         7. 

     7.1. ਬ ४ᨢ ணࠬ.

    ४ᨢ  ணࠬ  ,  筮, 
:

        () 祬 ணࠬ 稢 ࠡ?
        () 祬  ࠡ⠥ ࠢ쭮, ᫨ 稢
            ࠡ?

      () 筮 ஢,   (ᮤঠ  ४ᨢ
맮) ணࠬ ࠡ⠥ ࠢ쭮, ।,  뢠
    ணࠬ  ࠡ⠥  ࠢ쭮.  ᠬ , 
⮬ 砥  楯窥 ४ᨢ 뢠 ணࠬ    ண-
ࠬ ࠡ ࠢ쭮 (㡥  ⮬,    楯-
  砫).
     ⮡    (), 筮 ஢,    ४-
ᨢ 맮 祭 - ࠬ 㬥蠥,    
  த ᪮筮.

     7.1.1.  ४ᨢ 楤 ᫥ 䠪ਠ
楫  ⥫쭮  ᫠  n  (.. ந ᥫ 1..n,
砥 n!).

     襭. ᯮ㥬 ࠢ⢠ 1!=1, n!= (n-1)!*n.

        procedure factorial (n: integer; var fact: integer);
        | { fact ࠢ 䠪ਠ ᫠ y}
        begin
        | if n=1 then begin
        | | fact:=1;
        | end else begin {n>1}
        | | factorial (n-1, fact);
        | | fact:= fact*n;
        | end;
        end;

 ᯮ짮 楤-㭪権   ⠪:

        function factorial (n: integer): integer;
        begin
        | if n=1 then begin
        | | factorial:=1;
        | end else begin {n>1}
        | | factorial:=  factorial (n-1)*n;
        | end;
        end;

    ⢥ ᯮ짮 -
 factorial  ᠭ 㭪樨:  砥    -
,  ⠪  뢠 ४ᨢ 㭪.  ,  襬
砥  ࠧ    ᪮  ᫥  ,    ᫨  
㭪  뫠    ࠬ஢,      뫮  . (⠭-
⭠,  㤭 室 訡 , ᫨   -
,   ᯮ 祭 ६,    ⮬
  ४ᨢ 맮.)

    7.1.2.  筮  䠪ਠ ।   , , 
0!=1.  ணࠬ ᮮ⢥⢥.

    7.1.3.  ४ᨢ ணࠬ   楫 -
⥫ ⥯.

    7.1.4.  , ᫨ ॡ, ⮡ 㡨 ४ᨨ  -
室 C*log n,  n - ⥯.

    襭.

        function power (a,n: integer): integer;
        begin
        | if n = 0 then begin
        | | power:= 1;
        | end else if n mod 2 = 0 then begin
        | | power:= power(a*2, n div 2);
        | end else begin
        | | power:= power(a, n-1)*a;
        | end;
        end;

     7.1.5.  㤥, ᫨   ணࠬ,  ਢ  
襭 ।饩 ,  ப

        power:= power(a*2, n div 2)

        power:= power(a, n div 2)* power(a, n div 2)?

     襭. ணࠬ ⠭ ࠢ쭮.    ⠭
ࠡ  .   ⮬,  ⥯ 맮  த
 맮 (  )   -   ᫮  맮
     㡨 ४ᨨ. ணࠬ -० 
䬨 㡨 ४ᨨ,  ᫮ 蠣  ࠡ  ⠭-
   䬨᪮.
      ⮪  ࠭, ᠢ
        t:= power(a, n div 2);
        power:= t*t;
 ᯮ짮 㭪樥    (sqr).

     7.1.6. ᯮ   write(x)  x=0..9, 
४ᨢ ணࠬ  筮    楫  -
⥫쭮 ᫠ n.

     襭.    ᯮ짮  ४ᨨ  砥   
(஡  뫠  ⮬,      ,  -
   砫).

     procedure print (n:integer); {n>0}
     begin
     | if n<10 then begin
     | | write (n);
     | end else begin
     | | print (n div 10);
     | | write (n mod 10);
     | end;
     end;

     7.1.7.  "᪨ 譨" ⮨  ᫥饬.  
ভ.        ࠬ  n  (訥
 ᭨, 訥 ᢥ). ॡ ६    
㣮  থ. 蠥 ४뢠   ভ 
থ,    襥   襣 . -
⠢ ணࠬ, 㪠뢠 ॡ㥬 ⢨.

