                         .

                    ।⥫ ᢥ.
                   뢠  ?

                       '⥪'.
     ⥪ 㤥 뢠 ᫥⥫쭮 ⮢,  㯮冷-
祭  ६  㯫.   ᫥⥫쭮 㯭
⮫쪮    (設 ⥪).   ࠡ  ⥪ -
室 㪠⥫ 設 ⥪. ᭮ 樨  ⥪ ᫥-
騥: "  ⥪"  "  ⥪" (祬 
᫥   ᥭ  ⥪ ⮢ -     -
設 ⥪).  ⮬ ,  ⥪ --   ⨯ LIFO
-  "Last  In - First Out" - "᫥ 襫 -  襫".  
।⠢ ⥪   ணࠬ  筮  ᯮ  
ᨢ (  B),  㬥 ⮢ ண 稭 
.  ⮬ 㫥  ᨢ ࠭  ࢮ ᢮-
   ᨢ (.. 㢥祭  1  設 -
). ᫨ ᨢ ,  㪠⥫ ࠢ 1 (B[0]=1).
      X    ⥪  ॠ 祭  - 
ࢮ ᢮  ( ண ࠭  B[0])  -
 X,  ᫥ 祣  ࢮ ᢮  㢥稢
 1:

     B[B[0]]:=x;         {   ⥪ }
     B[0]:=B[0]+1;       {  㪠⥫ }

   ᫨ 室   x  ⥪,   ᫥-
  ᥭ ⮢ (⢥,  ⮫쪮   ⮬  砥,
᫨ ⥪ ),   㪠⥫  ࢮ ᢮  㬥-
蠥  1:

     if B[0]<>1 { ᫨ ⥪   }
     then
       begin
         x:=B[B[0]];     {   }
         B[0]:=B[0]-1;   {  㪠⥫ }
       end;

                      'ᯨ᮪'.
       ᯨ᪠  㪠⥫    ᫥騩    
  (㣨 ᫮ -- ࠭ ଠ  ᯮ ᫥-
饣 ),    ᫨  ᯨ᮪  吝 (㭠ࠢ),
   ⠪ 㪠⥫   ।騩 .  ஬ ⮣
 ६,  㪠뢠     ᯨ᪠. ਬ,
㭠ࠢ  ᯨ᮪   ॠ   㬥୮
ᨢ A[1..3,1..N],   ᮤন  A[2,i]  ।  
(,  ) ,  ।饣  A[1,i],  -
ন A[3,i] ।  , ᫥饣  A[1,i].
     ᭮ 樨  ᯨ᪮ ᫥騥:  "㤠  ᯨ᪠"
 "  ᯨ᮪".
     ਬ, 饭  ᯨ᮪   ᫥  A[1,i]
 룫拉 ⠪:
     A[1,j]:=x;         {   ᨢ }
     A[2,j]:=i;         {  㪠⥫ }
     A[3,j]:=A[3,i];
     A[3,i]:=j;
       j -  ᢮ 樨  ᨢ  .

                     '।'.
     ।  ணࠬ஢,    ।  ,  
砫  .  ᫨ 室  ,    ⠭  
 ।, ᫨ 室    ।,   -
   砫.  । 㤥 ।⠢      ᨢ.
     ࢮ - BEG  ᫥ - FIN ⮢
। (᫨ ।  ,    BEG=FIN+1;  ᭠砫    BEG=1,
FIN=0).
     । 襬 ⠪: var Queue=array[1..MaxQ] of element;
      MaxQ - ᨬ쭮 ᫮ ⮢  ।,  element -
- ⨯ .  ⢥ element    ᫥-
饣 :
        type element = record
                x: byte;
                y: byte;
             end;
      element -  ,    x-  y- -
.
      ।  ஢ 樨:
           ⠢    । InQueue,
           㤠  । OutQueue.

     Procedure InQueue (x : element);
     begin
       FIN:=FIN+1;      {  ࢮ ᢮ }
       Queue[FIN]:=x;   { ⠢  x }
     end;

     Procedure OutQueue (var x : element);
     begin
       x:=Queue[BEG];   { ६   }
       BEG:=BEG+1;      {  塞 㪠⥫ }
                        {  ᫥騩   }
     end;

    __________________________________________________________

                              1
      ᫥⥫쭮,      N    ᨬ
(ai,bi).    । 冷 ।⢮ ᨬ,
ਬ,  (b,) 砥,  ᨬ "b" । ᨬ
"".   浪 (b,)  (,a) ᫥ 冷  (b,a).  室
।,    ᫥⥫쭮:
 ) ,  ..   ᯮ짮  ନ஢  ᨬ
    (ᨢ  騥)    ந   楯 (A1,A2,
    ..., As)  浪 ।⢮;
 ) ⨢稢, ..   ᨬ x,y 
     ६ 冷  (x,y) ⠪  (y,x);

