-
Search8-1 8-2 (Sequential Search)8-3 (Binary Search)8-4
(Fibonacci Search)8-5 (Interpolation Search)
-
8-1
-
8-1-1
-
8-1-2 (Static Search)(Dynamic Search)
-
8-2(Sequential Search) O(nlogn)O(n)
-
(Sequential Search) n O ( n ) ( n + 1 ) /2 Procedure
Sequential(K,data)Beginfor i1 to Size [if Ki = Data thenreturn
found]return not foundEnd
-
8-3(Binary Search)Procedure
Binary(K,Data)BeginLeft1;RightSize;while Left 9
2
3
5
8
9
11
12
16
18
1
2
3
4
5
6
7
8
9
11
-
8 . 3 . 1
-
8 . 3 . 2 n (data record)1. (Sequential Search)(Search Length)2.
(Binary Search)3. 4. (comparison)? (1+2+3+...n)/n=(n+1)/2
log2(n+1) log2(n+1) -1 O(log2n)
-
8-4(Fibonacci Search)F ( n ) F0=0 ,F1=1Fi=Fi-1+Fi-2 i
20,1,1,2,3,5,8,13,21,34,55,89,...0 1
-
n k k Fib(k+1)n+1 k 2
Fib(k)(k-1)(Fib(k-1))(k-2)(Fib(k)+Fib(k-2))n+1 m
Fib(k+1)-m=n+1m=Fib(k+1)-(n+1) m 1
Fib(k)
Fib(k-1)
Fib(k)+Fib(k-2)
-Fib(k-2)
+Fib(k-2)
-Fib(k-3)
+Fib(k-3)
-Fib(k-4)
+Fib(k-4)
K-1
K-2
K
-
8 . 4 . 1 n=33
Fib(8+1)=33+1k=8Fib(8)=21Fib(7)=13Fib(8)+Fib(6)=21+8=29
21
13
29
8
18
26
32
5
11
16
20
24
28
31
33
3
7
10
12
15
17
19
23
25
27
30
24
2
1
4
6
9
14
22
-8
+8
+5
-5
-3
+3
-3
+3
-2
+2
-2
+2
-2
+2
-1
+1
-1
+1
-1
+1
-1
-1
+1
-1
+1
-1
-1
+1
-1
-1
-1
-1
-1
-
8 . 4 . 2 n=18
m=Fib(7+1)-(18+1)=21-19=2k=8Fib(7)=13-2=11Fib(6)=8-2=6Fib(7)+Fib(5)-2=13+5-2=16
13
8
18
5
11
16
20
3
7
10
12
15
17
19
2
1
4
6
9
14
+5
-5
-3
+3
-2
+2
-2
+2
-1
+1
-1
+1
-1
+1
-1
-1
-1
-1
-1
11
6
16
3
9
14
18
1
5
8
10
13
15
17
0
1
2
4
7
12
+5
-5
-3
+3
-2
+2
-2
+2
-1
+1
-1
+1
-1
+1
-1
-1
-1
-1
-1
-
n n Fib(k+1) n+1Fib(k)Fib(k-2)key Fib(k)key key key 1 Fib(k)-1 1
Fib(k)-1 Fib(k)key key Fib(k)+1 Fib(k+1)-1 Fib(k)+1 Fib(k+1)-1 O
(log2N )
-
Procedure
FibonacciSearch(K,Data)Begin//Fib(k+1)-m=n+1iFk-1;pFk-2;q Fk-3if
Data > Kii i+m;while i0 [case [:Data < Ki://if q=0[ i
0;]else[ i i-q; t p; p q; //Fibk-3 q t-q; //Fibk-4]:Data=Ki:return
i;:Data>Ki://if q=0 i 0;else[ i i+q; p p-q; //Fibk-4 q q-p;
//Fibk-5]]]End
Fib(k-1)
Fib(k-1)+Fib(k-3)
Fib(k-4)
Fib(k-2)
Fib(k-3)
-Fib(k-3)
+Fib(k-3)
-Fib(k-4)
+Fib(k-4)
-Fib(k-5)
+Fib(k-5)
-Fib(k-5)
i
q
p
i=i-q
q
p
i=i+q
q
p
- 8-5(Interpolation Search) Mid=low + (( key - data[low] ) / (
data[high] - data[low] ))* ( high - low )key data[high]data[low]n
1.1,2,3...n 2.low=1 high=n3.low
-
Procedure InterpolationSearch(K,Data)BeginLeft1;RightSize;while
Left Right then retirn -1;case [:Data <
KMiddle:RightMiddle-1;:Data = KMiddle:return Middle;:Data >
