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NL?><5@ A;0940 4< T*  H  0޽h ? 33y___PPT10Y+D=' p= @B +K  0 rjp (   N   # %0e0e0?03>;>2>: 1w@   J!B@C:BC@K 40==KE 2> 2B>@8G=>9 ?0<OB8 &$@   # !0e0e0?!>45@68<>5 2  V"8?8G=K9 H01;>= @01>BK A >1J5:B>< E, E@0=OI5<AO =0 6QAB:>< 48A:5 8<55B A;54CNI89 284: T* x = (T*)malloc(sizeof(T)); Disk_Read(x); //?5@0F88, >1@0I0NI85AO 8/8;8 87<5=ONI85 ?>;O E if(isChanged(x)) { //5 B@51C5BAO, 5A;8 ?>;O E =5 87<5=O;8AL Disk_Write(x); } //@>G85 >?5@0F88, =5 87<5=ONI85 ?>;O E, "@@4@.A/AA(AA%A@W       /  '    &xQvw   >2?0B0 3 l(. >23>@>4, 2011 3.     NtO?><5@ A;0940 4< T*  H   0޽h ? 33y___PPT10Y+D=' p= @B +% 0 LD(  (  # Ps0e0e0?03>;>2>: 1w@   \B-45@52> @   # w0e0e0?!>45@68<>5 2qI  z-45@52LO ?@54AB02;ONB A>1>9 A8;L=> 25B2OI85AO A10;0=A8@>20==K5 45@52LO ?>8A:0, A>740==K5 A?5F80;L=> 4;O MDD5:B82=>9 @01>BK A 48A:>2>9 ?0<OBLN (8 4@C38<8 B8?0<8 2B>@8G=>9 ?0<OB8 A =5?>A@54AB25==K< 4>ABC?><). 0==K9 ?>4E>4 1K; ?@54;>65= 2 1972 3>4C . 095@>< 8 -. 0:-@59B><, 0 B0:65 =57028A8<> >B =8E . 0CD<0=><.> >@  *xQvw  >p?0B0 3 l(. >23>@>4, 2011 3.    N?><5@ A;0940 4< T*  H  0޽h ? 33y___PPT10Y+D=' p= @B ++ 0 RJ  (   (   # 0e0e0?03>;>2>: 1w@   \B-45@52> @    # 0e0e0?!>45@68<>5 2q,  -45@52LO - 5AB5AB25==>5 >1>1I5=85 18=0@=KE 45@52L52 ?>8A:0. 0 @8A. 3 ?@8254Q= ?@8<5@ -45@520. A;8 2=CB@5==89 C75; -45@520 A>45@68B n[E] :;NG59, B> C =53> n[E] + 1 4>G5@=8E C7;>2. ;NG8 2 C7;5 E 8A?>;L7CNBAO :0: @0745;8B5;8 480?07>=0 :;NG59, A :>B>@K<8 8<55B 45;> 40==K9 C75;, =0 n[E] + 1 ?>4480?07>=>2, :064K9 87 :>B>@KE >B=>A8BAO : >4=><C 87 4>G5@=8E C7;>2 E.o BBBBBBVBBGBBBD  | QxQvw   >?0B0 3 l(. >23>@>4, 2011 3.     Nhʦ?><5@ A;0940 4< T*   ~ (   3  c"$ N   S X99?(    C Ԧ"` 2? ]M$B @    C ٦"`8  aD H$B @    C ߦ"`H" e Q T X$  B @     C "`E   aB C$B @    C 8"`8 E   aF G$B @    C @"`E   e J K L$  B @     C "`E   aN P$B @    C $"`6E   aR S$B @    C $"` E #  aV W$B @    C "` %E X(  aY Z$B @ NB  B S D HNB   S DH NB  B S D G NB  B S D  E NB   S DE NB  B S DtkE NB  B S DkE NB   S D G"E NB   S D!&E :   B z  8A. 3. -45@52> A A>3;0A=K<8 0=3;89A:>3> 0;D028B0 2 :0G5AB25 :;NG59 "FD@@H   0޽h ? 33y___PPT10Y+D=' p= @B +Q  0 x p ( (  (, ( #  $0e0e0?03>;>2>: 1w@   `(?@545;5=85 -45@520@ ( # H20e0e0?!>45@68<>5 2  H-45@52>< c <8=8<0;L=>9 AB5?5=LN t (t e" 2) =07K205BAO 45@52>, C4>2;5B2>@ONI55 A2>9AB20<: 1. 064K9 2=CB@5==89 C75;, =5 O2;ONI89AO :>@=52K<, 8<55B :0: <8=8<C< t 4>G5@=8E C7;>2 8 =5 1>;55 2t 4>G5@=8E C7;>2. 2. >@5=L, 5A;8 =5 O2;O5BAO ;8AB><, 8<55B <8=8<C< 2-CE ?>B><:>2. 3. A5 ;8ABLO @0A?>;>65=K =0 >4=>9 8 B>9 65 3;C18=5, :>B>@0O @02=0 2KA>B5 45@520 h. 4. 5;8AB>2>9 C75; A k ?>B><:0<8 A>45@68B k-1 :;NG59. @@@@@@@~@@@@@3@@\@@@@@ @@ @l ! b  "     qQfvgw@ ( >=?0B0 3 l(. >23>@>4, 2011 3.   ( N?><5@ A;0940 4< T*  H ( 0޽h ? 33y___PPT10Y+D=' p= @B +  0   ,< (  ,, , # j0e0e0?03>;>2>: 1w@   `(?@545;5=85 -45@520@ , # u0e0e0?!>45@68<>5 2  F\5. 064K9 C75; E A>45@68B A;54CNI85 ?>;O: 0) n[E] , :>;8G5AB2> :;NG59, E@0=OI8EAO 2 =0AB>OI89 <><5=B 2 C7;5 E. 1) !>1AB25==> :;NG8, :>;8G5AB2> :>B>@KE @02=> n[E] 8 :>B>@K5 E@0=OBAO 2 =52>7@0AB0NI5< ?>@O4:5, B0: GB> key1[x] d" key2[E] d" & d" keyn[x][E]. 2) >38G5A:>5 7=0G5=85 leaf[E], @02=>5 TRUE, 5A;8 E O2;O5BAO ;8AB><, 8 FALSE, 5A;8 E  2=CB@5==89 C75;. 3) n[E] +1 C:070B5;59 c1[E], c2[E] ,..., cn[x]+1[E] =0 4>G5@=85 C7;K. 8 @@@@;@@1@@6@@H @H@@@H@@@@ @@@@@@@@@@@ @@H@@@H@@@H@@p,  =  +  8       E       qQfvgw@ , >?0B0 3 l(. >23>@>4, 2011 3.   , Nh?><5@ A;0940 4< T*  H , 0޽h ? 33y___PPT10Y+D=' p= @B +3  0 Z R 0 (  0 0 # 0e0e0?03>;>2>: 1w@   NKA>B0 -45@520@ 0 # Я0e0e0?!>45@68<>5 2  @8254Q< >F5=:C 2KA>BK -45@520 2 =08EC4H5< A;CG05. "5>@5<0. KA>B0 -45@520 " A n e" 1 C7;0<8 8 <8=8<0;L=>9 AB5?5=LN t e" 2 =5 ?@52KH05B logt(n + 1)/2. >;8G5AB2> >1@0I5=89 : 48A:C, =5>1E>48<>5 4;O 2K?>;=5=8O 1>;LH8=AB20 >?5@0F89 A -45@52><, ?@>?>@F8>=0;L=> 53> 2KA>B5. A8<?B>B8G5A:85 >F5=:8 2KA>BK ;N1>3> 18=0@=>3> A10;0=A8@>20==>3> 45@520, =0?@8<5@ -45@520, 8 B-45@520 A>2?040NB, >4=0:> =0 ?@0:B8:5 2KA>B0 B-45@520 >:07K205BAO 2 =5A:>;L:> @07 <5=LH5 70 AGQB 2K1>@0 1>;LH>3> >A=>20=8O ;>30@8D<0, GB> 8 >1JOA=O5B 8A?>;L7>20=85 B-45@52L52 2 0;3>@8B<0E, @01>B0NI8E A 2=5H=59 ?0<OBLN.K 5@@@@@@@@@@H @@R     , u 5qQfvgw@ 0 >$?0B0 3 l(. >23>@>4, 2011 3.   0 Nh?><5@ A;0940 4< T*  H 0 0޽h ? 33y___PPT10Y+D=' p= @B +?  0 f ^ $ (  $ $ #  0e0e0?03>;>2>: 1w@   NKA>B0 -45@520@ $ # "0e0e0?!>45@68<>5 2  'B>1K <8=8<878@>20BL :>;8G5AB2> 2K?>;=O5<KE >?5@0F89 A 48A:>< Disk_Read 8 Disk_Write, 65;0B5;L=> <8=8<878@>20BL 8E :>;8G5AB2> ?@8 @01>B5 A :>=:@5B=K< C7;>< B-45@520 8 70 >48= @07 AG8BK20BL 8 70?8AK20BL :0: <>6=> 1>;LH5 8=D>@<0F88. 07<5@ C7;0 -45@520 >1KG=> A>>B25BAB2C5B 48A:>2>9 AB@0=8F5, 0 :>;8G5AB2> ?>B><:>2 C7;0 -45@520 >3@0=8G8205BAO @07<5@>< 48A:>2>9 AB@0=8FK. ;O 1>;LH8E -45@52L52, E@0=OI8EAO =0 48A:5, AB5?5=L 25B2;5=8O >1KG=> =0E>48BAO <564C 50 8 2000, 2 7028A8<>AB8 >B @07<5@0 :;NG0 >B=>A8B5;L=> @07<5@0 AB@0=8FK. >;LH0O AB5?5=L 25B2;5=8O @57:> A=8605B :0: 2KA>BC 45@520, B0: 8 :>;8G5AB2> >1@0I5=89 : 48A:C 4;O ?>8A:0 :;NG0.  >@ @@ @ @@w@@@@@@0  xQvw $ >%?0B0 3 l(. >23>@>4, 2011 3.   $ N 8?><5@ A;0940 4< T*  H $ 0޽h ? 33y___PPT10Y+D=' p= @B + 0 <44 (  4& 4 # H0e0e0?03>;>2>: 1w@   Z">8A: 2 -45@525 @  4 # ܃0e0e0?!>45@68<>5 2l TL___PPT9.& @>F54C@0 B_Tree_Search(x, k) 2 :0G5AB25 ?0@0<5B@>2 ?>;CG05B C:070B5;L =0 :>@=52>9 C75; E ?>445@520 8 :;NG k, :>B>@K9 A;54C5B =09B8 2 MB>< ?>445@525. 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A;8 >= =0945=, B> 2>72@0I05< (x, i). @>F54C@0 ;81> 7025@H05B A2>N @01>BC =5C40G59 (5A;8 E O2;O5BAO ;8AB><), ;81> @5:C@A82=> 2K7K205B A51O 4;O ?>8A:0 2 A>>B25BAB2CNI5< ?>445@525 E (?>A;5 2K?>;=5=8O GB5=8O A 48A:0 =5>1E>48<>3> 4>G5@=53> C7;0, O2;ONI53>AO :>@=5< 8AA;54C5<>3> ?>445@520). @>F54C@0 25@=5B C?>@O4>G5==CN ?0@C (C, i), B0:CN, GB> y  C75; 45@520, AG8B0==K9 2 >?5@0B82=CN ?0<OBL, 0 keyi[y] = k.  ?@>B82=>< A;CG05 ?@>F54C@0 25@=5B 7=0G5=85 NULL. 6  q @@:@@@@)@@-BB B BBBBBBBBB5BBXBBjBB$@@@@2@@H@/@@@R  O X         &  0   / qQ3Cd 4 >?0B0 3 l(. >23>@>4, 2011 3.   4 ND?><5@ A;0940 4< T*  H 4 0޽h ? 33y___PPT10Y+D=' = @B + 0 808(  8& 8 # 0e0e0?03>;>2>: 1w@   Z">8A: 2 -45@525 @ 8 >ð?0B0 3 l(. >23>@>4, 2011 3.   8 Nt?><5@ A;0940 4< T*   8 J?!>45@68<>5 2q >;8G5AB2> 48A:>2KE AB@0=8F, : :>B>@K< 2K?>;=O5BAO >1@0I5=85 ?@>F54C@>9 B_Tree_Search, @02=> (h) =  (logt n), 345 h  2KA>B0 -45@520, a n  :>;8G5AB2> A>45@60I8EAO 2 =5< C7;>2. >A:>;L:C n[E] < 2t, >1I55 2@5<O 2KG8A;5=89 A>AB02;O5B  (th) = O(tlogt n).  H@ @@ @H@@@@@1@ @$@@H@@l   !    qQ3CdZ 8 c $X99?"