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ΠΛΗ30 ΜΑΘΗΜΑ 1.1 (4in1)

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ΠΛΗ30 ΜΑΘΗΜΑ 1.1 (4in1)

  1. 1. 30 1: 1.1: !"# $!"# $ % " & '!( & ! " # # $ ! # ! !" # $ % % # # $ ! # $ ! # & ' # ( ) ! # " * + , # - . - . !)*& ! % !& ! !" # $ % )#)+ ! ," ! )$& +- + ! .! *& & " & )! ) ! * & +# *" !&, +# " )! ) ! * & + *& !"# ! , )$& )!/ #0! + )! !& *" !& +# ! ( +"!& 1 )"*. )#)+ ! 2)#)+ ! 2 )! ! *& & " & )! ) ! * & + 3"% $ "! $ )#)+ ! (-) 2. +$"# 1. +# *" !& *" !& +# # ! )! ! %, )! +) (+ 1 )"*. $& +-%&: 13+ +# ! ! + ! 1 $ ( ! * )! ! )"!. % !&) + +# + " / & !" 1 $ . $ ( )$ 1 + # )! $"#0+ ! )! ! %& – 30 4+ ! ) " + # 1-! ! + ! 1 $ ()! )+ ! #0+ ( ! )"!. % !&) &! !" # $ % " + # 1-! ! + ! 1 $ ()! )+ ! #0+ ( ! )"!. % !&) : /,01 2 2 0 32 2 2 '( ) ' ! $ " '( * + ' ,+$ + ) - ! $ " +$# . # ' /% •[5, 8, 9, 11, 14] •[4,12,7,9] +$# . # /% •[5, 8, 9, 11, 14],11 •[3,6,9,14,17],12 #' 0123456718745 9:;;<38745 83<3=56718745 >34?38745 @:6=A8745 #' B613C483C4=D 961C4E83C4=D F) + ' [5, 8, 9, 11, 14] [4,7,9,12] F) + ' GH0 I JKL
  2. 2. 2. +$"# 2. +# *& *" !& 5 & *& *" !& +# # )! !)! +# + ! 3+ + & )" -+ & )! + + +# # % & )"! " !(, *)$&: + ! 1& +) 4 &: for, while, do…while + ! % % &: if…else if…else ! 1& 3 " & M! !" # $ % ! 1& 3 " & " 1& )" -+ & (*)$& ).3. +,-,*,/,mod) … 6 ( + + % ! + +- + +)* + % ) 2. +$"# 3. $& . # ! + )! * ! !"# ! 1. 6"! % ! ) ! * 6"+ 0* + 1 " %" ! + # & ! )* ! *& +# 1 & *" !&. 3" !)! % ! + 3"! % )! ) ! * 3+ "* +" & )+"#) $ &. / ! + + +# * $& )"1)+ )" !( + +# 3"! % )! ) ! * + *& !"# ! : N! !" # $ % !( + * : " 3"! %& )! ) ! * & & SelectionSort +# : " 3"! %& )! ) ! * & & LinearSearch +# : ! "# $ % ! ! !& ' # $ # ( ( & # ( ) ( )T n n= 2 ( ) 3T n n n= + 2. +$"# 3. $& . # ! + )! * ! !"# ! 1. 6"! % ! ) ! * ( *" !& LinearSearch) & !( + 1 ) " + ( *" !& " %& 0% & – Linear Search) O! !" # $ % procedure LinearSearch(A,x) for i=1 to n if (A[i]==x) 7)! A +# 1 & )# & n ! 3+#$ , ! !)!#! 0 !( + ! ! 3+#! x. ! ! 3+#! ."