     襭.  襬  ४ᨢ  楤   ६饭   i
孨      m- ভ  n- (।,  -
⠫    ࠧ    ভ   -
).

    procedure move(i,m,n: integer);
    | var s: integer;
    begin
    | if i = 1 then begin
    | | writeln ('ᤥ 室', m, '->', n);
    | end else begin
    | | s:=6-m-n; {s - ⨩ থ: 㬬 ஢ ࠢ 6}
    | | move (i-1, m, s);
    | | writeln ('ᤥ 室', m, '->', n);
    | | move (i-1, s, n);
    | end;
    end;

(砫  ७  ࠬ  i-1    .
᫥ ⮣ i-  ᢮,    ७ -
 ᫥. ⠥    ࠬ.)

     7.2. ᨢ ࠡ⪠ ॢ쥢

      ॢ 뢠 ⨭ த

                   o
                    \
                     o   o
                      \ /
                   o   o
                    \ /
                     o

 設 뢠 ୥.   設    
  :    ࠢ . 設, 㤠  ,
뢠   ࠢ 뭮ﬨ  室  設.  設
    뭮,    ⮫쪮  뭠 (-
  ࠢ).       뭮,    ⮬
砥 뢠 ⮬.
      x - - 設 筮 ॢ.  ᠬ -
   뭮ﬨ, 㪠, ࠢ㪠  .. ࠧ ॢ 
୥  x - "ॢ ⮬ x".

       ᫥      ।,  設 ॢ
஭㬥஢ 楫묨 ⥫묨 ᫠, 祬   
設 ࠧ.  ⠥,    ࠭  ६-
 root.  ⠥,    ᨢ

        l,r: array [1..N] of integer

   ࠢ  設  ஬  i    ᮮ⢥⢥
  l[i]    r[i].  ᫨ 設  ஬ i   
( ࠢ) 뭠,  l[i] (ᮮ⢥⢥ r[i]) ࠢ  0.  (
ࠤ樨   ணࠬ  ᯮ㥬   ⠭
nil, ࠢ .)

      N - 筮 讥 ࠫ쭮 ᫮ ( 
設    ॢ室  N). ⬥⨬,   設  
易     ॢ     ᫠    1    N
易    ࠬ 設 (, ᫥⥫쭮,   
ᨢ l  r -  ).

    7.2.1.  N=7, root=3, ᨢ l  r ⠪:

         i  |   1  2  3  4  5  6  7
       l[i] |   0  0  1  0  6  0  7
       r[i] |   0  0  5  3  2  0  7

ᮢ ᮮ⢥饥 ॢ.

     ⢥:          6   2
                      \ /
                   1   5
                    \ /
                     3

     7.2.2.  ணࠬ  ᫠ 設  ॢ.

     襭. ᬮਬ 㭪 n(x),  ࠢ    設  
ॢ  ୥  設  x. ⠥,  n(nil)=0 (-
 ᮮ⢥饥 ॢ ),   ⨬  -
  nil(s)   ᥫ s,   ࠬ 設. -
ᨢ ணࠬ  s ⠪:

     function n (x:integer):integer;
     begin
     | if x = nil then begin
     | | n:= 0;
     | end else begin
     | | n:= n(l[x]) + n(r[x]) + 1;
     | end;
     end;

(᫮ 設  ॢ  設 x ࠢ 㬬 ᥫ  -
設     뭮ﬨ   ᠬ.) 㡨 ४ᨨ 筠,
⠪        蠣    ᮮ⢥饣   ॢ
㬥蠥.

     7.2.3.  ணࠬ  ᫠ 쥢  ॢ.

     ⢥.

     function n (x:integer):integer;
     begin
     | if x = nil then begin
     | | n:= 0;
     | end else if (l[x]=nil) and (r[x]=nil) then begin {}
     | | n:= 1;
     | end;
     | end else begin
     | | n:= n(l[x]) + n(r[x]);
     | end;
     end;

     7.2.4.  ணࠬ     ॢ  (७
  0,  뭮 -  1, 㪨 - 2  ..; 
ॢ -  ᨬ   設).

     .  ᨢ  ।  㭪  f(x) = 
ॢ  ୥  x.

     7.2.5.    ணࠬ,    n ⠥
᫮  設  n (  ॢ).

       ⢠ 設 ⮣   த 
  ᯨ᮪  設 ( ⮬   浪).

     7.2.6.  ணࠬ,  ⠥ (   -
)  設 ॢ.

