5. ୨ 㪠 (⥢  98/99 祡 )

᭨⥫쭠 ᪠
---------------------
    ஭㬥஢ ࠬ 1-9  㪢 a, b, c, d. 
   饭 ⮬᪮ ࠡ⪨ १-
⮢ ୨.
   ⥫쭮  ᫮  ᯮ ᫥騥 ࠧ-
.
     3:
   - ᯮ ᫥ 㡨  ᨬ "!"    -
࠭  ⭮;
   - ਧ⠫  ࠧ   ⠥  ⮫쪮 訬,
᪮쪮  室  襭 ;
   - 㡨  ᨬ  ᯮ   ப (
ࢮ) 稭   ⮫ ( ࢮ).
     4-8:
   - ᯮ   ப ᮢ襭 ந쭮;
   -  ࠧ蠥 ᬥ  ਧ⠫ 㡨, ⠢騥
;
   - ࠧ蠥 ᬥ     ப ,  
    : ᫥ 믮 ணࠬ ᯮ⥫
㡨  ᫥    㣮  ஬⪮  ०-
 浪;
   - ਧ⠫  ࠧ   ⠥  ⮫쪮 訬,
᪮쪮  室  襭 .

    9-c:
   - 㡨  ᨬ "a"    "b"  ᯮ  
ப  ( ᠬ ࢮ);
   - 㡨  ᨬ "a"  ᯮ    ⮫,
 ᠬ ࢮ;
   - ᫥ 믮 ணࠬ  㡨  ⠢ 
०  (஬  c,  㡨  ᨬ "c" 
६   ᫮ );
   - ਧ⠫  ⨪ ࠧ     -
⮫쪮 訬, ᪮쪮  室  襭 .

                             
                             ~~~~~~
                                   , 1998 (C) ..㢠

                          設   ᪮: ,
                          ,    ⢥,   ⠪
                             室.    
                          設    ᯮᮡ   
                          ન . ઠ    ந-
                             ६      
                          ᪮.  ᯮ  ﭨ,  
                            ⠭, 設 㡨 -
                          ,       ௨, 
                          ⠪  .
                                                   ᮢ


 1 (4 )
   -    ,    אַ㣮쭨,  ࠧ ⪠
(1,3), (1,7), (9,3),  (9,7), ᯮ 㡨   ᨬ-
.
     㡨  ६    (1,1).  砫-
  ᯮ⥫ ᯮ  ⪥ (1,1).

 2 (5 )
   -    ,    אַ㣮쭨,  ࠧ ⪠
(3,3), (3,7), (9,3), (9,7), ᯮ 㡨  㫥 ன.
   ⠭  㡨  ࢮ ⮫  ,  -
 ன ࠢ 祭   㡨.
    砫  ᯮ⥫ ᯮ  ⪥ (3,1).

 3 (7 )
     ப   ᯮ 㡨  ᨬ ⠪, 
   ⮥ ࠭⢮ -        
⮪. ⭮,  । 㡨    ⮫쪮   㡨 
ᨬ "!",   - ᠬ ᫥.  ணࠬ, -
 㯫 ᨬ - ᤢ   ப ⠪, ⮡  
諨   ஬⪮.  砫  ᯮ⥫ -
 ࠧ   ᨬ.
   ਬ 砫쭮 ⠭ ।:
                    1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
                   
                 1                
                   
                 2          !
                   

   । ᫥ 믮 ணࠬ:
                    1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
                   
                 1                
                   
                 2  ᳠!        
                   


 4  (5 )
    ணࠬ஢ 祭  ᯮ   -
 ᠭ ।.     ᯮ짮 
ᠭ 몠 ணࠬ஢ -60.
    몥 - ᯮ ᫥騥 ᨬ:
   <>    - ᪮, 뤥騥 ।塞 ⨥;
   ::=   - ᫮ ᨬ,  ⠥ " । ";
   |     - ᨬ, 騩 ୠ⨢, ⠥ "".
   ⠪ । ᫠.
। 1
-------------
<᫮> ::= <> | <᫮><>    (1)
<> ::= 0 | 1                       (2)

     ।  ⠪:
   "᫮"    । :  "",  ꥪ,  
  ,   "᫮",  ᫥      ᠭ
"".
   "" -   ᨬ "0",  ᨬ "1"
    , ࢠ ப  । ᮤন ४!
   ஢ਬ ᮮ⢥  । "᫮" ᫥騥 -
: "1", "01", "12".
   1) ꥪ "1" - ᫮, ⮬ :
   1 -  (ࠢ 2),    ᫮ (ࠢ 1).
   2) ꥪ "01" - ᫮, ⮬ :
   0 -   ᫮ (⠪  "0" -    ࠢ 2,  -
, ᫮  ࠢ 1). ᫮,    ᫥ , -
 ᫮ (ࠢ 1), , "01" - ᫮.
   3) ꥪ "12" -  ᫮, ⮬    ᫮ "1" ᫥
   ᫥ ࠢ 2.
    ࠧ,  । 1 ᫮    ᫥-
⥫쭮  㫥  .
   .  ணࠬ  㪠,  ஢,
      ᫮  ᫥ । 1.
    砫    ᯮ⥫ ᯮ । 㡨 
  ன ப:
                         
   ᫨ ஢塞    -  ᫮, ⠭ ᯮ⥫ 
 :
                         
   ᫨   -    ᫮,  ⠢  ᯮ⥫  
ப .

