Ï´Ù.


3. Mathematica ¸¦ ÀÌ¿ëÇÑ ±¸Çö

Mathematica ¸¦ ÀÌ¿ëÇÏ´Â °ÍÀº Mathematica °¡ Á¦°øÇÏ´Â ¸¹Àº ÇÔ¼öµé°ú Mathematica Notebook ÀÇ ÇÁ¸®Á¨Å×À̼Ç/ÃâÆÇ ±â´ÉÀ» »ç¿ëÇÏ´Â °ÍÀ» ÀǹÌÇÕ´Ï´Ù. ±âº»ÀûÀ¸·Î Mathematica ´Â ´ÙÀ½ÀÇ Combinatorics ÇÔ¼öµéÀ» Á¦°øÇÕ´Ï´Ù. (À̾îÁö´Â ±×¸²Àº, Mathematica°¡ Áö¿øÇÏ´Â Á¶ÇÕ·ÐÀÇ ÇÔ¼öµéÀ» Á÷Á¢ ÀÔ·ÂÇÏ°í ÀÛ¾÷ÇÏ´Â È­¸éÀ» ĸÃÄÇÑ °ÍÀÔ´Ï´Ù.



Mathematica °¡ Á¦°øÇÏ´Â Á¶ÇÕ·Ð ±â¹Ý ÇÔ¼öµéÀº À̰ͺ¸´Ù ÈξÀ ¸¹Áö¸¸, ÇÑ Çб⵿¾È ¹è¿î ³»¿ë°ú Áߺ¹µÇ´Â ºÎºÐ¸¸ Ã߸° °ÍÀÔ´Ï´Ù. Mathematica ¸¦ »ç¿ëÇÏ¸é ¼öÇÐ ÇÁ·Î±×·¡¹ÖÀÇ ÀÛ¾÷½Ã°£À» È¿°úÀûÀ¸·Î ÁÙÀÏ ¼ö ÀÖ½À´Ï´Ù.


4. È°¿ë ¿¹

4.1 Magic Square Applet

Magic Square ¶õ °¢ ¿­, Çà, ±×¸®°í µÎ°³ÀÇ ´ë°¢¼±¿¡ À§Ä¡ÇÑ ¼öÀÇ ÇÕÀÌ °°µµ·Ï ¸¸µç Çà·ÄÀ» ¸»ÇÕ´Ï´Ù.

µû¶ó¼­, order nÀÇ magic square´Â µ¿ÀÏÇÑ Magic Sum, Áï s = n (n2 + 1) / 2 ¸¦ °¡Áý´Ï´Ù. ¿©±â¼­ ¹®Á¦´Â ¾î¶»°Ô Çϸé order nÀÇ magic square¸¦ ±¸ÇÏ´Â ÀϹÝÀûÀÎ ¹æ¹ýÀ» ±¸ÃàÇÒ ¼ö Àִ°¡ ÇÏ´Â Á¡ÀÔ´Ï´Ù. ÀÌ Àý¿¡¼­´Â, 17¼¼±âÀÇ ¼öÇÐÀÚ la LoubereÀÇ ¹æ¹ýÀ¸·Î nÀÌ È¦¼öÀÎ °æ¿ìÀÇ magic square¸¦ ¸¸µå´Â Java AppletÀ» ¸¸µé¾î º¾´Ï´Ù.

la LoubereÀÇ ¾Ë°í¸®ÁòÀº ´ÙÀ½°ú °°ÀÌ ºÐ¼®ÇÒ ¼ö ÀÖ½À´Ï´Ù.