     襭.  楤  print_subtree(x)  ⠥  設
ॢ  ୥  x   ࠧ;  ணࠬ  ᮤ-
 맮 print_subtree(root).

     procedure print_subtree (x:integer);
     begin
     | if x = nil then begin
     | | {祣  }
     | end else begin
     | | writeln (x);
     | | print_subtree (l[x]);
     | | print_subtree (r[x]);
     | end;
     end;

 ணࠬ ⠥ ᭠砫 ७ ॢ, ⥬ -
ॢ   뭮,  ⥬  ࠢ.  ப  else--
    ⠢ 6 ᯮᮡ,     ᯮ-
  ᢮ 冷  設.

     7.3. ஦  ꥪ⮢, ॡ

     ᨢ ணࠬ  㤮 ᯮᮡ  ஦
 ꥪ⮢  .  訬  ᪮쪮
 ᮮ饩 .

     7.3.1.  ணࠬ,  ⠥    ࠧ
  ᫥⥫쭮   n, ⠢  ᥫ 1..k (
⢮ ࠢ k  ⥯ n).

     襭. ணࠬ 㤥 ஢  ᨢ  a[1]..a[n]
 ᫮ t. ᨢ 楤 generate ⠥  ᫥-
⥫쭮, 稭騥  a[1]..a[t]; ᫥    砭  t
   祭,    砫:

     procedure generate;
     | var i,j : integer;
     begin
     | if t = n then begin
     | | for i:=1 to n do begin
     | | | write(a[i]);
     | | end;
     | | writeln;
     | end else begin {t < n}
     | | for j:=1 to k do begin
     | | | t:=t+1;
     | | | a[t]:=j;
     | | | generate;
     | | | t:=t-1;
     | | end;
     | end;
     end;

᭮ ணࠬ ⥯ ⮨   ஢:
     t:=0; generate;

     7.3.2.  ணࠬ,  ⠫   -
 ᥫ 1..n   ࠧ.

     襭. ணࠬ   ᨢ a[1]..a[n],  -
஬  ࠭  ⠭  ᥫ  1..n.  ᨢ 楤
generate  ⠪ 樨 ⠥  ⠭,   
  t  ᮢ  ⠭ a;  室  
६ t  a    祭,    室.  ᭮
ணࠬ ⠪:

    for i:=1 to n do begin a[i]:=i; end;
    t:=0;
    generate;

 ᠭ 楤:

     procedure generate;
     | var i,j : integer;
     begin
     | if t = n then begin
     | | for i:=1 to n do begin
     | | | write(a[i]);
     | | end;
     | | writeln;
     | end else begin {t < n}
     | | for j:=t+1 to n do begin
     | | |  ⠬ a[t+1]  a[j]
     | | | t:=t+1;
     | | | generate;
     | | | t:=t-1;
     | | |  ⠬ a[t+1]  a[j]
     | | end;
     | end;
     end;

     7.3.3.   騥 ᫥⥫쭮 
k, ⠬   ࠫ  ᫠    1    n.
(।,  k  ॢ室 n -  ⠪ ᫥-
⥫쭮⥩  .)

     襭. ணࠬ   ᨢ a[1]..a[k]   楫
६  t. ।,  a[1]..a[t] -  ᫥-
⥫쭮 ᥫ ࠫ ᥫ  १ 1..n, ४ᨢ-
 । 楤 generate ⠥    騥
த  k.

     procedure generate;
     | var i: integer;
     begin
     | if t = k then begin
     | |  a[1]..a[k]
     | end else begin
     | | t:=t+1;
     | | for i:=a[t-1]+1 to t-k+n do begin
     | | | a[t]:=i;
     | | | generate;
     | | end;
     | | t:=t-1;
     | end;
     end;

     砭.  for    孥 ࠭楩 n (
t-k+n).  ਠ   ࠡ,  뢠    䠪,
  ।᫥  (k-1-)  童      ॢ室 n-1,
k-2- 童   ॢ室 n-2  ..
     ᭮ ணࠬ ⥯ 룫廊 ⠪:

        t:=1;
        for j:=1 to 1-k+n do begin
        | a[1]:=j;
        | generate;
        end;

 뫮    ᨢ a ᫥   a[0]=0,  
t=0  ࠭ ⢥ 맮 楤 generate.

     7.3.4.  ᫨  ।⠢ ⥫쭮 楫
᫠ n   㬬 ᫥⥫쭮  楫 -
⥫ ᫠.