`  8 0ذVVs33"`  ]M$B @   8 0貰VVs"` s  aD H$B @   8 0tVVs33"` B  e Q T X$  B @    8 0VVs"` Ij  aB C$B @   8 0VVs"` sj  aF G$B @   8 0 VVs"`  j  e J K L$  B @   8 04VVs"`  j  aN P$B @  8 0䡰VVs33"` H j  aR S$B @  8 0VVs"` qj  aV W$B @  8 0VVs"` :j  aY Z$B @ LB 8@ c $DB XB 8 0D3fjJ " LB 8@ c $D  LB 8@ c $D BB LB 8 c $D  LB 8@ c $D ] XB 8@ 0D3fjJ ] LB 8 c $D rA LB 8 c $D j  8 0 I X 8A. 4. 0?@>AK 2 B-45@525 5;Q=K< F25B>< 2K45;5=K C7;K, ?@>A<>B@5==K5 2 ?@>F5AA5 ?>8A:0 :;NG0 R. Hc 2@D33=@@@( N H 8 0޽h ? 33y___PPT10Y+D=' = @B +O  0 v n < (  <6 < # @)0e0e0?03>;>2>: 1w@   j2AB02:0 :;NG0 2 -45@52> @ < # 0e0e0?!>45@68<>5 2j  F@8 2AB02:5, :0: 8 2 A;CG05 18=0@=KE 45@52L52 ?>8A:0, <K 8I5< ?>78F8N ;8AB0, 2 :>B>@K9 1C45B 2AB02;5= =>2K9 :;NG. 4=0:> ?@8 @01>B5 A -45@52>< <K =5 <>65< ?@>AB> A>740BL =>2K9 ;8AB 8 2AB028BL 2 =53> :;NG, ?>A:>;L:C B0:>5 45@52> =5 1C45B O2;OBLAO :>@@5:B=K< -45@52><. <5AB> MB>3> <K 2A5340 2AB02;O5< =>2K9 :;NG 2 ACI5AB2CNI89 ;8AB. >A:>;L:C 2AB028BL =>2K9 :;NG 2 70?>;=5==K9 ;8AB =52>7<>6=>, <K 22>48< =>2CN >?5@0F8N  @07185=85 (splitting) 70?>;=5==>3> (B.5. A>45@60I53> 2t  1 :;NG59) C7;0 =0 420, :064K9 87 :>B>@KE A>45@68B ?> t  1 :;NG59. `$ @ @+@@4@@ @ GqQ3Cd < >=?0B0 3 l(. >23>@>4, 2011 3.   < NK?><5@ A;0940 4< T*  H < 0޽h ? 33y___PPT10Y+D=' = @B +  0 . & @ (  @4 @ # g0e0e0?03>;>2>: 1w@   h0 07185=85 C7;0 -45@520 @ @ # j0e0e0?!>45@68<>5 2j  ,@>F54C@0 B_Tree_Split_Child ?>;CG05B 2 :0G5AB25 2E>4=>3> ?0@0<5B@0 =570?>;=5==K9 2=CB@5==89 C75; E (=0E>4OI89AO 2 >?5@0B82=>9 ?0<OB8), 8=45:A i 8 C75; C (B0:65 =0E>4OI89AO 2 >?5@0B82=>9 ?0<OB8), B0:>9 GB> C = Ai[E] O2;O5BAO 70?>;=5==K< 4>G5@=8< C7;>< E. @>F54C@0 @0718205B 4>G5@=89 C75; =0 420 8 A>>B25BAB2CNI8< >1@07>< >1=>2;O5B ?>;O E, 2=>AO 2 =53> 8=D>@<0F8N > =>2>< 4>G5@=5< C7;5. ;O @07185=8O 70?>;=5==>3> :>@=52>3> C7;0 <K A=0G0;0 45;05< :>@5=L 4>G5@=8< C7;>< =>2>3> ?CAB>3> :>@=52>3> C7;0, ?>A;5 G53> <>65< 8A?>;L7>20BL 2K7>2 B_Tree_Split_Child. @8 MB>< 2KA>B0 45@520 C25;8G8205BAO =0 1. 07185=85  548=AB25==>5 A@54AB2> C25;8G5=8O 2KA>BK -45@520.   @@F@@,@@@@5@@H@%@@@R@@!@@@j@D C + qQ3Cd @ >n?0B0 3 l(. >23>@>4, 2011 3.   @ NL?><5@ A;0940 4< T*  H @ 0޽h ? 33y___PPT10Y+D=' = @B +2 0 11OODz1(  D4 D # О0e0e0?03>;>2>: 1w@   h0 07185=85 C7;0 -45@520 @ D >ب?0B0 3 l(. >23>@>4, 2011 3.   D N?><5@ A;0940 4< T*  L D 6 DzF q  8A. 5. 07185=85 C7;0 A <8=8<0;L=>9 AB5?5=LN t = 4 0?>;=5==K9 C75; C @0718205BAO <5480=>9 S, :>B>@0O ?5@5<5I05BAO 2 @>48B5;LA:89 C75;. "5 :;NG8 87 C, :>B>@K5 1>;LH5 <5480=K, ?><5I0NBAO 2 =>2K9 C75; z, :>B>@K9 AB0=>28BAO =>2K< 4>G5@=8< C7;>< E. B,@@@@D338@@2@@*@@@0 X *~ * 7: D3  c"$T N D S X99?* 7: D C $ʲ"`#:? v & N W & "B@   D C Ѳ"` V  P Q R S T U V BBF33 B@ NB  D S D   D C Lײ"`FN  keyi-1[x]@ BJB@    D C Tܲ"`  keyi[x]@BJB@ HB  D C D2#HB DB C Dj# D C "` j   y = c i[x]@ BJB@  fB D 6D8c  " ~N TGp D TGpNB D S DbGc D C "`Tp lT12B J @ h TGp D# #" GNB D S DbGc D C |"`Tp lT22B J @ h TGp D# #" ~GNB D S DbGc D C "`Tp lT32B J @ h TGp D# #" "G>NB D S DbGc D C "`Tp lT42B J @ h TGp D# #" GNB D S DbGc D C  "`Tp lT52B J @ h TGp  D# #" .GJNB !D S DbGc "D C "`Tp lT62B J @ h TGp #D# #" GNB $D S DbGc %D C "`Tp lT72B J @ h TGp &D# #" :GVNB 'D S DbGc (D C "`Tp lT82B J @  )D C "` [x"B@  *D C $"`J(#3? * & N S W & B BF33B@  +D C *"`& 6- h P Q R "B@ NB ,DB S D),  -D C /"`z%+  keyi-1[x]@ BJB@   .D C p6"`+"2 keyi[x]@BJB@ HB /D C D)+#HB 0DB C D--# 1D C >"`$ f*   y = c i[x]@ BJB@  h TGp 2D# #" &G(NB 3D S DbGc 4D C D"`Tp lT12B J @ h TGp 5D# #" 'G*NB 6D S DbGc 7D C J"`Tp lT22B J @ h TGp 8D# #" )G+NB 9D S DbGc :D C P"`Tp lT32B J @ h TGp ;D# #" V+Gr-NB D C ^"`y&p( [x"B@  ?D C c"`"2v8  keyi+1[x]@ BJB@  HB @DB C D0"2# AD C j"`R/ 4 d T U V " B@  NB BD S D."2 h TGp CD# #" .G0NB DD S DbGc ED C p"`Tp lT52B J @ h TGp FD# #" Q0Gm2NB GD S DbGc HD C Dv"`Tp lT62B J @ h TGp ID# #" 1G3NB JD S DbGc KD C t|"`Tp lT72B J @ h TGp LD# #" ]3Gy5NB MD S DbGc ND C "`Tp lT82B J @  OD C "`"2 :   z = ci+1[x] @ BJB@  H D 0޽h ? 