  1. nÀº Ȧ¼ö¿©¾ß ÇÕ´Ï´Ù. (nÀÌ È¦¼ö°¡ ¾Æ´Ñ°æ¿ì error)
  2. 0th ¿­ÀÇ °¡¿îµ¥ Çà¿¡ 1À» ³Ö°í Ãâ¹ßÇÕ´Ï´Ù.
  3. ±×ÈÄ, ´ÙÀ½ ±×¸²°ú °°Àº ¹æ½ÄÀ¸·Î ÁøÇàÇÕ´Ï´Ù.
    ¿À¸¥ÂÊ À­ÂÊ ´ë°¢¼± ¹æÇâÀ¸·Î À̵¿Çϸ鼭, À­ÂÊ °æ°è¿¡ À̸£¸é ´Ù½Ã ¾Æ·¡ÂÊÀ¸·Î µ¹¾Æ¿À°í, ÀÌ¹Ì ¼ýÀÚ°¡ ä¿öÁ®ÀÖ´Â Ä­À» ¸¸³ª¸é, ÇÑÄ­ ¾Æ·¡·Î À̵¿ÇÑ ÈÄ, ´Ù½Ã °°Àº ¹æ¹ýÀ¸·Î ÁøÇàÇϸ鼭 Áö³ªÄ¡´Â Ä­¿¡ ¼ýÀÚ¸¦ ä¿ì´Â °ÍÀÔ´Ï´Ù.

ÀÌ°ÍÀ» Ç¥ÇöÇÒ ¼ö ÀÖ´Â Java AppletÀº ´ÙÀ½°ú °°À¸¸ç n = 3 ºÎÅÍ n = 11 ±îÁö ÀÛµ¿ÇÕ´Ï´Ù.

ÀÌ ÇÁ·Î±×·¥ÀÇ ¼Ò½ºÄÚµå´Â MagicSquare.java ÀÔ´Ï´Ù. ¼Ò½ºÀÇ ¾Ë°í¸®Áò ±¸ÇöºÎºÐÀº ´ÙÀ½°ú °°½À´Ï´Ù.

Àü·«...
-------


    public void actionPerformed( ActionEvent e )
    {
        int magicSumValue;
        
        number = Integer.parseInt( num.getText() );
        if( number <= 11 && number > 1 )
        {
            magicSumValue = magicSum( number );
            status.setText( "Magic Sum˼ " + 
                Integer.toString( magicSumValue ) + "ÀÔ´Ï´Ù." );
            repaint();
        }
        else 
        {
            status.setText( "1 º¸´Ù Å©°í, 11 ÀÌÇÏÀÎ ¼ö¸¦ ÀÔ·ÂÇϼ¼¿ä." );
        }

    }
    
    int magicSum( int n )
    {
        return (n*n*n + n) / 2;
    }
    
    void drawBox( Graphics g, int n )
    {
        ...;    
    }
    
    void drawMagicSquare( Graphics g, int n )
    {
        int i,j,k,l,num;
            
        num = 1;
        k = 0;
        i = (n-1)/2;
       
        for(l = 0; l < n; l++ )
        {
            for( j = 0; j < n; j++ )
            {
                try { Thread.sleep(500);
                } catch (InterruptedException e) {}
                
                g.drawString(Integer.toString(num), 
                             10 +  3 + (300/n)*((i+10*n)%n),
                             65 + 13 + (300/n)*((k+10*n)%n)
                             );
                k--;
                i++;
                num++;
            }
            k = k + 2;
            i--;
        }
    }

-------
ÈÄ·«...

4.2 n-Queens Problem

´ÙÀ½Àº n by n ü½ºÆÇ¿¡ n°³ÀÇ QueenµéÀ» ¼­·Î °ø°ÝÇÏÁö ¾Êµµ·Ï ¹èÄ¡ÇÏ´Â ¸ðµç °¡Áö¼ö¸¦ ±¸ÇÏ´Â AppletÀÔ´Ï´Ù. ÀÌ AppletÀº 1ºÎÅÍ 10±îÁöÀÇ n-Queens ProblemÀ» Ç® ¼ö ÀÖµµ·Ï ¼³°èµÇ¾î ÀÖ½À´Ï´Ù. ÀÌ AppletÀº Á»´õ º¹ÀâÇÑ ±â´ÉµéÀ» ¿ä±¸Çϱ⠶§¹®¿¡ µÎ°³ÀÇ java source È­ÀÏ·Î ±¸¼ºµÇ¾î ÀÖ½À´Ï´Ù. (NQueens.java, ChessBoard.java)

ÀÌ ÇÁ·Î±×·¥Àº ´ÙÀ½°ú °°ÀÌ ±¸¼ºµÇ¾î ÀÖ½À´Ï´Ù.