     襭.  ணࠬ      ᨢ a[1..n] (-
쭮 ᫮ ᫠ ࠢ n)   楫 ६ t. ।-
,  a[1],...,a[t] -  ᫥⥫쭮 -
 ᥫ, 㬬   ॢ室  n,  楤  generate
⠥    ।⠢  ॡ㥬  , த騥 
᫥⥫쭮.   ᫥ 㬬  a[1]+...+a[t]
࠭  ᯥ樠쭮 ६ s.

     procedure generate;
     | var i: integer;
     begin
     | if s = n then begin
     | |  ᫥⥫쭮 a[1]..a[t]
     | end else begin
     | | for i:=1 to min(a[t], n-s) do begin
     | | | t:=t+1;
     | | | a[t]:=i;
     | | | s:=s+i;
     | | | generate;
     | | | s:=s-i;
     | | | t:=t-1;
     | | end;
     | end;
     end;

᭮ ணࠬ  ⮬   ⠪:

     t:=1;
     for j:=1 to n do begin
     | a[1]:=j
     | s:=j;
     | generate;
     end;

     砭.    , 뭥 樨 㢥-
祭  㬥襭 t  横,  ⠪   s  ࠧ
 室 祭 ( 㢥稢   1    室-
 祭  ). ஬ ⮣,    䨪⨢  
a[0]=n,   ᭮ ணࠬ:

     t:=0; s:=0; a[0]:=n; generate;

     7.3.5.    ४ᨢ  ணࠬ 室 ॢ (-
     ஢ન,      室  -
).

     襭.  楤  ࠡ_ ࠡ뢠  
 ⥪饩 設  稢 ࠡ  ⮩  設,  
 砫.   ४ᨢ ᠭ:

     procedure ࠡ_;
     begin
     | if _ᢥ then begin
     | | _;
     | | ࠡ_;
     | | while _ࠢ do begin
     | | | ࠢ;
     | | | ࠡ_;
     | | end;
     | | ;
     | end else begin
     | | ࠡ;
     | end;
     end;

     7.4. 㣨 ਬ ४ᨨ

     ᪠ ஢. ।⠢  ᥡ  n  稭,
      뤠 ࠢ । .  ⨬
   ࠢ,  ᮡ  ࠭祭,  ⠭
稭.  ࠭祭   ⮬,    稭
 ᯨ᮪ ࠢ,  㦭 ᮡ  ।  饭  
.    ,  ᫨  奬  ᨬ⥩    横
(ࠢ  A     B, B  C,..., Y  Z  Z 
A). ।,  ⠪ 横 , ॡ ⠢ ,
㪠뢠騩    浪 祭 ࠢ.

     ࠦ 稭 窠,   ᨬ  -  ५,
室   ⠪ 㫨஢.  n 祪, ஭㬥஢
 1  n.   窨  ᪮쪮 (, 0) ५
 㣨 窨. ( ⨭ 뢠 ਥ஢  -
䮬.)   . ॡ ᯮ 設  (窨) 
⠪ 浪, ⮡   ५ ।⢮   -
.   뢠 ⮯᪮ ஢.

     7.4.1. ,   ᥣ .

     襭.    ᫮  ⢨ 横 ⥪,  
設,  ன   室 ५ (   -
    ५,   横).  㤥  -
. 모뢠  ५,   騥,   ᢮    
  訬 ᫮ 設  த 㦤  -
樨.

     7.4.2.  ।,    ਥ஢    横
࠭  ⠪ ଥ:   i  1  n  num[i] ࠭-
 ᫮ 室  i ५,  adr[i][1],..., adr[i][num[i]]
-  設, 㤠  ५ . ⠢ (४ᨢ)
,  ந ⮯ ஢   
祬  C*(n+m) ⢨,  m - ᫮ ॡ  (५).

     砭.  ।⢥  ॠ  ਢ 
⥫⢠ ⢮   ॡ㥬 業;  -
  ࠢ.

     襭.  ணࠬ 㤥      設.  
ᨢ  printed: array[1..n] of boolean  㤥 ࠭ ᢥ-
  ⮬,  設 ⠭ ( ४஢   -
६      設).  㤥 ,  ⠭
᫥⥫쭮 設 ४⭠, ᫨  設  -
⠭      i, 室饣   ᫥-
⥫쭮,   設,    ५  i, -
,  ⮬  i.