33y___PPT10Y+D=' = @B + 0 HH(  HJ H # 0e0e0?03>;>2>: 1w@   ~FAB02:0 :;NG0 2 =570?>;=5==K9 C75; $"@  H # |0e0e0?!>45@68<>5 2j h`___PPT9B: FA?><>30B5;L=0O ?@>F54C@0 B_Tree_Insert_Nonfull(x, k) 2AB02;O5B :;NG k 2 C75; E, :>B>@K9 4>;65= 1KBL =570?>;=5==K< ?@8 2K7>25 ?@>F54C@K. A;8 E O2;O5BAO ;8AB><, B>340 :;NG k ?@>AB> 2AB02;O5BAO 2 40==K9 ;8AB E ?CBQ< >BKA:0=8O ?>78F88 2AB02:8 MB>3> :;NG0. >A;5 87<5=5=8O ?>;59 MB>3> C7;0 2K?>;=O5< 48A:>2CN >?5@0F8N Disk_Write(x). =0G5 ?@545;O5< 4>G5@=89 C75; E, 2 :>B>@K9 A?CAB8BAO @5:C@A8O (?CABL MB> C75; ci[x]). K?>;=O5< 48A:>2CN >?5@0F8N Disk_Read(ci[x]). A;8 C75; ci[x] 70?>;=5=, B>340 @0718205< 53> =0 420 =570?>;=5==KE C7;0 ?CBQ< 2K7>20 ?@>F54C@K B_Tree_Split_Child(x, i, ci[x]) 8 >?@545;O5<, 2 :0:>9 87 42CE ?>;CG82H8EAO 2 @57C;LB0B5 @07185=8O C7;>2 4>;6=0 A?CAB8BLAO @5:C@A8O. 5:C@A82=> 2K7K205< ?@>F54C@C B_Tree_Insert_Nonfull(ci[x], k) 4;O 2AB02:8 k 2 A>>B25BAB2CNI55 ?>445@52>.  q qBBBBBBB BBF3F3BBBF3BB"BBkB BBBF3 B  B . B  B  J  B  B   B  J  B  B  F  B  B  J  B  B  F @ B  B  J  B   d B    B  B  J  B    B  B  B         C $        b        qQ3Cd H >?0B0 3 l(. >23>@>4, 2011 3.   H N ?><5@ A;0940 4< n*  H H 0޽h ? 33y___PPT10Y+D=' = @B +] 0 | L(  L6 L # /0e0e0?03>;>2>: 1w@   j2AB02:0 :;NG0 2 -45@52> @  L # 0e0e0?!>45@68<>5 2jD,  ;O 2AB02:8 :;NG0 k 2 B-45@52> " 2KA>BK h <K 2>A?>;L7C5<AO ?@>F54C@>9 B_Tree_Insert(T, k). 1. r ! root[T] 2. A;8 :>@5=L 45@520 T 70?>;=5=, B.5. n[r] = 2t-l, B>340: 1) K45;O5< 48A:>2CN AB@0=8FC 4;O =>2>3> C7;0 s. 2) root[T] ! s , leaf[s] ! FALSE, n[s] ! 0, ci [s] ! r 0?>;=O5< ?>;O =>2>3> C7;0 s. #75; s (C :>B>@>3> 420 4>G5@=8E C7;0) 45;05< =>2K< :>@=5< -45@520. 3) K7K205< ?@>F54C@C B_Tree_Split_Child(s, 1, r) 4;O 30@0=B88 B>3>, GB> @5:C@A8O =8:>340 =5 AB>;:=5BAO A 70?>;=5==K< C7;><. 4) K7K205< ?@>F54C@C B_Tree_Insert_Nonfull(s, k), 2K?>;=ONICN 2AB02:C :;NG0 k 2 45@52> A =570?>;=5==K< :>@=5< s. =0G5 2K7K205< ?@>F54C@C B_Tree_Insert_Nonfull (r, k), 2K?>;=ONICN 2AB02:C :;NG0 k 2 45@52> A =570?>;=5==K< :>@=5< r. N BB BBBBBBBBB BBBF3BBBB BF30BBB BBBBJBBBB>BBBMBBB#BB)B BF3BBB!BB   "          7       y c # ) "  !  Q L >J?0B0 3 l(. >23>@>4, 2011 3.   L NlU?><5@ A;0940 4< n*  H L 0޽h ? 33y___PPT10Y+D=' = @B +X/ 0 .w.0FFP.(  P6 P # H0e0e0?03>;>2>: 1w@   j2AB02:0 :;NG0 2 -45@52> @> P # x70e0e0?!>45@68<>5 2jD<`  pAB02:0 :;NG0 k 2 -45@52> T 2KA>BK h 2K?>;=O5BAO 70 >48= =8AE>4OI89 ?@>E>4 ?> 45@52C, B@51CNI89 (h) >1@0I5=89 : 48A:C. 5>1E>48<>5 ?@>F5AA>@=>5 2@5<O A>AB02;O5B (th) = (tlogtn). 07185=85 :>@=O (@8A. 9)  548=AB25==K9 ?CBL C25;8G5=8O 2KA>BK -45@520.  >B;8G85 >B 18=0@=KE 45@52L52 ?>8A:0, C -45@52L52 2KA>B0 C25;8G8205BAO "A25@EC", 0 =5 "A=87C". d BB BBBB<BB?BBJBBB   F >    qQ3Cd P >&?0B0 3 l(. >23>@>4, 2011 3.   P NPƴ?