+ +# ) + & ) + 76 . return « » end if end for return « » end procedure 2. +$"# 3. $& . # ! + )! * ! !"# ! 1. 6"! % ! ) ! * ( *" !& LinearSearch) ) "3! "+ & "*)! ( ! + 3"! % )! ) ! * ! !"# ! : 3+ "* +" & )+"#) $ & ( % )* + ! *" !& + & )+" * +"+& 1& )" -+ &). ! + " 1 ! *" !, * ! ! 3+#! + ) "3+ ! )# , " ! )" -+ & +# : P! !" # $ % .1 & )+"#) $ & ( % )* + ! *" !& + & * +"+& 1& )" -+ &). ! + " 1 ! *" ! * ! ! 3+#! +# )" 1 ! )# , " ! )" -+ & +# : 1 & )+"#) $ & +# )"!3$" 1 1 ! !& & & )! ) ! * & ) +# ) ! % $ + ! 1 $ + * ! . !( + 1 ! ! ()! ( + & + +)* + % . 1 ( ) 1 n i T n n = = = ( ) 1T n =
  3. 3. 2. +$"# 3. $& . # ! + )! * ! !"# ! 1. 6"! % ! ) ! * ( *" !& SelectionSort) * 1 ) " + (! *" !& - * & SelectionSort) Q! !" # $ % procedure SelectionSort(A) for i=1 to n pos=i for j=i+1 to n if (A[j]<A[pos]) 7)! A +# 1 & ( - * !&) )# & n ! 3+#$ if (A[j]<A[pos]) pos=j end if end for temp=A[i]; A[i]=A[pos]; A[pos]=temp end for end procedure 2. +$"# 3. $& . # ! + )! * ! !"# ! 1. 6"! % ! ) ! * (O *" !& SelectionSort) 7 13! + 1 () ! )+"#) ! !) *" ! )"!& + 1 , * +# ! + + !( + .% -.% + )! " * ) + 1 + &. + ! "*)! * . # ! + )$& + ! " +# ! *" !&. .3. + +# ! ! [4 3 5 1 2] 13! + .% .% + 1 + : ! !" # $ % 1 2 3 4 5 1 2 3 4 52% 1: 2% 4: 4 3 5 1 2 1 2 3 4 5 1 3 5 4 2 1 2 3 4 5 1 2 5 4 3 1 2 3 4 5 2% 1: 2% 2: 2% 3: 2% 4: 2% 5: + !&: 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 2. +$"# 3. $& . # ! + )! * ! !"# ! 1. 6"! % ! ) ! * (O *" !& SelectionSort) 3+ "* +" & )+"#) $ &. 3+ "* +" )+"#) $ +# * ! *" !& + +3+#& 3$"% + & ( ! .% & if) * ."# + "* +"! ! 3+#! ( * . # + * ! )# & +# - ! 1 !& + / # ! + " ). * + ! *" !& + & +-%& )" -+ &: ! !" # $ % 1 1 ( ) [1 ( 2) 3] n n i j i T n = = + = + + =1 1 1 1 1 1 1 1 1 1 2 2 1 2 [4 2( 1)] [4 2( ( 1) 1)] [4 2( )] [4 2 2 ] 4 (2 ) (2 ) ( 1) 4 2 2 4 2 2 2 3 i j i n n i j i n i n i n i n n n i i i n i n i n i n i n i n n n n i n n n n = = + = = + = = = = = = = = + = = + − + + = = + − = = + − = = + − = + = + − = + − = = + 2. +$"# 3. $& . # ! + )! * ! !"# ! 1. 6"! % ! ) ! * (O *" !& SelectionSort) ( +" & )+"#) $ &. ( +" )+"#) $ +# * ! )# & +# % - ! 