     procedure add (i: 1..n);
     | {: ⠭ ४⭮;}
     | {: ⠭ ४⭮  砥 設 i}
     begin
     | if printed [i] then begin {設 i 㦥 ⠭}
     | | {祣   }
     | end else begin
     | | {⠭ ४⭮}
     | | for j:=1 to num[i] do begin
     | | | add(adr[i][j]);
     | | end;
     | | {⠭ ४⭮,  設,   
     | |  i  ५, 㦥 ⠭ - ⠪  
     | |   i,   ४⭮}
     | |  if not printed[i] then begin
     | |  | writeln(i); printed [i]:= TRUE;
     | |  end;
     | end;
     end;

᭮ ணࠬ:

     for i:=1 to n do begin
     | printed[i]:= FALSE;
     end;
     for i:=1 to n do begin
     | add(i)
     end;

     7.4.3.    ਢ  ணࠬ   ஢,

          if not printed[i] then begin
          | writeln(i); printed [i]:= TRUE;
          end;

          writeln(i); printed [i]:= TRUE;
祬?   ᯥ䨪 楤?

     襭.  䨪   ⠪:
       : ⠭ ४⭮
       : ⠭ ४⭮  砥 設 i;
               ⠭ 設 㯭  i.

     7.4.4.  ᯮ짮  䠪,     横?

     襭.   ⨫ ⥫⢮ 筮 㡨 -
ᨨ.   設  ᬮਬ    "㡨"  -  -
    ५,   室饣.  ᫮  -
⢨ 横 ࠭,   稭 筠.  -
  㫥 㡨 ५  室. 㡨  ५ 
ࠩ   1 , 祬 㡨 砫.  ࠡ  -
  add(i)   ४ᨢ 맮 add(j) ⭮  設
襩 㡨.

     吝    .  ਥ஢  - 
祪 (設),    ᮥ  ﬨ  (ॡ-
). ਥ஢     砥 ਥ-
஢ ,  ஬   ५  ⭠.
     吝 ⮩ 設 i 뢠 ⢮  
設,      i,   ॡࠬ . (-
   ਥ஢, ⭮襭 "j ਭ 吝
 i"  ⭮襭 ⭮.)

     7.4.5.  ਥ஢  (  設  㪠-
  ᫮  ᥤ   ᨢ ஢ ᥤ,   ।饩
). ⠢ ,    i ⠥ 
設 吝  i   ࠧ ( ⮫쪮 ). ᫮
⢨   ॢ室 C*(饥 ᫮ 設  ॡ  
吝 ).

     襭.  ணࠬ     ࠡ 㤥 "訢"
 設 . 襭   㤥  -
 ,  ⠭, ᫨   襭 設 
騥   ॡ. 楤 add(i) 訢 吝 -
  i  襭  (   祣, ᫨ 設
i 㦥 襭).

     procedure  add (i:1..n);
     begin
     | if 設 i 襭 then begin
     | | 祣   
     | end else begin
     | |  i (    襭)
     | |   j, ᥤ  i
     | | | add(j);
     | | end;
     | end;
     end;

,   楤  ࠢ쭮 ( ।,
 ४ᨢ 맮 ࠡ ࠢ쭮).  ᠬ ,  -
, ஬ 吝  襭 ,  
  . ஢ਬ,    㤥 襭.  k - -
設, 㯭  設  i      i-j-...-k,  室饬
⮫쪮  襭 設. 㤥 ᬠਢ ⮫쪮 -
,    騥  ᭮   i.   ⠪ ⥩ 롥६
  訬 j ( 浪 ᬮ ᥤ  横   -
楤).      ᬮ७ । ᥤ   
設 j-...-k  㤥 襭 (  j    뫮    -
)  ⮬ k   吝  襭
   맮 add(j).   ॡ.
     ⮡ ⠭ 筮 㡨 ४ᨨ, ⨬,  
  ஢ ४ᨨ ᫮ 襭 設 㬥蠥
   1.
     業 ᫮ ⢨.  設 訢   -
   ࠧ -   맮 add(i)   i.  -
騥 맮 ந室  訢 ᥤ - ⢮
⠪  맮     ᫠ ᥤ -  ᢮  ஢થ
⮣,  設 i 㦥 襭.     맮  ⮨  
ᬮ    ᥤ    ४ᨢ 맮 add(j)  
.  ࠧ, 饥 ᫮ ⢨, 易    設
i,  ॢ室 ⠭, 㬭  ᫮  ᥤ. -
  ⥪ ॡ㥬 業.

     7.4.6.       ਥ஢  (-
  設, 㯭    ५;   -
 ᮤঠ 横).

     ⢥.          ணࠬ (ப "
 ᥤ"     "    設,  㤠  
५").