><5@ A;0940 4< n*  9$~ 7 P3  c"$2tN P S X99?7 P S @ѴP"`. J   A D F H L N P "B@(  NB  P S D~N fB  P 6D8c& $ N TGp  P T pNB  P S DbGc  P S ״ P"`Tp lT12B J @ h TGp P# #"  NB P S DbGc P S t,P"`Tp lT22B J @ h TGp P# #" ~ NB P S DbGc P S dP"`Tp lT32B J @ h TGp P# #" " >NB P S DbGc P S P"`Tp lT42B J @ h TGp P# #"  NB P S DbGc P S $P"`Tp lT52B J @ h TGp P# #" . JNB P S DbGc P S TP"`Tp lT62B J @ h TGp P# #"  NB P S DbGc P S P"`Tp lT72B J @ h TGp  P# #" : VNB !P S DbGc "P S "P"`Tp lT82B J @  #P S #P"`?[  [r"B@  $P S $$P"`,#R/? ]H$B@  %P S %P"`& 6- h A D F "B@ NB &PB S D),  'P S  'P"`'. aroot[T]"B@ NB (P S D+-# )P S )P"`' )  [r"B@ h TGp *P# #" &G(NB +P S DbGc ,P S ,P"`Tp lT12B J @ h TGp -P# #" 'G*NB .P S DbGc /P S /P"`Tp lT22B J @ h TGp 0P# #" )G+NB 1P S DbGc 2P S T 2P"`Tp lT32B J @ h TGp 3P# #" V+Gr-NB 4P S DbGc 5P S ,&5P"`Tp lT42B J @  6P S 6P"`r-40P [s"B@  7P S L07P"`R/ 4 e L N P " B@  NB 8P S D."2 h TGp 9P# #" .G0NB :P S DbGc ;P S 5;P"`Tp lT52B J @ h TGp P S ;>P"`Tp lT62B J @ h TGp ?P# #" 1G3NB @P S DbGc AP S (BAP"`Tp lT72B J @ h TGp BP# #" ]3Gy5NB CP S DbGc DP S tJDP"`Tp lT82B J @  EP S tOEP"`#j? aroot[T]"B@ < FP BT j 8A. 9 07185=85 :>@=O A <8=8<0;L=>9 AB5?5=LN t = 4  64@@ 0H P 0޽h ? 33y___PPT10Y+D=' = @B +X 0 w@))T(  T6 T # j0e0e0?03>;>2>: 1w@   j2AB02:0 :;NG0 2 -45@52> @ T >0n?0B0 3"`  l(. >23>@>4, 2011 3.   T Nw?><5@ A;0940 4< n*   T 6 N z 8A. 10. AB02:0 :;NG0 L 2 -45@52> A <8=8<0;L=>9 AB5?5=LN 3. #7;K, 87<5=O5<K5 2 ?@>F5AA5 2AB02:8, 2K45;5=K 75;Q=K< F25B><.  40==>< ?@8<5@5 ?@>8AE>48B >1@07>20=85 =>2>3> :>@=O, 0 A :>@=5< 8AE>4=>3> 45@520 ?@>8AE>48B @0AI5?;5=85.X@F3%@1@D33s@0 &  ~ "2c T3  c"$'GH T C X?"2c T S T"`r  s G M P T X"B @   T S   T"` F mA B C D E$B @   T S @ T"`E } aJ K$B @   T S < T"` ! h Q R S $  B @    T S   T"`" .' aU V$B @ 6B  TB   [  6B TB  [  6B T  :[  6B T  [ z%  T S T"`  aN O$B @ 6B TB  [   T S 쬵T"`J( , aY Z$B @ 6B T   )  ~ S"2c T3  c"$P H T C X?S"2c T C 33"` ]P$B @  T C t33"`v   aG M$B @  T C 33"`" '  aT X$B @  T C \õ"` Z  mA B C D E$B @  T C ǵ33"` b m J K L, B F3   T C <͵"`  " e Q R S$  B @   T C ҵ"`$ K( aU V$B @  T C ׵"`) - aY Z$B @ 6B TB   "j 6B  T  "$ 6B !TB   * 6B "TB    6B #TB   ^# 6B $T  !% .& 6B %T  & +  &T C  v"`~  aN O$B @ 6B 'T     (T s BC#DEFjJ^.s'#@  "`67  )T 0"  x2AB02:0 L& 2@D3 H T 0޽h ? 33y___PPT10Y+D=' = @B +m  0   PX$ (  X: X # D0e0e0?03>;>2>: 1w@   n6#40;5=85 :;NG0 87 -45@520 @ X # h_0e0e0?!>45@68<>5 2j  K 4>;6=K >15A?5G8BL, GB>1K ?@8 2K?>;=5=88 >?5@0F88 C40;5=8O C75; =5 AB0=>28BAO A;8H:>< <0;> 70?>;=5= (70 8A:;NG5=85< :>@=52>3> C7;0, :>B>@K9 <>65B 8<5BL <5=55 t  1 :;NG59). B0:, ?CABL ?@>F54C@0 B_Tree_Delete 4>;6=0 C40;8BL :;NG k 87 ?>445@520, :>@=5< :>B>@>3> O2;O5BAO C75; E. @8 5Q @5:C@A82=>< 2K7>25 4;O C7;0 E 30@0=B8@>20=> =0;8G85 2 MB>< C7;5 ?> :@09=59 <5@5 t :;NG59. -B> CA;>285 B@51C5B =0;8G8O 2 C7;5 1>;LH53> :>;8G5AB20 :;NG59, G5< <8=8<0;L=>5 2 >1KG=>< -45@525, B0: GB> 8=>340 :;NG <>65B 1KBL ?5@5<5I5= 2 4>G5@=89 C75; ?5@54 B5<, :0: @5:C@A8O >1@0B8BAO : MB><C 4>G5@=5<C C7;C. "0:>5 C65AB>G5=85 A2>9AB20 -45@520 (=0;8G85 "70?0A=>3>" :;NG0) 405B =0< 2>7<>6=>ABL 2K?>;=8BL C40;5=85 :;NG0 70 >48= =8AE>4OI89 ?@>E>4 ?> 45@52C.  4@@d@@ @@ @@@-@@%@@3@@L@ @@ qQ3Cd X >?0B0 3 l(. >23>@>4, 2011 3.   X Nx?><5@ A;0940 4< n*  H X 0޽h ? 33y___PPT10Y+D=' = @B +# 0 # #`44\"(  \: \ # /0e0e0?03>;>2>: 1w@   n6#40;5=85 :;NG0 87 -45@520 @ \ # C0e0e0?!>45@68<>5 2j  . 0AA<>B@8< @07;8G=K5 2>7=8:0NI85 ?@8 C40;5=88 :;NG0 A8BC0F88. 1. A;8 :;NG k =0E>48BAO 2 C7;5 E 8 E O2;O5BAO ;8AB><  C40;O5< k 87 E.  