¿©±â¼­ ÇØ°¡ "73025164" ¶ó°í Ç¥ÇöµÈ°ÍÀº

½ÇÁ¦·Î ÀÛµ¿ÇÏ´Â AppletÀº ´ÙÀ½°ú °°½À´Ï´Ù.

Non-Attacking QueensÀÇ Çظ¦ ±¸ÇÏ´Â ÇÔ¼ö´Â ´ÙÀ½°ú °°½À´Ï´Ù.

    boolean Threatens(int x, int y, int numPiecesPlaced)
    {
        int i = 0;
        boolean threats = false;

        int temp;

        while ((i < numPiecesPlaced) && (threats == false)) {
            if (board[i] == y)
                threats = true;

            temp = x-i;
            if ((y == (board[i]-temp)) || (y == (board[i]+temp)))
                threats = true;

            ++i;
        }

        return threats;
    }

    void FindSolution(int piecesPlaced) {

        int i;

        for (i=0; i<NUM_QUEENS; ++i) {
            if (!Threatens(piecesPlaced, i, piecesPlaced)) {
                board[piecesPlaced] = i;

                if (piecesPlaced == (NUM_QUEENS-1)) {
                    PrintSolution(NUM_QUEENS, solutionsFound);
                    ++(solutionsFound);
                }

                FindSolution(piecesPlaced+1);
            }
        }

        return;
    }

    void PrintSolution(int numQueens, int s)
    {
        int i;
        sol = new StringBuffer("");

        for (i = 0; i<numQueens; ++i) {
            sol.append(Integer.toString(board[i]));
        }

        c.setSolution(sol.toString());
        sol.append(": #" + Integer.toString(s));
        solutions.addItem(sol.toString());
    }

°á·Ð

Java / Java Applet °ú Mathematica µîÀÇ »õ·Î¿î µµ±¸¸¦ »ç¿ëÇÏ¸é ¼öÇÐÀûÀÎ ³»¿ëÀ» ½±°Ô Ç¥ÇöÇÏ°í ±¸ÇöÇÒ ¼ö ÀÖÀ¸¸ç, ƯÈ÷ ±³À°À» ¸ñÇ¥·Î »ç¿ëµÉ¶§ ±× È¿°ú°¡ Å©´Ù°í ÇÏ°Ú½À´Ï´Ù.

Java ¿Í Mathematica µîÀÇ µµ±¸µé, ±×¸®°í º¯È­ÇÏ´Â Çö½Ç¿¡ ÀûÀÀÇÏ´Â °ÍÀÌ Çй®À» ÇÏ´Â »ç¶÷ÀÇ ÀÚ¼¼¶ó°í »ý°¢ÇÕ´Ï´Ù.


Âü°íÀÚ·á.


  1. fibonacci ¸Þ½îµåÀÇ °¢ ¼øȯ´Ü°è¿¡¼­ ¸Þ½îµå È£ÃâÀÇ ¼ö°¡ µÎ¹è·Î µÇ´Â È¿°ú°¡ ¹ß»ý°¡±â ¶§¹®¿¡ ÀÌ°ÍÀº ±Ý¹æ °ÈÀâÀ» ¼ö ¾øÀÌ Ä¿Áý´Ï´Ù. 30¹ø° fibonacci number¸¦ °è»êÇϱâ À§Çؼ­´Â 2,692,537 ¹øÀÇ ¼øȯȣÃâÀÌ ÇÊ¿äÇϱ⠶§¹®¿¡ ±×º¸´Ù ´õ Å« ¼ö¸¦ ³ÖÀ» °æ¿ì, Applet¿¡¼­ °á°ú¸¦ ³ªÅ¸³»±â ±îÁö´Â ¾ÆÁÖ ¸¹Àº ½Ã°£ÀÌ ÇÊ¿äÇÒ °ÍÀÔ´Ï´Ù.