                         .

                             1.
      p    ⥭    筮 ஡ -
.襬  ( N=5),  祣 㦤   魮.
 ⠢ ⠪,     ᯮ ⠭
N ᥫ ᯮ ᨪ᪨ ( ᫮୮ 浪). 
,    ⠭ ࠢ ᫥ ࠢ ⭮.
 ,   ன  ࠭  ⨫  ,    ᮮ-
饣     ன ⠭.(ਬ,  ᫨
S=(3,5,4,6,7), L=(3,5,6,4,7),  S<L).
     ਭ樯 ࠡ ⬠ ࠧ᭨  ਬ.  ⨬, -
室 p  ⠭  3,4,5,6,7. ࢮ -
⠭ ⠥ ⠭ (3,4,5,6,7).  ᫥ ந-
 ⠭ 㤥 (7,6,5,4,3).
   ।,   ஬ 蠣  ࠡ  ⬠  祭
⠭

                          P=(5,6,7,4,3).

    ⮣  ⮡ । ।⢥ ᫥   -
⠭,  室,  ᬠਢ  ⠭ ࠢ
,  ᫥  ⥬,  ⮡  ᫥饥 ᫮ 뫮 
।饣,  ⠭ ࠧ ,  ⮫쪮  ࠢ -
.  ⠭ 㪠 ५:

                              (5,6,7,4,3).
                                 ^
                                 

   ⥬   ᬠਢ  ன  ( ࠢ  ) 
 ,     ࢮ ᫠, ஥ 㦥  ⬥-
祭.   ண ⠭ ⬥祭  ५.

                               (5,6,7,4,3).
                                  ^ ^
                                   

   塞 ⠬ ⬥祭 ᫠:

                               (5,7,6,4,3).
                                  ^ ^
                                   
     , ᯮ ࠢ   ५, 㯮冷-
稬   ᫠  浪 ⠭.        뫨
㯮冷祭  뢠 ,    ᤥ, ॢ 㪠-
 १. 稬:

                          Q=(5,7,3,4,6).

Q       ⠭,     ந -
।⢥ ᫥ P.
   ⢨⥫쭮, P<Q,  ⠪  ,  ᬠਢ   ⠭
᫥ ࠢ, (P(2)=6,Q(2)=7).   ⠪ ⠭
R,   P<R<Q.   P(1)=R(1)=Q(1).  ஥  Q(2) -- 
襥    ⢥  Q\Q(1)={3,4,6,7}  ᫮,   ⠪,   
Q(2)>P(2). ⮬  R(2) ୮    ࠢ: R(2)=Q(2)
 R(2)=P(2).   ⠪   P ,  稭  P(3), 뢠,
  P<R ᫥,   ᫨ P(2)=R(2),    P=R. 筮, ⠪
  Q ,  稭  Q(3),  ,   R<Q ᫥,
 ᫨ R(2)=Q(2),   R=Q.

                             2.
      ᨢ B[0..n]  (n+1) .  B[i]=0,  ᫨ i-
  ⢮  室,   B[i]=1  .  ..  ⮬
 㤥 ᮮ⢥⢮   n 㫥,   n--
  -   n  .      ⭠  
⢠   ।⠢ ᫠.
     : 㤥 ஢ ᫠  0  2^n-1, 室 
筮 ।⠢,   ନ஢ ⢮  ⮢ 
ᠬ  ⮢  ⮬ ।⠢.
      ᫮ 2^n-1     ࠧ來  設.
⮬  㤥 ஢, ᯮ ᨢ B:
     砫 B[i]=0   i,   ᮮ⢥ ⮬ -
.
     㤥 ᬠਢ ᨢ B   筮 ᫠
                         B[N]...B[1]B[0],
 ஢  ᫮ ⮣ ᫠  楩.   ᫮-
 㤥 ᬠਢ ᫮ ࠢ      
 ﬨ   ,     㫥 ,   -
ᥬ 1.    稢,   ⮫쪮  B[N]=1
(। 䨣 뫠 1...1 = 2^n-1).
                                   2

     while B[N]<>0 do begin
       i:=0;  {   筮 ᫠ }
       while (B[i]=1) do begin
         B[i]:=0;  { 㥬 ७  ᫥騩 ࠧ, }
         i:=i+1    { 騩  ᫮ }
       end;
       B[i]:=1;
       { ᯥ뢠   ⮢ ᨢ B --
          ᣥ஢ ⢮ }
       For i:=0 to N-1 do
          if B[i]=1 then write(i);
       writeln; { 室   ப   }
     end;