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"` ]P$B @   \ s *,d  "` b  e C G M$  B @    \ s *h  "`" '  aT X$B @   \ s *l  "` = aA B$B @   \ s *Xq  "` F m D E F, B F3    \ s *v  "` N e J K L$  B @   \ s *T{  "`  " e Q R S$  B @   \ s *X  "`$ K( aU V$B @  \ s *  "`) - aY Z$B @ 6B \B   "j 6B \  "$ 6B \B  " v 6B \B  v  6B \  F ~ 6B \B   ^# 6B \  !% .& 6B \  & +  \ s *d  "`  aN O$B @ 6B \     ~ S.c \3  c"$ =V \ C X?"`S.c \ s *D  "` ]P$B @  \ s *  "` b  e C G M$  B @   \ s *  "`" '  aT X$B @   \ s *  "` = aA B$B @  !\ s *  33"` F cD E $B @  "\ s *  "` N e J K L$  B @   #\ s *  "`  " e Q R S$  B @   $\ s *  "`$ K( aU V$B @  %\ s *  "`) - aY Z$B @ 6B &\B   "j 6B '\  "$ 6B (\B  " v 6B )\B  v  6B *\  F ~ 6B +\B   ^# 6B ,\  !% .& 6B -\  & +  .\ s *P  "`  aN O$B @ 6B /\     0\@ s BC#DEFjJ^.s'#@  "`}Z  1\@ 0ŸF zC40;5=85 F& 2 @D3   2\ 6˸ T=  8A. 11. #40;5=85 C7;0 F 87 -45@520 A <8=8<0;L=>9 AB5?5=LN 3. >48D8F8@C5<K5 C7;K ?>:070=K 75;Q=K< F25B><. Tm @@D3D@D33 @0  T 3\ 0Ըu  :E 2D 4\ 0<ٸJ ]  1  :E 2DH \ 0޽h ? 33y___PPT10Y+D=' = @B +( 0 ''p99`'(  `: ` # 0e0e0?03>;>2>: 1w@   n6#40;5=85 :;NG0 87 -45@520 @ ` # 0e0e0?!>45@68<>5 2jD  2.0) A;8 4>G5@=89 ?> >B=>H5=8N : 2=CB@5==5<C C7;C E C75; C, ?@54H5AB2CNI89 :;NGC k 2 C7;5 E, A>45@68B =5 <5=55 t :;NG59, B> =0E>48< k`  ?@54H5AB25==8:0 k 2 ?>445@525, :>@=5< :>B>@>3> O2;O5BAO C. 5:C@A82=> C40;O5< k` 8 70<5=O5< k 2 E :;NG>< k`. * 3@D@@@@@D@@@@@@'@@@@ @@@D@@@R    =     qQ3Cd ` >"?0B0 3 l(. >23>@>4, 2011 3.   ` N,?><5@ A;0940 4< n*   ~ S.c `3  c"$"LZ V ` C X?"`S.c ` s *$:  "` ]P$B @   ` s *H;  "` b  m C G M, B F 3    ` s *C  "`" '  aT X$B @   ` s *D  "` = aA B$B @   ` s *8I  "` F YD E B    ` s *HM  "` N m J K L, B F   ` s *Q  "`  " e Q R S$  B @   ` s *xV  "`$ K( aU V$B @  ` s *|[  "`) - aY Z$B @ 6B `B   "j 6B `  "$ 6B `B  " v 6B `B  v  6B `  F ~ 6B `B   ^# 6B `  !% .& 6B `  & +  ` s *\a  "`  aN O$B @ 6B `     `@ s BC#DEFjJ^.s'#@  "`}Z  `@ 0fF zC40;5=85 M& 2 @D3   ` 6l T=  8A. 12. #40;5=85 C7;0 M 87 -45@520 A <8=8<0;L=>9 AB5?5=LN 3. >48D8F8@C5<K5 C7;K ?>:070=K 75;Q=K< F25B><. Tm @@D3D@D33 @0  T ` 0vV!= :E 2DF 1  `  V  ` C X?"`1  !` 0z  "`G h  ]P$B @ 0 F  x  "`  j  #` s *  33"` b  m C G L, B F   $` s *  "` b  aT X$B @  %` s *  "`   aA B$B @  &` s *  "`   dD E $ B @  '` s *h  33"`2  v  aJ K$B @  (` s *d  "`i   e Q R S$  B @   )` s *̟  "`   aU V$B @  *` s *Ȥ  "`5 x  aY Z$B @ 6B +`B    6B ,`  &  6B -`B  u , $  6B .`B  $ ,  6B /`   ,  6B 0`B  A, O 6B 1`  , ' 6B 2`  ],   3` s *  "`  %  aN O$B @ 6B 4`  h ,   5` 0gf  Qy 2@ , 6` 6( W   2k` (L  ?@54H5AB25==8: M)dBFBF3B  RB 7` s *D J  8` 0ܽ k   :E 2D 9` 0|M 4  Qy 2@ H ` 0޽h ? 33y___PPT10Y+D=' = @B +& 0 &&66d%(  d: d # 0e0e0?03>;>2>: 1w@   n6#40;5=85 :;NG0 87 -45@520 @ d # 0e0e0?!>45@68<>5 2jDP  2.1) A;8 4>G5@=89 ?> >B=>H5=8N : E C75; z, A;54CNI89 70 :;NG>< k 2 C7;5 E, A>45@68B =5 <5=55 t :;NG59, B> =0E>48< k` A;54CNI89 70 k :;NG 2 ?>445@525, :>@=5< :>B>@>3> O2;O5BAO z. 5:C@A82=> C40;O5< k` 8 70<5=O5< k 2 E :;NG>< k`.2 "@D@@@@@D@@@@@@,@@@@ @@@D@@@)     ,      qQ3Cd d >?0B0 3 l(. >23>@>4, 2011 3.   d N?><5@ A;0940 4< n*   d s *P  "`A   m M N O, FB    F 8  d }'  d s *  "`0 ]P$B @   d s *8   "`9 m C G L, B F 3    d s *  "` /  aT X$B @   d s *  "`8L {  aA B$B @   d s *  "`L   [ D E F  B     d s *  "`L   WJ KB   d s *#  "` L  e Q R S$  B @   d s *(  "` L d  aU V$B @  d s *-  "` L   aY Z$B @ 6B dB  aU6B d  V 6B dB  tL 6B dB  t,L 6B d  tL 6B dB   t L 6B d  r t L 6B d   tr L 6B d  tL  d@ s BC#DEFjJ^.s'#@  "`}Z  d@ 0x5F zC40;5=85 L& 2 @D3   d 68; T=  8A. 13. #40;5=85 C7;0 L 87 -45@520 A <8=8<0;L=>9 AB5?5=LN 3. >48D8F8@C5<K5 C7;K ?