 5  (7 )
     4,   ᫨    ᫮, ⠭-
 ᯮ⥫    ᨬ   . -
:
                         1021
                           
   ᫨  - ᫮, ⠭ ᯮ⥫   ᫥ 
ᨬ. ਬ:
                         1011

 6. (8 )

  ᫥饥 । ᫠:
। 2
-------------
<᫮>   ::= <楫> | <஡>
<楫>   ::= <> | <楫><>
<஡> ::= .<楫> | <楫>. | <楫>.<楫>
<>   ::= 0 | 1

   .  ணࠬ  㪠,  ஢,
      ᫮  ᫥ । 2.
    砫    ᯮ⥫ ᯮ । 㡨 
  ன ப:
                         
   ᫨ ஢塞    -  ᫮, ⠭ ᯮ⥫ 
 :
                         
   ᫨  -  ᫮, ⠢ ᯮ⥫   -
 ᨬ:
                         
                           
   ਬ १⮢ 믮 ணࠬ:

1)   1010

2)   121.34
      
3)   .00

4)   .10.0
        

 7. (9 )
  ᫥饥 । ᫠:
। 3
-------------
<᫮>   ::= <楫> | <஡>
<楫>   ::= <> | <楫><>
<஡>   ::= <> | <筠>
<> ::= <楫>/<楫>
<筠> ::= .<楫> | <楫>. | <楫>.<楫>
<>   ::= 0 | 1

   .  ணࠬ  㪠,  ஢,
      ᫮  ᫥ । 3.
    砫    ᯮ⥫ ᯮ । 㡨 
  ன ப:
                         
   ᫨ ஢塞    -  ᫮, ⠭ ᯮ⥫ 
 :
                         
   ᫨  -  ᫮, ⠢ ᯮ⥫   -
 ᨬ:
                         
                           

 8. (9 )

  ᫥饥 । ࠦ
। 4
-------------
<ࠦ> ::= <᫮>+<᫮> | <᫮>+<ࠦ>
<᫮>   ::= <> | <᫮><>
<> ::= 0 | 1
   .  ணࠬ  㪠,  ஢,
       ࠦ  ᫥ ।
4.
    砫    ᯮ⥫ ᯮ । 㡨 
  ன ப:
                         
   ᫨ ஢塞  - ࠦ, ⠭ ᯮ⥫ 
 :
                         
   ᫨  -  ࠦ, ⠢ ᯮ⥫  
 ᨬ:
                         
                           

 9 (5 )
   㪠 .
   । 5
   -------------
   㤥 ᬠਢ        ᯮ⥫ 
 . न 窨 뢠   
孥 㣫      窨  ᪮-
 ன ᥫ (x,y). ᫮ x -  ப,  y -  ⮫-
,   祭    ᯮ ⪠-窠. ࢮ
᫮ x 㤥 뢠 ப 窨, ஥ y  - ⮫殬 -
. 窨  㤥  묨 ⨭᪨ 㪢, ਯ-
  ,   砥  室, न. 窠 o, ᮮ-
 ࢮ  ⪥    ࢮ  ப,  न
(1,1).  ࠧ,  砥  o(1,1).

   । 6
   -------------
   ਧ⠫ १   㪠  㯮冷祭-
  祪,    ப.    ⮬  ⮫
ࢮ 窨   ⮫ ன.  १ 㤥 -
  ⨭᪨  㪢  - ﬨ 祪,  ࠧ-
.   室    ᪮  㪠뢠 न
祪, ⤥    㣠 ⮩.
   ਬ, ਧ⠫  १, ࠧ㥬   窠
a(x,y1)     b(x,y2),            ab    
ab((x,y1),(x,y2)).
     ਧ⠫쭮  १  ab((x,y1),(x,y2))  
᫮ y2-y1.   ਧ⠫ १ 㤥 
Pab  Pab((x,y1),(x,y2)).  ࠧ,  :
                 Pab((x,y1),(x,y2)) = y2-y1
   㤥 ,   窠  t(t1,t2)   ᯮ⥫ -
 ਧ⠫쭮 १ ab((x,y1),(x,y2)), ᫨:
                      t1 = x
                      y1 <= t2 <= y2
(१ "<=" 祭  "  ࠢ")