1 !& + (-! + " , !)* + + 3"+ 0+ # + 3 " & if. * + ! *" !& + & +-%& )" -+ &: ! !" # $ % ( ) [1 ( 1) 3] n n T n = + + =1 1 1 1 1 1 1 1 2 2 1 2 ( ) [1 ( 1) 3] [4 ( ( 1) 1)] [4 ] [4 ] 4 ( ) ( ) ( 1) 4 4 2 0.5 2.5 n n i j i n i n i n i n n n i i i n i T n n i n i n i n i n n n n i n n n n = = + = = = = = = = = + + = = + − + + = = + − = = + − = = + − = + = + − = + − = = +
  4. 4. 2. +$"# 3. $& . # ! + )! * ! !"# ! 2. ) $ % # 6"! %& ! ) ! * & )!"!( + ) " "% ! + * : )! ) ! * 3+ "* +" & )+"#) $ & & LinearSearch +# / & + ( +" )* )! ) ! * ( +" & )+"#) $ &. )! ) ! * 3+ "* +" & )+"#) $ & & SelectionSort +# )! ( ! )! ) ! * & ( +" & )+"#) $ &. ! !" # $ % "! + 1 ! ) !)! % ! + * # : " !$ ! & ! * " & ) ( ! & " ! & # + , - )' 2. +$"# 3. $& . # ! + )! * ! !"# ! 2. ) $ % # 6"! %& ! ) ! * & + 3"% $ ) " ) $: 1 + * : )! ) ! * & LinearSearch 3+ "* +" )+"#) $ : 53+ " )! ) ! * & : 8 ) $ : &! !" # $ % ( )n nΤ = )()( nn Θ=Τ8 ) $ : )! ) ! * & LinearSearch ( +" )+"#) $ : 53+ " )! ) ! * & : 8 ) $ : )! ) ! * & SelectionSort 3+ "* +" )+"#) $ : 53+ " )! ) ! * & : 8 ) $ : )! ) ! * & SelectionSort ( +" )+"#) $ : 53+ " )! ) ! * & : 8 ) $ : )()( nn Θ=Τ ( ) 1nΤ = )1()( Θ=Τ n 2 ( ) 3n n nΤ = + 2 ( ) 0.5 2.5n n nΤ = + )()( 2 nn Θ=Τ )()( 2 nn Θ=Τ 2. +$"# 3. $& . # ! + )! * ! !"# ! 2. ) $ % # 6"! %& ! ) ! * & $& * $& -1"! + )! !& +# ! 1 !& *"!& + *& "!# !&; 3(+ +-%& +" "3# & " % + & )! ) ! * &: *)! : M! !" # $ % *)! : +"1& +# " % + & )! + ) "3+ ! n. 3! +: ! " 1& +# " % + & & !"/%&: 7)! k +# +" >0 ! $ 1& +# " % + & & !"/%&: 7)! k +# +" >0 + 1& +# " % + & & !"/%&: 7)! a +# +" >1 )+"+ + 1& +# ! +-%& (! " % + &: + )()( k nn Θ=Τ )()( n an Θ=Τ )(log)( nn k Θ=Τ )!()( nn Θ=Τ )()( n nn Θ=Τ n nn <! ( ) (1)nΤ = Θ 2. +$"# 3. $& . # ! + )! * ! !"# ! 3. 6$" % ! ) ! * + )! +& +/ " ! 1& +# 3"% ! -1"! + )* +& 1 + & % & ) !( + 1 + ! !"# ! . & )+" ) + & 1& + " + )* +& + . 1& ) !( + 1 + ! !"# ! . N! !" # $ % "! !3%! 5 & )# & + 1 ! & n, +# n + . 1&. 3 3" !)! +# ! .! !& (.) 13! + # ) $ % + # ! 3 "! + 1 + & ! !"# ! .