      ஢ .  祭 ਢ ४ᨢ
 ஢ ᨢ,   ࠪ⨪   
  ᠬ .   ᨢ a[1]..a[n]. ᨢ -
楤  sort (l,r:integer)  ⮪ ᨢ  ᠬ
 㨭ࢠ (l,r] (.. a[l+1]..a[r]),    ࠣ  -
⠫쭮 ᨢ.

     procedure sort (l,r: integer);
     begin
     | if (l = r) then begin
     | | 祣    - ⮪ 
     | end else begin
     | |  砩 ᫮ s  㨭ࢠ (l,r]
     | | b := a[s]
     | | ⠢  㥬 ⪠ ⠪, ⮡
     | |   ᭠砫 諨 , 訥 b - ⮪ (l,ll]
     | |   ⥬ , ࠢ b        - ⮪ (ll,rr]
     | |   ⥬ , 訥 b       - ⮪ (rr,r]
     | | sort (l,ll);
     | | sort (rr,r);
     | end;
     end;

⠭  ⮢  㥬  ⪠ ᬠਢ 
  ᨢ (  ᤥ   ६,  ய樮쭮
 ⪠). 筮 㡨 ४ᨨ  ࠭  ⥬,
     㥬  ⪠      ஢  ४ᨨ
㬥蠥    1.

     7.4.7. (   ᭮ ⥮ਨ ⭮⥩). -
,  ⥬᪮  ᫠ 権  ࠡ -
 ⬠  ॢ室 C*n*log n, 祬 ⠭ C  -
  㥬 ᨢ.

     .  T(n) -  ᨬ  ⥬᪮  
᫠  権   室  n.  ⥪ 楤 -
⥪ ⠪ ࠢ⢮:

     T(n) <= Cn + 1/n [㬬  ᥬ  k+l=(n-1) ᥫ T(k)+T(l)]

 童 ᮮ⢥ ।  ⮢    訥,
ࠢ   訥. ன 童 -  । ⥬᪮ -
   ਠ⮢ 砩 롮. (ண , -
 । ⮢   ࠢ,  ࠢ   
T(k)  T(l)   ᨬ T(x)  ᥬ x,  ॢ-
騬  k  l,    蠥 쭥訬 㦤.) 
樥  n 㦭 뢠 業 T(n)  <=  C'nlog  n.  
⮬      ᫥  ।  祭  x  log  x    ᥬ
x=1,..,n-1 㦭 ⥣஢ x lnx    lnx * d(x*x).
 筮 讬 C' 童 Cn  ࠢ   ॢ訢
  ⥣ࠫ x*x*d(ln x),  ⨢ 蠣 室.

     7.4.8.  ᨢ  n ࠧ 楫 ᥫ a[1]..a[n]
 ᫮ k. ॡ  k-  稭 ᫮  ⮬  -
,  ᤥ    C*n ⢨,  C -  ⠭,
   k.

     砭. ஢  祢  ࠧ  ᤥ
    C*n*log(n) ⢨. 祢 ᯮᮡ:  訩
, ⥬  ன, ⥬ ⨩,..., k- ॡ  -
浪  k*n ⢨,     (⠭  n 
 k).

      .    (  ࠪ᪨    ᯮ   -
⠭ ᫨誮 ) ᯮᮡ ᤥ  ⠪:
     . 쥬  ᨢ  n/5 㯯,     
5 ⮢.  㯯 㯮冷稬.
     .  ᬮਬ ।   㯯  ९襬  
ᨢ  n/5 ⮢.    ४ᨢ  맮  
।  稭  ⮣ ᨢ.
     .  ࠢ    ᥬ ⠬ 室 -
ᨢ:  ࠧ  訥   訥  (  ࠢ
). ⠢ ⢮   㣨,  㧭,     
  ⥩   室 ᪮ (k-)    
⠬  浪.
     . ਬ ४ᨢ    ࠭ .

       T(n)  -  ᨬ쭮   ᫮ ⢨, ᫨
 ᯮᮡ ਬ  ᨢ    祬 n ⮢  (k
   㣮).  業:
     T(n) <= Cn + T(n/5) + T(ਬ୮ 0.7n)
᫥ ᫠  ⠪:  ࠧ   -
  ᮤন   0.3n ⮢.  ᠬ , ᫨ x
-  ।   ।,  ਬ୮   । 
x.  ᫨  થ ।   x,    -
  x.  ᠬ  ࠩ  3/5   ⮢
 x.
        樨   業 T(n) <= Cn (-
 ஫  ⮬ ࠥ  ⥫⢮,  1/5 + 0.7 < 1).