                             3.
    ᯮ㥬 ᫥騬  ⬮  樨  ⠭  k
⮢  ⢠ A:
     ᨢ  B    室  ᯮ㥬  
蠣 ⮢  A (饥  ᫮ k).   ⢥ 砫쭮 -
䨣樥 쬥 ᫥: B[j]=j, j=1,...,k.
    饬 B[j]  ᨬ ᮬ j ⠪, 
                           B[j]<n+j-k,
㢥稢   B[j]  1,     m>j  B[m]=B[m-1]+1
(B[j]   ⮬ j,   饬  㢥稢  1 ⠪ B[j] 
ᨬ ஬ j,  ⮡   騬 -
ﬨ ⮢ ᨢ B[m],  m>j, ᫥  B[k]  -
室  n). ᫨ ⠪ B[j]  ,   -
⠭   k 祭.

                            4.2.
       ॠ ᫥騬 ४ᨢ  ⬮  -
᪠  饭 ( ᫮  A 㯮冷祭  ࠬ):
     ) ᫨ ப ,     ஢ -
,   ࠧ ⥪  ஢塞 [i] (  i 
1  n)  宦  砫 㥬    ப.
    ) ᫨ - A[i] 室  ப  䨪,   -
  i ⮣ ᫮,  ⥬ 뤥塞 ᫮    ப,    
⪮ ⥪ ந  ࠧ  㭪 ).
    ᫨    A[i]  室  ⢥ 䨪  -
 ᥩ ப,   ⢫塞   㭪 ), ।-
⥫쭮    砫 ப ᫥ 㤠 㤠 ᫮,
 ⠥ 뤥  ⥪ ᫮  訬 ஬    A.  ᫨
 ⢨  (. .  室  砫 室-
 ப),    稢 ᢮ ࠡ.    
஢ .

                             5.
     蠥 ᯮ ॡ  ⮬ (Backtracking),  -
   4.

                             6.
     ) ᥣ   4 䬥᪨  樨 - "+","-","*",
"/".  㬥㥬   0  3.        "?"
     樨.   ᨢ A  5 楫
ᥫ,  i-  ᨢ 㤥 ࠭  ᮮ⢥饩
i-  "?" 樨,  .. ᫮  0  3. 砫쭠 䨣-
 -   ᨢ 㫥,  筠 -   ࠢ 3.
  ।  䨣樨   ࠢᨫ쭠 ਡ
  ⢥筮 ⥬  ᫥,    ன  ࠧ蠥
짮  ⮫쪮  ࠬ  0  3 ( ⮤ 襭 
㦥 砫   2).
     ਢ ணࠬ ࠣ 樨 䨣権.
      㤮⢠ 쬥 ᨢ A    5,      6  ⮢.
 祭  ᫥ 䨣樨  㤥 ᢨ⥫⢮
 1  ⮬ ࠧ拉 (᫨  33333  ਡ 1,  -
                                          4
稬 100000 ).
          4

     for i:=1 to 6 do A[i]:=0;
     while A[6]=0 do
      begin
              ....
     { ஢ઠ, 稫   㦭 १ }
              ....
        i:=1;
        while A[i]=3  do { ७  ᫥騩 ࠧ  }
         begin           { ਡ  }
           A[i]:=0;
           i:=i+1;
         end;
        A[i]:=A[i]+1;
      end;

                             7.
      ᯮ짮  ᯮᮡ 襭  22 
""     ४ᨢ  ᫥  ⥩
 砫쭮 設  .

                              8.
     । ⮩  ᯮᮡ ஥  ࠧ ᫠
 ᫠.    ந    浪,  ⭮
ᨪ᪮.  祢,    ࠧ  ⠪
浪 㤥 ࠧ, ᮤঠ饥  ᫠, ࠢ , 
᫥ - ࠧ  ᫠, ࠢ 1.
      룫廊 ࠧ, ᫥饥 ।⢥  ࠧ-

      n=[1]+...+[]                  (1)
     㤥 ᪠  ࠧ,஥  ᠬ 讥 ᫮
砫 ᫠,  ࠢ 砫 ᫠ ࠧ (1)
-  稬  ᫠ [1],...,[t-1] -  ⠢訥 ᫠-
 ண । ࠧ,  ।⢥ ᫥-
騬  ࠧ
    s=a[t]+a[t+1]+...+a[k].
       ,   ᫮ 筮 । -
祭 t
        t=max{i:a[i]>1}.
       ࠧ,   ᢥ   宦  ࠧ,
।⢥  ᫥饣  ࠧ s=a[t]+1+...+1,  
a[t]>1,   ⢮  ࠢ k-t. ࠧ  -
 ࠧ s1=p+p+...+p+(s mod p),  p=a[t]-1.