  5. 5. 2. +$"# 3. $& . # ! + )! * ! !"# ! 3. 6$" % ! ) ! * ( *" !& Fibonacci) ! !( + + 1 ) " + : ! ! # Fibonacci !"#0+ $&: O! !" # $ % = = = 2,1 1,1 n n fn 9 + )! ! # ! + ! n-! * *"! & ! ! # & + 1 *" !. & !( + ! & )" ! & *"! & & ! ! # & >+ −− 2,21 nff nn n 1 2 3 4 5 6 7 8 9 10 1 1 2 3 5 8 13 21 34 55 ... 2. +$"# 3. $& . # ! + )! * ! !"# ! 3. 6$" % ! ) ! * ( *" !& Fibonacci) # !)!# )! ! !( ! n-! !( Fibonacci +# * ! : P! !" # $ % procedure Fibonacci(n) A[1]=1 A[2]=1 for i=3 to n A[i]=A[i-1]+A[i-2] + . 1& )! 3" !)! +# ! )"* " +# : n + . 1& ! )# A (! + . 1& n i +) & 3$" % )! ) ! * +# T(n)=n+2 ) $ T(n)= (n) A[i]=A[i-1]+A[i-2] end for return A[n] end procedure 2. +$"# 3. $& . # ! + )! * ! !"# ! 3. 6$" % ! ) ! * ( *" !& Fibonacci) )!"!( + ! + ( +" 3+#" & % &; Q! !" # $ % procedure Fibonacci(n) if (n=1) return 1 else if (n=2) return 1 else a=1 + . 1& )! 3" !)! +# ! )"* " +# : )1 + + . 1& i,n,a,b,c +) & 3$" % )! ) ! * +# T(n)=5 ) $ T(n)= (1) a=1 b=1 for (i=3 to n) c=a+b a=b b=c end for end if return c end procedure 2. +$"# 3. $& . # ! + )! * ! !"# ! 4. ( " !"# $ 5 )"*. )!"+# +# )* /!"+ !(& *" ! &. )!/ # ! + )! !& *" !& +# ( +"!&: )! ! #0! + ) $ % )! ) ! * ( % ! (.) ) 3+ "* +" )+"#) $ . ) 1 ! + ! *" ! )! 13+ "* +" )! ) ! * . ! !" # $ % ) 1 ! + ! *" ! )! 13+ "* +" )! ) ! * . +)* + % !( + )"!. % )! + + % + * : 4 ! 5 # 6 # ! # $ ! 5 # B613C483C4=D RS T U RS1T 961C4E83C4=D RS T U RS<7? 1T 9:;;<38745 RS1 T RS1 T RS1 T 0123456718745 RS1T U RS1 T 83<3=56718745 RS1 T RS1 T RS1 T >34?38745 RS1 <7?1T RS1 <7?1T RS1 <7?1T @:6=A8745 RS1 <7?1T RS1 <7?1T RS1 T
  6. 6. . + ! ! ! # % +$ 1. )! ! *& ! ) ! * & 1. + " % 13! + !3 % )"! 1 ! + & # ! 3+& )! ) ! * +&: ! !" # $ % .... )! ) ! * +# +2+ .... . + ! ! ! # % +$ 1. )! ! *& ! ) ! * & 2. )! ! *& & for 8 + for # + 1 "! + $ *" ! "3% ! for ) $ *" ! ! 1 !& ! for. .3.: ! !" # $ % . .: for (i=A to B) )! ) ! * +# 6"% / !( +-%& "!# : for (i=A to B) ... K ... end for = = B Ai KnT )( = +Α−Β= B Ai 11 = += n i nni 1 2/)1( = ++= n i nnni 1 2 6/)12)(1( = + − − = n i n i x x x 0 1 1 1 .:,1 σταθccc B Ai B Ai= = = == = +=+ n i n i n i BABA 11 1 )( . + ! ! ! # % +$ 1. )! ! *& ! ) ! * & 3. /$ 1 ! 2"*3! + + /$ 1 ! & ."*3! &, "!( + ! & # ! & * +& )! +# + 1 ) * ."*3!. .3.: ! !" # $ % for (i= to ) for (j=C to D) ... K ... )! ) ! * +# ... K ... end for end for ( ) B D i A j C T n K = = = . + ! ! ! # % +$ 2. .! *& (.) +- ! + ! (.) & " & )! ) ! * &, )"1)+ ! + & *)! +& +) +" 1& * +& 1 + 13! + « " » "!# . 5)+ +) 1 ! + ! 1 ! )* ! & *"! & ! "!# !&, ! + ! + ! (.) &! !" # $ % " +# 1. 2. "! !3% * ) +#/! ! +"1& )! +# )! ) 1 +& + ! & *"! & ! "!# !&. )()1()( 22 nnnnnn Θ=+=+=Τ )( 6 1 6 3 6 2 6 )12)(( 6 )12)(1( )( 323 2 nnnn nnnnnn n Θ=++= ++ = ++ =Τ