>:070=K 75;Q=K< F25B><. Tm @@D3D@D33 @0  T d 0pGu  Qz 2@  d 0MH_/ :E 2D* d 6X |T +  2k` (L  ?@54H5AB25==8: M)bBF3BDB  RB  d s *D w N !d C X?"`   "d s *\Y  "` H   ]P$B @  #d s *H  33"` ~ A  m C G M, B F   $d s *b  "` W5  aT X$B @  %d s *g  "`  y  aA B$B @  &d s *p  "` G y  e D E F$  B @   'd s *s  "` # g z  aJ K$B @  (d s *|  "` -y  e Q R S$  B @   )d s *@  "` Iy  aU V$B @  *d s *8  "` <y  aY Z$B @ .B +d@   ~ .B ,d    .B -d@   9 .B .d@   U .B /d   .B 0d@    .B 1d    .B 2d   !  3d s *  33"`   aN O$B @ .B 4d   , H  5d 0t 8  :E 2D 6d 0) C  Qz 2@ H d 0޽h ? 33y___PPT10Y+D=' = @B +' 0 &&77hn&(  h: h # 0e0e0?03>;>2>: 1w@   n6#40;5=85 :;NG0 87 -45@520 @b h # 0e0e0?!>45@68<>5 2jD  2.2) A;8 8 C, 8 z A>45@60B ?> t  1 :;NG59, 2=>A8< k 8 2A5 :;NG8 z 2 C (?@8 MB>< 87 E C40;O5BAO k 8 C:070B5;L =0 z, 0 C75; C ?>A;5 MB>3> A>45@68B 2t  1 :;NG59), 0 70B5< >A2>1>6405< z 8 @5:C@A82=> C40;O5< k 87 C.N @@@@ @@@@ @@@@@D @@@@ @@@@@@@@@@@X  , l qQ3Cd h >?0B0 3 l(. >23>@>4, 2011 3.   h N ?><5@ A;0940 4< n*   ~ S.c h3  c"$"LZ V h C X?"`S.c h s *t  "` ]P$B @   h s *l  "` b  zC G L: B F3B    h s *  "`" '  aT X$B @   h s *   "` = aA B$B @   h s *@  "` F YD E B    h s *  "` N lJ K , B F  h s *T  "`  " e Q R S$  B @   h s *L  "`$ K( aU V$B @  h s *H  "`) - aY Z$B @ 6B hB   "j 6B h  "$ 6B hB  " v 6B hB  v  6B h  F ~ 6B hB   ^# 6B h  !% .& 6B h  & +  h s *  "`  aN O$B @ 6B h     h@ s BC#DEFjJ^.s'#@  "`}Z  h@ 0 F zC40;5=85 G& 2 @D3   h 6! 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Zy @@ @D@@H@%@@5@@H@@@@@@@V@@%@@@@H@@  3 ( 6   _ %  qQ3Cd l >?0B0 3 l(. >23>@>4, 2011 3.   l N~?><5@ A;0940 4< n*  H l 0޽h ? 33y___PPT10Y+D=' = @B +  0   p^ (  p: p # 0e0e0?03>;>2>: 1w@   n6#40;5=85 :;NG0 87 -45@520 @  p # 0e0e0?!>45@68<>5 2jl TL___PPT9.&  3.0) A;8 Ai[E] A>45@68B B>;L:> t  1 :;NG59, => ?@8 MB>< >48= 87 53> =5?>A@54AB25==KE A>A5459 (?>4 :>B>@K< <K ?>=8<05< 4>G5@=89 ?> >B=>H5=8N : E C75;, >B45;5==K9 >B @0AA<0B@8205<>3> @>2=> >4=8< :;NG><-@0745;8B5;5<) A>45@68B :0: <8=8<C< t :;NG59, B>340: 5@54048< 2 Ai[E] :;NG-@0745;8B5;L <564C 40==K< C7;>< 8 53> =5?>A@54AB25==K< A>A54>< 87 E. 0 53> <5AB> ?><5AB8< :@09=89 :;NG 87 A>A54=53> C7;0 8 ?5@5=5A5< A>>B25BAB2CNI89 C:070B5;L 87 A>A54=53> C7;0 2 Ai[E]. 3.1) A;8 Ai[E] 8 >10 53> =5?>A@54AB25==KE A>A540 A>45@60B ?> t  1 :;NG59, >1J548=8< Ai[E] A >4=8< 87 53> A>A5459 (?@8 MB>< 1K2H89 :;NG-@0745;8B5;L 87 E AB0=5B <5480=>9 =>2>3> C7;0). q @@H@@@k@D\@@@ @@H@G@Do@@H@@ @@H@/@@@@H@=@D@         2  `qQ3Cd p >?0B0 3 l(. >23>@>4, 2011 3.   p N?><5@ A;0940 4< n*  H p 0޽h ? 33y___PPT10Y+D=' = @B +  0   tT (  t: t # "0e0e0?03>;>2>: 1w@   n6#40;5=85 :;NG0 87 -45@520 @ t # D(0e0e0?!>45@68<>5 2jq  6>A:>;L:C 1>;LH8=AB2> :;NG59 2 -45@525 =0E>48BAO 2 ;8ABLOE, <>6=> >6840BL, GB> =0 ?@0:B8:5 G0I5 2A53> C40;5=8O 1C4CB 2K?>;=OBLAO 87 ;8ABL52. @>F54C@0 B_Tree_Delete 2 MB>< A;CG05 2K?>;=O5BAO 70 >48= =8AE>4OI89 ?@>E>4 ?> 45@52C, 157 2>72@0B>2. 4=0:> ?@8 C40;5=88 :;NG0 87 2=CB@5==53> C7;0 ?@>F54C@5 <>65B ?>B@51>20BLAO 2>72@0B : C7;C, :;NG 87 :>B>@>3> 1K; C40;5= 8 70<5I5= 53> ?@54H5AB25==8:>< 8;8 ?>A;54CNI8< 70 =8< :;NG>< (A;CG08 2.0 8 2.1). @>F54C@0 B_Tree_Delete B@51C5B 2A53> ;8HL (h) 48A:>2KE >?5@0F89 4;O 45@520 2KA>B>9 h, ?