Title: ???????? ???????? Graphs
1(No Transcript)
2???????? ???????? Graphs Networks ?????
????? ???????? ?????? ??????????? 1289
????? ?. ???? ?????
3????? ?????? ???????
- ????? ????? ???????? ???????? ????? ??????.
- ???? ???????? ???????? ???? ??????.
- ?????? ??????? ???????? Dijkstra??????
- ???? ??? ??? ????? ?? ???????.
- ?????? ??????? ???????? Floyed ??????
- ??????? ??? ????? ?? ???????.
4????????? GRAPHSKS
???????? NETWORK
5???????????? (Graphs)
????? ????????
?? ?????? ?????? ???? ??????? ??????? ??
??????? ??????? ??? ???? ??????? ??????? ??? ??
????? ????????
6 ??? ?? ????? ??????? ??? ?????????
?????? ?????? ????? ?? ??????? ??????? ???
?????? ??? ?????? ????? ?????? ????????
?????????? ?????? ??????? ?? ???? ??? ?????
7????? ???
??? ???? ????? ???? ?????? ?? ???????? ?????????
?? ???? ??????? ??? ??? ???? ?????? ????? ??????
????? ???? ?? ???? ?????? ?????? ?? ?????? ?????
????? ?????? ???? ?? ???? ?????? ??????? ??? ???
?????
8???? ?? ????
??? ?????? ?? ???? ??????? ????????? ?? ???? ????
???????? ??? ??????? ???????? ?? ??????
(Vertices) ?????? ??????? ????? (Edges) ????? ??
???? ?????? ?? ??? ??????? ??? ??? ?????
???????? ??? ?????? ?????????
9????? ???????? ?? ?????? ?????? ???
- ?????? ?? ??????? (Element)
- ?? ????? (Node) ????? ?????? V
- (Vertices)
- ?????? ?????? E (edge)
- ????? ???? ??? ?????? ???? ???? ??? ???
- G(V,E)
-
10?????? ???????? Graphs Type
???? ????? ??????? ?? ???????? ??
- ???????? ????? ?????
- (UNDIRECTED GRAPHS)
- ???????? ???????
- (DIGRAPH )
11 ????
???????? ????? ????? (UNDIRECTED GRAPHS)
???? ?????? ??? ???? ????? ???? ?? ???? ??? ???
??? ?? ????? ????? ?????
12????? ??? ?? ???? ?????? ???? ???? ??? ????
?????? ?????? ????
??? ??? ??????
???? ????? (v1,v2) ?????? ????? (v2,v1)
13v2
v3
v5
v1
v4
14?????
???????? ??????? (DIGRAPHS)
?????? ???? ???? ??? ???? ?? ?????? ?????? ????
??? ??? ???? ?? ????? ????? ???? ??? ?????
??????? ?? ?? ?????? ??????? ?????? ???? ????
??? ??? ?????
15v1
v2
v4
v3
v5
v7
v6
16????? ????????Representation of Graphs
???? ??? ??? ?????? ???????? ????
- ??????? ??????? (Linked Representation)
- ?????? ?????? (Adjacency Matrices)
-
17????
??????? ??????? (Linked Representation)
????? ?? ???? ????? ???????? ???????? ??????
????? ????? ?? ??? ?? ?????? ??? ????? ???
???????????? ???? ???? ?? ??????? ??????? ??
???? ?? ???? ??? ??? ?????? ?? ????? ??? ?????
18???? ???????? ????????? ?????? ?? ?????? ?? ????
??? ????? ?? ????? ???? ??? ?? ?????? ?? ???
??? ?????? ???? ?? ???? ????? ?????? ??? ????
19?? ??? ?? ?????? ?? ????? ???????? ??? ???
??????(??? ?????) ??? ???? ?? ??? ??????????? ??
?????? ?? ???? ??? ?? ????? ???? ????????? ??????
20?????
??? ?????? ?????? ???????? ?????? ?????
1
4
2
3
21?????
??? ????? ?????? ?? ???? ???????
- ????? ???????
- ????? ???????
22??????? ??????
????? ???????
2
1
1
1
3
3
2
2
4
4
4
3
1
NULL
2
NULL
NULL
3
NULL
4
23 ?????? ?????? (Adjacency Matrices)
?????
?? ????? ?? ?????? ?????? ??????? ???? ????????
????? ???????? ??? ??? ?? ?????? ??????? ??????
A(aij)?? ?????? ?? ????? n x n ??? ???? ??
?????? aij ???? ?????
24??? ??? ???? ???? ?? ????? i ??? ????? j ?????
0 ??? ?? ??? ???? ???? ???? ??? ???????
????? ??? ??????? ??????? ???? ?????? ??????
aij 1 if there is an edge from i to j
0 if there is no edge
25 ?????
??? ????? ?????? ???????? ?????? ??????
v2
v1
v4
v3
v5
v7
v6
26?????
???? ????? ?????? ?????? ??????? ?????? ???????
V7 V6 V5 V4 V3 V2 V1
0 0 0 0 0 1 0 V1
0 0 1 0 0 0 0 V2
0 1 0 0 0 0 1 V3
0 0 1 0 1 0 0 V4
1 0 0 0 0 0 0 V5
0 0 0 0 0 0 0 V6
0 1 0 0 0 0 0 V7
27????? ?? ?????? ?????? ????? ????? ??? ????????
0 ? 1 ????? ????? ???? ????? ???????? ????????
28???? ?????? ??????? ???????? ?? ?? ???? ??