  7. 7. . + ! ! ! # % +$ 3. * +& +$ # +" +- $ % ! (.) 3 )"! () + ! )! ! * +$ . ! ! !( ! * +"+& * +& +$ " 0 : M! !" # $ % 0 1 1a a a = = 1 0.52 B x x x= = ( ) ( ) ( ) n n m n n m nm m m a a a a a = = =1 1 1/ 1/k k a a a a a a − − = = = B BA A x x= ( ) / / ( / ) m m m n m n m n m n m m m a a a a a a a a a b a b + − = = = = . % + & 8 * & 1 )! ! # + # ) $ % + # $ +- & " % +$ )! ) ! * &: N! !" # $ % 2 1 2 0 2 ( ) (2 1) ( ) 2 (2 1) ( ) 5 ( 4 ) log n n n f n n n n f n f n n n = + + = + = + +0 2 3 22 4 6 5 0.01 6 7 62 44 8 ( ) 5 ( 4 ) log ( ) (2 ) ( ) log ! 1000 14 ( ) 1000 4( ) 2 ( ) 4 n n n n n n f n n n f n n f n n n n f n n f n f n n n n = + + = + = + + + + = + = = + + . % + & 8 * & 2 )! ! # + " .% )! ) ! * ! ) " $ % !& : O! !" # $ % for i=1 to n for j=1 to n a=a+1 end for b=a+a*a end forend for . % + & 8 * & 3 )! ! # + " .% )! ) ! * ! ) " $ % !& : P! !" # $ % for i=1 to n a=a/2 for j=1 to n a=a*10 end for b=a+a*a/2b=a+a*a/2 for j=i+1 to n a=a+9 end for end for
  8. 8. . % + & / " ! % 1 +("+ ! + 3 ! " !( + 1 )# " * )!"+# !)! +# + +-%& "! # : Q! !" # $ % procedure minArray(A) min=A[1] for i=2 to nfor i=2 to n if (A[i]<min) min=A[i] end if end for end procedure . % + & / " ! % 1 1. 3+ "* +" )+"#) $ 1. )! ! # + " .% )! ) ! * 2. + # ) $ % + # & )! ) ! * & 2. ( +" )+"#) $ 1. )! ! # + " .% )! ) ! * ! !" # $ % 1. )! ! # + " .% )! ) ! * 2. + ) $ % + # & )! ) ! * & . % + & / " ! % 2 & 1 +"!& *" !& - * & +# ! *" !& - * & + + $ % (InsertionSort). " $ / # + !)!# ! !"# ! !( + 4+ ! : ! !" # $ % procedure InsertionSort(A) for i=2 to n for j=i-1 to 1 if (A[j]>A[j+1]) temp=A[j] A[j]=A[j+1] A[j+1]=temp else break end if end for end for end procedure . % + & / " ! % 2 1. + 1 + 1 "* ! )! ).3. ! [5 4 3 1 2] # + ) * )$& ! +(+ ! *" !&. 2. * + 13! + 3+ "* +" )+"#) $ & + 1 + & ! !"# ! ; 3. ! )! ) ! * & 3+ "* +" & )+"#) $ &; 4. + ) $ % + # & )! ) ! * & & 3+ "* +" & ! !" # $ % 4. + ) $ % + # & )! ) ! * & & 3+ "* +" & )+"#) $ &. 5. * + 13! + ( +" )+"#) $ & + 1 + & ! !"# ! ; 6. ! )! ) ! * & ( +" & )+"#) $ &; 7. + ) $ % + # & )! ) ! * & & ( +" & )+"#) $ &.

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