>A:>;L:C <564C @5:C@A82=K<8 2K7>20<8 ?@>F54C@K 2K?>;=O5BAO B>;L:> (1) 2K7>2>2 ?@>F54C@ Disk_Read 8;8 Disk_Write. 5>1E>48<>5 ?@>F5AA>@=>5 2@5<O A>AB02;O5B  (th) = O(tlogt n). . @ @ @@@@ @ @@@&@@E@@@ @@ @+@@@H@@0   qQ3Cd t >H+?0B0 3 l(. >23>@>4, 2011 3.   t NV?><5@ A;0940 4< n*  H t 0޽h ? 33y___PPT10Y+D=' = @B + 0 .&0(  l  # b0e0e0?03>;>2>: 1P   J@8<5=5=85 8 @07=>284=>AB8 B-45@52L52&&@  b  <d޽h ?"` 33y___PPT10Y+D=' = @B +a  0   x (  xP x # 0e0e0?03>;>2>: 1w@   L@8<5=5=85 8 @07=>284=>AB8 -45@52L52 '%@ x # p0e0e0?!>45@68<>5 2j  B-45@52LO 8 8E @07=>284=>AB8 H8@>:> 8A?>;L7CNBAO ?@8 ?@>5:B8@>20=88 A>2@5<5==KE D09;>2KE A8AB5<. (8@>:>5 ?@8<5=5=85 B-45@52LO ?>;CG8;8 2 @07;8G=KE !# 4;O >@30=870F88 8=45:A8@>20=8O ?> :;NG52K< ?>;O<.  D09;>2>9 A8AB5<5 NTFS B-45@52LO 8A?>;L7CNBAO 4;O >?B8<870F88 ?>8A:0 D09;>2 8 AB@C:BC@8@>20=8O <5B08=D>@<0F88 D09;0.  D09;>2KE A8AB5<0E HFS 8 Reiser4 4;O >@30=870F88 @01>BK D09;>2>9 A8AB5<K 8A?>;L7C5BAO B*-45@52>.  MB>9 @07=>284=>AB8 B-45@520 C7;K 45@520 4>;6=K 1KBL 70?>;=5=K =5 <5=55 G5< =0 2/3 >B <0:A8<0;L=>9 70?>;=5==>AB8. -B> >3@0=8G5=85 ?@82>48B : 1>;55 MDD5:B82=><C 8A?>;L7>20=8N <5AB0 =0 6QAB:>< 48A:5.2i BBB r g p  5  M VqQ3Cd x >?0B0 3 l(. >23>@>4, 2011 3.   x N?><5@ A;0940 4< n*  H x 0޽h ? 33y___PPT10Y+D=' = @B +  0 . & ` (  P  # D0e0e0?03>;>2>: 1w@   L@8<5=5=85 8 @07=>284=>AB8 -45@52L52 '%@X  # T0e0e0?!>45@68<>5 2j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{BBB@` O   qQ3Cd  >x?0B0 3 l(. >23>@>4, 2011 3.    N?><5@ A;0940 4< n*  H  0޽h ? 33y___PPT10Y+D=' = @B + 0 " ((  (` ( # 0e0e0?03>;>2>: 1P   b@>3@0<<=0O @50;870F8O 8 @57C;LB0BK M:A?5@8<5=B>222@b ( <d޽h ?"` 33y___PPT10Y+D=' = @B +  0   N (  0  # 0e0e0?03>;>2>: 1w@   d,A>15==>AB8 @50;870F88@  # 0e0e0?!>45@68<>5 2j  :x'B>1K ?@>25AB8 =081>;55 >1J5:B82=>5 A@02=5=85 @07;8G=KE B8?>2 45@52L52 ?> @01>B5 A 2=5H=59 ?0<OBLN <K @50;87>20;8 B5AB>2CN A8AB5<C, ?>72>;ONICN 01AB@038@>20BL @01>BC 2=5H=59 ?0<OB8 >B 0;3>@8B<>2 @01>BK A 45@52LO<8 A ?><>ILN 8=B5@D59A0 2=5H=53> E@0=8;8I0 IStorage. class IStorage { public: virtual I Allocate() = 0; virtual void Free(I index) = 0; virtual void Read(I index, T* value) = 0; virtual void Write(I index, const T* value) = 0; }; @@@C CCCCCCC'CC"C  _   qQ3Cd  >@?0B0 3 l(. >23>@>4, 2011 3.    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N<5@ A;0940 4< n*  H  0޽h ? 33y___PPT10Y+D=' = @B + 0  (  &  # t`0e0e0?03>;>2>: 1w@   Z* 50;87>20==K5 45@52LO@n  # |e0e0e0?!>45@68<>5 2j   @0<:0E =0H59 @01>BK <K @50;87>20;8 A;54CNI85 B8?K 45@52L52: B-45@52> B+-45@52> -45@52> 8=0@=>5 45@52> ,> . m@X>     qQ3Cd  >$w?0B0 3 l(. >23>@>4, 2011 3.    Ng?><5@ A;0940 4< n*  H  0޽h ? 33y___PPT10Y+D=' = @B +G 0 nf(     # 0e0e0?03>;>2>: 1w@   T$!@02=5=85 45@52L52@  # $0e0e0?!>45@68<>5 2j  .;O B5AB8@>20=8O 8A?>;L7>20;8AL A;54CNI85 ?0@0<5B@K: 07<5@ 70?8A8 100 109B 07<5@ :;NG0 8 109B '8A;> 70?8A59 >B 1 4> 1000000 0@0<5B@ t = 20 ;O B5AB8@>20=8O 35=5@8@>20;AO A;CG09=K9 =01>@ 40==KE A C=8:0;L=K<8 :;NG0<8. >102;5=85 8 ?>8A: :;NG59 ?@>872>48;8AL 2 A;CG09=>< ?>@O4:5.X5 Y @@@@@0  qQ3Cd  >?0B0 3 l(. >23>@>4, 2011 3.    N?><5@ A;0940 4< n*  H  0޽h ? 33y___PPT10Y+D=' = @B +[ 0 z (  :  3 A :  # [0e0e0?03>;>2>: 1w@  [ n>AB02:0 M;5<5=B0  G8A;> GB5=89 @  >#[?0B0 3 l(. >23>@>4, 2011 3.    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