                             2.
      饣 ⮨ N 祫,   뤥 ,
  ⠫  㬥஢    ᮢ ५ ᫠  2  N.
騩,  稭  -,    M.   ஬
⠭ , 室  㣠.  த  ᫥-
 祫  ⠪   ,   ⠭  祫.
     ।
     a)  ⠢襣 祫, ᫨ ⭮ M  ,  
稭  ࢮ 祫;
     b)  祫 c ண 稭 ,  ᫨ ⭮ M
  ⠢襣 祫 L.

                             3.
      ᪠  2^k ⮪  ਭ   . -
  ᣨ   ⠪,  ⮡ ࠢ   
.  த   ,  ᢥ 室 -
   ⪨.  室  ஭㬥஢ ⪨ ⠪ ࠧ,
⮡ ᫥ 砭 ᣨ   ⮪  稢襩
 뫨 ᯮ  浪 1,2,3,4,...,2^k.

                            3.1.
                     "᪠". ஢ ..
     ᯮ  ⨪쭮  אַ㣮 㬠  
९  殬 ⠫ ᪫뢠 ᫥騬 ࠧ:
     -  ࢮ 蠣  ᮣ㫨  ⠪,   
        ᯥ।  (  -  ᣨ)  ᧠ ( -
ᣨ),
     -    ᫥ n-1 蠣 믮﫨 筮 ⢨ 
饩    ।饬 蠣 ᮣ⮩ 窮,   
楫.
     ⥬   ࠧ㫨 , ਢ   室 ﭨ.
    ⠫  ᣨ - ॡ  ॣ, 祬  
ॡ    ࠢ묨  㪫    ( - ॡ), 
  -      ( -ॡ).  ஭㬥஢ ᢥ 
᫠  1  2^n-1.
     . ⠢ ணࠬ, 訢:
     -  ப  ᨬ  ய 㪢 ""  "", ।
᫥⥫쭮 ⨯ ᣨ,
     -  ॡ,
  ᮮ  ⨯  ⮣   ॡ,  稢訩   ᫥  
᫥⥫쭮 ᣨ.
     .  ⠢  ணࠬ,  訢  ப  ᨬ 
ய  㪢  ""   "",  宦  i-⮬  ᨬ
""    ""  ।  ⨯  ॡ   ࠢ ᪥, 
뤠   ப      ய   ""      "",   ।
᫥⥫쭮  ⨯  ᣨ,  ।⢮  祭
窠    室 ᫥⥫쭮 ॡ. ᫨ ⠪ ப
 , ᮮ  ⮬.


                             4.
      ࠧ  4^ ࠢ  ⮪. 
ॣ । ⭮⥫쭮 ⨪쭮 (ࠢ 
뢠  )  ਧ⠫쭮 (   -
뢠  )  ᨬਨ   ,    ⪨
  ᯮ   㣮. ॡ 㬥஢ -
 室  ⠪ ࠧ, ⮡  १ 믮
権 ॣ  ⮪,  ᯮ     㣮,
ࠧ  ᫮  ᫥⥫쭮 1,2,3,...,4^,  稭 
孥 ⪨.

                             5.
      祭    嬠⭮ ᪨ (ਬ,  A5 
C2).  쭮 ᫮ 室,   㦭 嬠⭮ 
 室  ࢮ   ஥.

                             6.
      筠 ᫥⥫쭮,     ࠢ
᪮ p  ⨯.  ।,   
     䬥᪨ ⢨ ⠪,  ⮡ 稫
ࠢ쭮 䬥᪮ ࠦ.

                             7.
      ⠡  ࠧ N   ᬮ 室  -
   訩 ᫥騩   ,  -
 .  ᫨ ⠪  ,      . 
ᯮ짮 ⥫ .

     =1 3 2 5 3 4
      =3 5 5 0 4 0

                             8.
      த ᯮ  n  ⮡  ⠭,  祭
᫠  N={1,2,....,n}.   R ⮡ ⮢, -
 ᫥⥫쭮ﬨ ᥤ ⠭    ⮡
  ࠢ:
                      1={I11,I12,...,I1m1},
                      2={I21,I22,...,I2m2},
                              .....
                      Mr={Ir1,Ir2,...,Irmr},
 Ijk ࠫ쭮.
      ணࠬ,    ࠬ ⠭ I 
J ।    ६饭 ᠦ   -
 I    ⠭ J  ᯮ짮  ⮢ -
ᮢ  ᫮,   ६   ᥤ ⠭
    ⮢      3 ࠧ  ६ 
. ஬ ⮣, ⮡     ࠢ-
.

