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ΠΛΗ30 ΜΑΘΗΜΑ 1.2 (4in1) Slide 1 ΠΛΗ30 ΜΑΘΗΜΑ 1.2 (4in1) Slide 2 ΠΛΗ30 ΜΑΘΗΜΑ 1.2 (4in1) Slide 3 ΠΛΗ30 ΜΑΘΗΜΑ 1.2 (4in1) Slide 4 ΠΛΗ30 ΜΑΘΗΜΑ 1.2 (4in1) Slide 5 ΠΛΗ30 ΜΑΘΗΜΑ 1.2 (4in1) Slide 6 ΠΛΗ30 ΜΑΘΗΜΑ 1.2 (4in1) Slide 7
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ΠΛΗ30 ΜΑΘΗΜΑ 1.2 (4in1)

  1. 1. 30 1: 1.2: ! "! #$ %! "! #$ % & % ' ( % ! " # $ % & ' ( # # $ # # )*+,-./0 + ! " # $# %& % & ' ( # # $ # # )*+,-./0 + 1 2 3 2 & 2 $ 4$ 5# " $ $ " 6 $ $ ( 2 2 # 4$ 5# 7 8 9 $ 2: 8 . # "$% % ) $ ) % ): " " * ( $! % )% )*)$ % ! + * ! + , % " % " ( ) ( )% " ! "! #$ %. ! " # $# %& )% " ! "! #$ %. " " * - (-) " " * (-) -. 1. + ) ) 1. ) $% + '! " # $# %& ! " # $%& $ # $ ' # $# $ ( $# $ # ) # *# $%& $ # $ ' log x bx a b aανν= = logb a ) # *# $%& $ # $ ' * + : 3 2 4 3 3 5 2 2 1/4 2 log 8 3 2 8 log 81 4 3 81 log 125 3 5 125 1 1 1 log 1/16 2 4 4 16 αϕο αϕο αϕο αϕο = = = = = = = = =
  2. 2. -. 1. + ) ) 2. & *)# + ) ) (! " # $# %& 30, * # . ) / ! + , ) $ ) / ) 2, 0 $ * *)# (% ! + ) % 1 ) 2 % ): % * ( % * *)# (% ! + ) % # " ) 0 )#3 ) 3 : ; ./0; 2log logx x= ; ./0;; ./0; 1 log1=0 2 log2=1 4 log4=2 8 log8=3 16 log16=4 32 log32=5 64 log64=6 … 1024 log1024=10 ; ./0; 2048 log2048=11 4096 log4096=12 8192 log8192=13 … 220 log220=20 230 log230=30 240 log240=40 … -. 1. + ) ) 3. *)$ % + (& )% + ) %) )! " # $# %& 4* "$ " + ( *) 0 ) ) 0,% $ ) ) ( ): & ! * # , % ) ( «",0 )» " "$ ! + ) . ,2 $ ) *, ) ! + ) % ) 5 , % # " ) *( : log logK b ba K a= ,2 $ ) *, ) ! + ) % ) 5 , % # " ) *( : $ $ " ) ( # ) % 2 %: 6 ) " $ ) # , % $% & «",0 )». 5 . %: # ) )*)# +) * *)# (% ! + ) %: (log )X b a logX b a log log log (log ) K b b X X b b a K a a a = = log log log (log ) K X X a K a a a = = -. 1. + ) ) 3. *)$ % + ( !! + - %) *! " # $# %& ) )# )*)$ , ) $ , " ! + # " ) ! + ) «" + » / , ) #$! : log log log c b c a a b = )*)$ ) " !( ) $ / # ) *) % ) $% ) *( 2. * + : 2 8 2 64 3 9 3 log 32 5 log 32 1.66 log 8 3 log 2048 11 log 2048 1.83 log64 6 log 27 3 log 27 1.5 log 9 2 = = = = = = = = = -. 1. + ) ) 3. *)$ % + ( + ) % ) , # ) 6! %) +! " # $# %& ( # ) ) 2 % *( )*)$ %: log ( ) log log log log log b b b b b b xy x y x x y y = + = − 6 ) )*)# +) * *)# (% ! + ) %: + ! " " " . ! + ) % , ) " * 0 + %: " " ) , )% " , )% "$ ) * " " , )% ! )"$ : log( ) log log log log log xy x y x x y y = + = − log (log )b bxy x y= ⋅ log log ( )b bxy xy≠
  3. 3. -. 1. + ) ) 3. *)$ % + ( #0 % *( ) ,! " # $# %& 1 # ) 2 % (" !( )# ) )*)$ 0 +,%: logb x b x= 2 5 10 log 2 log ( ) 5 10 n n n n n n+ = = + )*)$ % 0 )*) ) $ ) )% " ! "! #$ %, $" #0 . )% )% % # )#,% / 2. * + : 2 2 log log4 log4 2 2 4 2 2 2 n n n n n n = = = = 10log ( ) 10 n n n n+ = + -. 1. + ) ) 4. 0)# % f(x)=log x ! " # $# %& 30 ! " )0 " )# ( " ) ) % 2 ) ) + 0)# " % f(x)=log x: ( $ ): f(x) 2 ) " !( + ( ) )# $ "$ " ) * " " ! )# ). $ " )# " ," ) + . $ ) ) " ) . -. 1. + ) ) 5. &)"!$% # ) )"!$% + ) % ! " # $# %& # ) )% 2 % )%: % + 0 % ) : 1 2 ( ) loglog ( ) logloglog f n n f n n = = % + 0 % ) : 1 ) ". . , : ) )% " % " ," ) + . : !! # ) $ ) " )# " % " ) 1 2 ( ) log(log ) ( ) log(log(log )) f n n f n n = = log(log 256) log(8) 3 log(log(log16)) log(log 4) log(2) 1 = = = = = logloglog loglog logn n n< < . * ! + # 1. 5 *) + ! " # $# %& < # = < # - .! & / . 0. 1 log x bx a b aανν= = log 2x x a aανν= = log ( ) log logb b bxy x y= + log( ) log logxy x y= + x x / . 2# ! 3## / 4 ! ! . & ! # / . 5%6 ! " log log logb b b x x y y = − log log log x x y y = − log log log c b c a a b = log log log 2 c c a a = log logK b ba K a= log logK a K a= log (log )X X b ba a= log (log )X X a a= logb x b x= log 2 x x=