   । 7
   -------------
   ⨪ १   㪠  㯮冷祭
 祪,   ⮫.   ⮬ ப ࢮ
窨   ப ன. १ 㤥  
⨭᪨ 㪢 - ﬨ 祪,   ࠧ.  -
室  ᪮  㪠뢠 न 祪, ⤥
   㣠 ⮩.
   ਬ,  ⨪ १,  ࠧ㥬    窠
a(x1,y)     b(x2,y),            ab    
ab((x1,y),(x2,y)).
    ⨪쭮 १ ab((x1,y),(x2,y))  ᫮
x2-x1.     ਧ⠫ १ 㤥  Pab
 Pab((x1,y),(x2,y)).  ࠧ,  :
                 Pab((x1,y),(x2,y)) = x2-x1
   㤥 ,   窠  t(t1,t2)   ᯮ⥫ -
 ⨪쭮 १ ab((x1,y),(x2,y)), ᫨:
                      x1 <= t1 <= x2
                      t2 = y
(१ "<=" 祭  "  ࠢ")

 .
   㪢 a   b   ᯮ⥫ ࠧ ਧ⠫ -
१ ab.  砫  㪠 ᯮ  ⮬ १-
 ࠧ  㪢 a.
    ணࠬ,   ⠢ 㪠   -
 㣮 , ஥   १  ab    孥
 ஭.
   ਬ.  ⠪ ᯮ 㪢 a  b  :
                    1 2 3 4 5 6 7 8 9
                   
                 1          
                   
                 2  a   b  
                   
                 3          
                   
                 4          
                   
                 5          
                   
                 6          
                   
                 7          
                   

   㪠   ⠭   (7,7):
                    1 2 3 4 5 6 7 8 9
                   
                 1          
                   
                 2  a    b  
                   
                 3          
                   
                 4          
                   
                 5          
                   
                 6          
                   
                 7         
                   

 a (6 )
   । 8
   -------------
  ਧ⠫ १,  楢  窠  ண ᮢ 
  祪 ⨪쭮 १, 뢠 ௥஬
 ⨪쭮 १.
   ⢥⢥ ⨪ १, 楢 窠 ண
ᮢ     祪 ਧ⠫쭮 १, 뢠
௥஬  ਧ⠫쭮 १.
   ௥   १ 뢠 ।, ᫨  -
楢 窠 ᮢ  窮, ᯮ  筮  ।
१. ⭮,  ।  ௥   ந
⮫쪮  १  , ࠦ饩  ᫮.
   .
   㪢 a   b   ᯮ⥫ ࠧ ਧ⠫ -
१ ab.  ⭮,      १  ab ࠦ 
᫮.  砫  㪠 ᯮ  ⮬ १,
ࠧ  㪢 a.
   ⠭ ᯮ⥫    ।  ௥,
஥  १  ab   ⠪, ⮡  ⨪쭮
१, ࠦ饣 ௥,  ࠢ﫠  
१ ab.

   ਬ.  ⠪ ᯮ 㪢 a  b  :
                    1 2 3 4 5 6 7 8 9
                   
                 1          
                   
                 2  a    b 
                   
                 3          
                   
                 4          
                   
                 5          
                   

   㪠   ⠭   (5,5):
                    1 2 3 4 5 6 7 8 9
                   
                 1          
                   
                 2  a     b 
                   
                 3          
                   
                 4          
                   
                 5         
                   


 b (8 )
   ᯮ⥫ ᯮ -  ਧ⠫쭮 १
ab.      室   Pab. ⭮,
 ⮫ 窨 a  2.
   ਬ 砫쭮 ⠭ ।:
                    1 2 3 4 5 6 7 8 9
                   
                 1          
                   
                 2   a   b 
                   
                 3          
                   
                 4          
                   
                 5          
                   

   । ᫥ 믮 ணࠬ:
                    1 2 3 4 5 6 7 8 9
                   
                 1          
                   
                 2   a    b 
                   
                 3          
                   
                 4          
                   
                 5          
                   
                 6          
                   
                 7         
                   


 c (10 )
   㪢 a   b   ᯮ⥫ ࠧ ਧ⠫ -
१ ab.  砫  㪠 ᯮ  ⮬ १-
 ࠧ  㪢 a. 㪢  c ⠭   ⠪,  -
ࠧ ⨪ १  bc  2. ந   
㪢 a, b, c  ᯮ⥫ אַ㣮쭨 abc.   -
஭ אַ㣮쭨    ࠢ   室 १
ab,  㣮 (஭ bc) -   ࠧ :

                    ab
                        
                            Pbc = 2*Pab
                        
                    c

    d (10  )  ਤ㬠 ᢮ ᮡ⢥  
㪠,   ᫮   襭.      
। ਣ쭮 ᫮  ⢮ 襭.