KMiddle:LeftMiddle+1;]]return -1;EndO(log n)
-
A
A
10
11
12
13
14
15
16
17
18
11
1
2
3
4
5
6
7
8
9
11=11
10
11
12
13
14
15
16
17
18
15
1
2
3
4
5
6
7
8
9
15=15
(15-10)/(18-10)*(9-1)+1=6
10
13
14
15
21
23
29
31
55
29
1
2
3
(11-10)/(18-10)*(9-1)+1=2
4
5
6
7
8
9
10
13
14
15
(29-10)/(55-10)*(9-1)+1=4
29>15
21
23
29
31
55
1
2
3
4
5
6
7
8
9
(29-21)/(55-21)*(9-5)+5=5
29>21
10
13
14
15
21
23
29
31
55
1
2
3
4
5
6
7
8
9
(29-23)/(55-23)*(9-6)+6=6
29>23
10
13
14
15
21
23
29
31
55
1
2
3
4
5
6
7
8
9
(29-29)/(55-29)*(9-7)+7=7
29=23
10
13
14
15
21
23
29
31
55
16
1
2
3
4
5
6
7
8
9
(16-10)/(55-10)*(9-1)+1=2
16>13
10
13
14
15
21
23
29
31
55
1
2
3
4
5
6
7
8
9
(16-14)/(55-14)*(9-3)+3=3
16>14
10
13
14
15
21
23
29
31
55
1
2
3
4
5
6
7
8
9
(16-15)/(55-15)*(9-4)+4=4
16>15
10
13
14
15
21
23
29
31
55
1
2
3
4
5
6
7
8
9
-
AVLC
-
AVL-Treeheight balanced binary
tree1962Adelson-VelskiiLandisAVL-TreeAVL TreeTTLTR1.TLTRAVL
Tree2.|Htl-Htr|1HtlHtrTLTRbalanced factorBF(P)PBF(P)= Htl-Htr
BF=-2
Q
S
R
BF=1
N
BF=0
M
BF=1
P
BF=0
8
7
4,5,6,7,8
6
5
4
-
NAVL Tree1.2.AVL TreeLLLRRLRRNBF2-2PLLNPLRNPRLNPRRNP
-
LL
P
1
PR
Q
QL
0
QR
h
h
h
2
PR
QL
1
QR
h+1
P
Q
h
h
N
0
PR
QL
0
QR
h+1
P
Q
h
h
N
30
50
50
40
40
30
2
1
0
40
30
50
1
1
1
50
40
20
50
40
60
30
45
50
40
60
60
30
45
30
45
20
2
1
1
20
-
LR
1
PR
QL
0
QR
h
P
Q
h
h
2
PR
QL
-1
b
h
P
Q
h+1
h
CR
-1/0
PR
QL
1/0
0
h
P
Q
h-1 or h
h
CL
C
CR
CL
C
h-1 or h
N
N
N
N
h-1 or h
h-1 or h
50
40
45
50
40
45
2
-1
0
45
40
50
1
1
1
50
40
42
60
30
45
50
40
60
30
45
50
40
60
30
45
42
2
1
1
42
-
RL
-1
PL
QR
0
QL
h
P
Q
h
h
-2
PL
QR
1
QL
h+1
P
Q
h
h
N
0
PL
QR
0
QL
h+1
P
Q
h
h
N
50
60
56
50
60
56
2
1
0
56
60
50
1
1
1
50
40
52
60
70
56
50
60
40
70
56
50
56
40
60
52
52
-2
1
1
70
-
RR
-1
PL
QR
0
QL
h
P
Q
h
h
-2
PL
QL
-1
b
h
P
Q
h+1
h
CR
CL
C
PL
QL
-1/0
h
P
Q
h-1 or h
h
CL
CR
C
1/0
0
h-1 or h
N
N
N
N
h-1 or h
h-1 or h
50
60
70
50
60
70
-2
-1
0
60
70
50
1
1
1
50
60
80
40
70
55
50
60
40
70
55
70
60
60
50
55
80
-2
-1
-1
40
-
AVL Tree1.AVL TreeR0R1R-1L0L1L-1NBF2-2PLLNPLRNPRLNPRRNP
-
R0
1
PR
QL
0
QR
h
P
Q
h
h
2
PR
QL
0
QR
h
P
Q
h
h-1
N
1
PR
QL
-1
QR
h
P
Q
h
h-1
50
60
42
40
45
2
55
2
2
50
60
42
40
45
2
38
2
1
43
50
60
40
45
2
42
43
1
43
38
2
38
2
0
-1
0
1
-
R1
1
PR
QL
1
QR
h
P
Q
h-1
h
2
PR
QL
1
QR
h-1
P
Q
h
h-1
N
0
PR
QL
0
QR
h-1
P
Q
h
h-1
1
32
55
50
70
35
50
70
35
40
45
2
40
45
1
2
2
1
1
32
2
1
40
50
35
45
2
1
2
32
70
0
0
-
R-1
2
50
60
20
30
1
50
60
2
35
40
43
20
30
1
1