  4. 4. . * ! + # 2. ! "! #$ % % #03 2 : 6 ) % * 5-6 )%. " " # ! ( * ! + " ) 2 % / : ! " # $# %& (2 ) " )# % " ! "! #$ % )% " # )% ) 2 % / : 1. - # (.) " ) ). 1. ) )% " ( 2) ( (* ! * * " ) # " ) " *)$ ) ) * ) %, !!)3% " / 2 2. #0 . )% )% % # )#,% / 2, ) " )3 % )*)$ 3. 6 " 2 )% % # , % ( % )*)$ % ! + ) 4. +# % # , % # ) 0, " ,! )% )#,% )% log 2 x x = . * ! + # 2. ! "! #$ % 1. ( (.) " + ( * " % " ( 2 + (.) ) % %. ) 2 + + (.) " ) ) , «# »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
  5. 5. . * ! + # 2. ! "! #$ % 3. 2 )% % # , % 1" ) " 3 % # , % # ) # )% " 2 )% ! + " , 0 ) (%. $ % # ) " !) ) , # # ) , ", ) $! % ) * )% " ) % ) (% ! + " * )+ " ! *! " # $# %& . * ! + # 2. ! "! #$ % 4. (+# ) # 3 !)# / . (2 ) % # , % , 0 ( )% " 2 )% , " "$ )% + ,% 0,%. - )#$ * +$ ) +) " 0 ( ) " # % )% + ,% 0,% " ! "! #$ %. !!! " " , ) " #(5 ) ) " "! # ( , ) $ ) , " #(5 ) +) $ /# ) , $ : +! " # $# %& , ) $ ) , " #(5 ) +) $ /# ) , $ : " . + !( $ "$ $ % ) " " " "$ )% , *) + !( $ , $ " 0 . " ) ) + !( "$ ,%: # ) 3 % , % "$ $ " ) " !! "! ) , . . : , # ) " !) ) " ! , $ # ) # ) "$ $ %. . .: / $, ) ,% , ! 9 * " ! " ) # , % "$ % $ % " , " #(5 ). 5 6 logn n n n< < 2 4 2 logn n n+ < + ) "$0 % ) % ) .$ "$ $ ) 8" , "!, ") ! )# : . * ! + # 2. ! "! #$ % 4. (+# ) # 3 ,3 # ! . 7.% ! .%8 3#/ " ( ) (1)nΤ = Θ )(log)( nn k Θ=Τ )()( k nn Θ=Τ )()( n an Θ=Τ )!()( nn Θ=Τ )()( n nn Θ=Τ 8" , "!, ") ! )# : ' $ $ 6 2 (1) 6 6>1 «# $» n 6 6 «# $» n 6 6 1<a<2, ,/: ,% «# $» n 6 6 «# $» n log log log logK n n n< < 2 3 ... K n n n n< < < < ... 2 3 ...n n n n a b< < < < < ! n n n< . * ! + # 2. ! "! #$ % 4. (+# ) # 3 1 ) #! " * )+ " ! % 2 %: ! " # $# %& ( ): 9 ," ): 2 3log log 2.32n n n< < 1 2 3f f f< <
  6. 6. . * ! + # 2. ! "! #$ % % * ( 3 " % " ," ) ) " % )% 2 )%: ! " # $# %& . # )% # 6 $ % 1 " ! + % #$! % ! + % % " ! +) . * " " ! + # )/3%, # ) 2( " ) *( 0 )#3 ) 3 # ) ! + ) % ! " # $# %& 5 4 1.log 25 2.log 644 8 3 4 9 6 2.log 64 3.log 64 4.log7 5.log 45 6.log 62 7.log 33 8.log 80 9.log 244 . # )% # 6 $ % 2 " ! + % #$! % ! + ) % # % !! + / %: ! " # $# %& 128 4 1.log 32 2.log 5124 9 4 2.log 512 3.log 27 4.log 1/ 2 . # )% 0 + 1 )% " # )% (2 ) " )# % " ! "! #$ %: '! " # $# %& log 1 log 2 ( ) 1.5 ( ) 10log ( ) 0.005log n n n f n n f n n f n n = = =3 4 ( ) 0.005log ( ) 1.15 n n f n n f n n = =
  7. 7. . # )% 0 + 2 )% " # )% (2 ) " )# % " ! "! #$ %: (! " # $# %& log 1 5 2 6 2 ( ) 8log 4 ( ) 10( ) n n f n n n n f n n n n = + = + + 2 5 7 3 4 4 ( ) ( ) log n f n n n n f n n = ⋅ + = . # )% 0 + 3 )% " # )% (2 ) " )# % " ! "! #$ %: )! " # $# %& 1 2 ( ) 3 ( ) log( ) n n f n f n n = = log 3 5 4 ( ) 2 ( ) ( ) n n f n f n n = =

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