.

1. 30
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:
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•[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. +$"#
2. +# *& *" !&
5 & *& *" !& +# # )! !)! +# +
! 3+ + & )" -+ & )! + + +# # % & )"! " !(,
*)$&:
+ ! 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. 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. 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. 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. . + ! ! ! # % +$
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. . + ! ! ! # % +$
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. . % + &
/ " ! % 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. + ) $ % + # & )! ) ! * & & ( +" &
)+"#) $ &.