35
40
43
-1
50
60
20
30
1
1
35
40
43
55
PR
h-1
1
PR
QL
-1
h-1
P
Q
h
QL
h-1 or h-2
h-1
P
Q
CL
0
CR
C
h-1 or h-2
h-1 or h-2
h-1 or h-2
CL
b
CR
C
2
PR
QL
-1
h-1
P
Q
h-1
CL
b
CR
C
N
-
L0
-1
PL
QR
0
QL
h
P
Q
h
h
-2
PL
QR
0
QL
h
P
Q
h
h-1
N
-1
PL
QR
1
QL
h
P
Q
h
h-1
50
40
62
60
55
2
2
2
50
40
62
60
55
2
2
1
50
40
60
1
45
64
58
58
64
62
2
64
55
2
58
-2
0
1
-1
-
L-1
-1
PL
QR
-1
QL
h
P
Q
h-1
h
-2
PL
QR
-1
QL
h-1
P
Q
h
h-1
N
0
PL
QR
0
QL
h-1
P
Q
h
h-1
50
40
65
60
55
2
1
2
68
45
50
40
65
60
55
2
1
1
68
-2
-1
60
65
50
55
2
1
2
40
68
0
0
1
-
L1
-1
PL
QR
1
h-1
P
Q
h
CR
b
CL
C
-2
PL
QR
1
h-1
P
Q
h-1
CR
b
CL
C
N
QR
h-1
P
Q
CR
CL
C
0
PL
h-1
h-1 or h-2
h-1 or h-2
h-1 or h-2
h-1 or h-2
0
50
40
65
60
1
2
58
55
54
45
50
40
65
60
1
1
58
55
54
2
-1
50
40
65
60
1
1
58
54
55
0
-
2-3C
-
2-3 TreeC2-3 Tree2-3 TreeLdataLdataLdata
L
R
L
R
LR
-
2-3 Tree1.2.
L
L
L
R
L
R
L
R
L
R
L
R
-
2-3 Tree
45
30
70
10
20
40
50
60
80
85
60
-
2-3 Tree
45
30
70
10
20
40
50
60
80
85
90
90
45
30
70
85
10
20
40
50
60
80
90
-
2-3 Tree
55
45
30
70
85
45
70
10
20
40
50
60
80
90
55
45
30
70
85
30
10
20
40
50
60
85
80
90
55
10
20
40
50
60
80
90
55
-
2-3 Tree
45
70
30
85
15
20
40
50
60
80
90
55
15
10
45
70
30
85
15
20
40
50
60
80
90
55
10
45
70
15
30
85
20
40
50
60
80
90
55
10
-
2-3 Tree
45
70
15
30
85
20
40
50
60
80
90
55
10
25
45
70
15
30
85
20
40
50
60
80
90
55
10
25
-
2-3 Tree
45
70
15
30
85
20
40
50
60
80
90
55
10
25
17
17
45
70
15
30
85
20
40
50
60
80
90
55
10
25
17
45
70
15
30
85
20
40
50
60
80
90
55
10
25
17
-
2-3 TreeP
90
96
85
70
80
75
95
95
90
90
70
80
75
96
96
85
70
80
75
95
95
80
70
75
96
95
90
96
85
70
80
90
96
90
85
85
80
70
80
96
90
96
85
70
80
90
70
80
96
80
85
70
95
-
2-3 Tree
50
80
35
60
15
95
70
96
80
35
70
50
15
95
96
90
85
90
85
30
70
60
65
75
18
35
17
20
25
70
35
65
75
18
17
20
25
30
-
m-wayC
-
m-way Treem-way TreenA0,(K1,A1) ,(K2,A2)..
,(Kn,An)AiKiAiK1...Kn
-
m-1m-1
5
5
5
7
7
5
7
12
12
5
7
6
12
6
5
7
18
12
18
6
5
7
14
12
18
6
14
-
5
7
8
12
6
10
4
8
5
7
10
12
6
5
7
10
4
6
4
7
5
10
6
4
-
BC
-
BBm-way1.2.P1.Pm-12.Pm-12-3
-
B
50
54
20
40
45
10
25
30
62
67
53
72
76
85
88
48
98
5
60
70
80
90
95
98
50
20
40
10
25
30
5
45
48
54
62
67
53
72
76
85
88
60
70
80
90
95
98
-
B
50
20
40
10
25
30
99
5
45
48
54
62
67
53
72
76
85
88
60
70
80
91
93
95
50
20
40
10
25
30
5
45
48
54
62
67
53
72
76
85
88
60
70
80
90
98
99
98
99
90
95
50
20
40
10
25
30
5
45
48
54
62
67
53
72
76
85
88
60
70
80
90
98
99
95