                             9.
        ஫  室  ᪮筮 嬠⭮ ᪥.
⭠  ᫥⥫쭮  N  室 (,  ,  ,
ࠢ, -  ..). ணࠬ, । -
   ஫     ⮬    쭮 -
   N ᫮ ᫥.

                             10
        ᯮ N  ࡠ   M  ࡠ
. 室   室 ᮢ ५, ॢ稢  S
- .   ࠧ  稭  ࡠ.   浪
 ⠢ , ⮡ ᫥ K 室 ⠫ L , 
ࡠ .

                             11.
     N   M  襩 ᨤ  .  誠 室  
  ᮢ  ५   ꥤ  S - .    ࠧ
 稭  ன 誨. ⠢  ।騩 -
冷  ஬ ᨤ 誨,  ᫨ १ ஥ ६ ⠫
K   L  襩.

                             12.
       ⮩ 㬠 ࠧ஬ *N ⮪ 㤠 -
 ⪨. ᪮쪮 ᪮ ᯠ  ⠢    ?
     ਬ. ᫨    嬠⭮  ᪨  㤠  ⪨ 
梥, ⠢  ᯠ  32 ᪠.
     .  ,   । 㤠 ⮪  ᪫ 
樫 ⮩ N.

                             13.
      n    祪,  ᫮  ⮯.  -
窨 ᪫뢠  ⮫    ᫥騬 ࠧ:  -
   ⮫,    ⮯, -  ⮫, -
 -   ⮯  ..,   窨   뫮-
    ⮫.      室 ᯮ 祪 
⮯, ⮡ ࠧ  ⮫ 窨 ।  梥:
, ୠ, , ୠ  ..

                             14.
     p ⥫  p楩   pp  M  x  N.  
p - p ᫠.   ( i,j ) ᮮ⢥ -
 p⠫쭮 p⭮ 頤 pp 1 x  1  ⭮⥫쭮
 ᭮. ᭮ p ਧ⠫쭮.
     p " ⥪襩 , ᫨
     a)   ᪠   , ⥬ ;
     ਬ:

               5  3  1
           =  5  2  5
               2  5  5

       ᫥ ꥬ  ⠭ ⮫쪮  ७ 㣫㡫,
        ⮬ (2,2)=1.
       ꥬ  ࠢ 1.

     b)   (i0,j0) 뫨 ꥬ  V.

                             15.
      ࠧ  N*M ।  ਭ.  B 
 1 砥 ⥭,  0 । ᢮ .  -
  ப  । 室 x(i),    ᫥ 室
y(i), i=1,..,k,    㫥묨 ⠬.
     室 ।,  
     ) ஢ k 祫  室  x(i)    室  y(i)  ᮮ-
⢥,  i=1,..,k, ⠪ ࠧ, ⮡  ᢮ 
頫    ࠧ.
     )   ,  祫  뢮 p   室.
     ਬ砭:    ਭ  ⢫  ⮫쪮  
⨪  ਧ⠫.

                             16.
      ᪮筮 䬥᪮ ࠦ.   ࠦ -
    뢠   뢠 㣫 ᪮ (  ),
 権 +,  -,  *, / ( - 楫᫥)    0
 9.  祭 ⮣ ᪮筮 ࠦ.
     ਬ:  '(3+5*2)/3-1'=3.

                             17.
      ⢮  N 稭,  N ࠫ쭮 ᫮. 
  稭    稭,⠪    砫쭨-
,祬  ࠢ  ࠢ:  稭  稭 -
 稭, 砫쭨  砫쭨 -  砫쭨, 
砫쭨      稭,    稭  
 ।⢥ 砫쭨.
    ⮣ ⮡  業  뢮  室 -
  1- 稭 - 砫쭨  稭. ஡-
 ᫮ ⥬,   稭,  ,  -
ॡ "",  ..     ᢮  ।⢥
稭   - ⭮ ⢮ ஢.   
稭 ⥭ ⮩ ᯨ᮪  ஢ ""  ᮮ-
   ⪠.⮩  砥, 
稭  ॡ    砥.  ⠢ ᢮ -
    ᫥  ⮣,  ।⠢    
஢ ""  㯫祭 ᮮ⢥ ⪠.
      室 ।    뢥   㬬 㯫-
祭 ⮪ ⨬ 冷 祭 ᥩ  業 
⮨.
      N<100. ⢮ ஢   稭  ॢ-
 15.