?????? ???????? ?????? ??????
????? ??? ?????? ???????
?????? ??? ?????? n ????? ?????? ?? ??????
?????? ????? ??? ???? ????? ????? 1 ?? ??????
??????
29????? ??????? ????? ?????? ???????
??? ?????? ??? ?????? n ????? ???? ?? ??????
?????? ????? ??? ???? ???? ????? 1 ?? ??? ????
?????? ??? ???? ???? ????? 1 ??? ?????? ???????
?? ?? ???? ?? ??????.
30?????
????? ?????? ??????? ???????? ?? ???? ?? ????
?? ?????? ???????? ????? ?????? ?????? ????
?????? ???????
buildadjm(intadjMAX, int n)
31void buildadjm(int adjMAX, int n)
int i,j for(i0iltni)
for(j0jltnj)
coutltlt"Enter 1 if there is an edge from "ltlt i ltlt"
ltlt "to" ltlt" "ltlt j ltlt"
otherwise enter 0 "ltltendl
cingtgtadjij
32?? ??????
?? ???? ?????? indegree ??? ???? ??? ???? ????
????? 1 ?? ?? ???? ?? ?????? ?????? ????????
??? ?????? ???? ???? ???? ??????? ??????? ???
????? ???? ???? ????????
33 ??? ???????
Int indegree (intadjMAX,intx,int n)
int i, count 0 for(i0iltni)
if( adjix 1) count
return(count)
34 ?? ??????
?? ???? ?????? outdegree ??? ???? ??? ????
???? ????? 1?? ?? ?? ?? ?????? ?????? ????????
??? ?????? (?????) ???? ????? ??? ??? ??????
35??? ???????
int outdegree(int adjMAX,int x,int n)
int i, count 0 for(i0iltni)
if( adjxi 1) count
return(count)
36?? ??????
???? ???? ???????? ??????? ???????
void main() int adjMAXMAX, n, i
coutltlt"Enter the number of nodes in graph
maximum ltltMAXltltendl cingtgtn
buildadjm(adj,n)
37 for(i0iltni) coutltlt"The indegree of
the node "ltltiltlt" is ltltindegree(adj,i,n)ltltendl
coutltlt"The outdegree of the nodeltltiltlt"is ltltout
degree(adj,i,n)ltlt endl
38- ??? ????????
- ???? ??? ???????? ???? ????? ?????? ??????
- ?? ???? ?????? ??????buildadjm???
- ??? ???? ?? ???? ??????? ?????? ??????
??????? ???????? ??? ???? ?? ?????? - ?? ???? ?????? ??????...........
indegree?outdegree??? ???????.
39- ??????indegree ???? ??? ????
- ???? ????? 1 ?? ?? ???? ?? ??????
- ?????? ???????? ??? ?????? ?????
- ???? ???? ?????? ??????? ??? ?????
- ???? ???? ????????.
40- ??????outdegree ???? ???
- ???? ???? ????? 1 ?? ?? ??
- ?? ?????? ?????? ???????? ???
- ?????? ???? ????? ??? ??? ??????.
41?????
??????? NETWORKS
???? ?????? ??? ???? ???? ????? Diagram ?????
?? ???? ????? A ????? ????? F?????? ???? ??????
??????? ??????? ?? ????? Nods ????? ??? ????
?? ?????? Edges
42(?? ???? ??? ??? ?????? ?? ???? ) ???? ???? ??
????? ???? ????? ????? ???? ??? ??? ??????
43??? ????? ???? ??????? SHORTEST PATH
?? ????? ???? ??????? ?? ?????? ?????? ????? ???
???? ??? ??? ?? ?????? ?? ?????? ???? ???? ?????
????? ?????? ?? ?????
44????? ?????? ?????? ?????? ?????? ?? ???? ???
??? ?? ???? ????? ???? ??? ????? ???? ???????
??? ??? ??????? ?? ???? ??? ???? ????? ???????
??? ?????? ??????? ????? ?? ???? ????????
???????? ??? ?????? ????????
45??????? ???? ??????? ?????? ???? ?????????
- ??????? ??????
- ???????? ???????? ???????? (Dijkstra)
- ??????? ???????
- ???????? ???????? ????? (Floyd)
46- ??????? ??????
- ???????? ???????? ???????? Dijkstra
???? ?????? ?? ??????????? ?????? ??????? ?? ???
??? ???? ?? ?????? ???? ???????? Dijkstra ???
???? ??? ?????????? ??? ????? ??????? ?? ???
????? ????? ????? ?????? ?? ??????
47???? ???????? Dijkstra ?? ??? ????? ???? ????
?????? (source) ?? ?????? ?????? ????? ??? ???
??? ???? ????? ?????? ?? ?????? ????? ??? ?????
??????? ?????? ?? ????? ???????? ??? ?????
?????? ?????? ?????
48???????? ???? ???? ???????? Dijkstra ??? ?????
????? ??? ????? ?????? ?? ???? ??????? ??? ????
??????? ??? ?????? ?????? ?? ????? ???
?????????? ?? O(n2)
49- ?????? ????? ?????? (Adjacency Matrix Cost)
- ?????? ????? ( Distance Matrix)
- ?????? ??????? (Path Matrix)
- ?????? ??????? (Include Matrix)
????? ??? ?????????? ??? ???? ??????? ???
50???????? ?????? ?????? ????? ??????
(Adjacency Matrix Cost)
?? ????? ?????? ???? ????? ??????
51A
B
D
C
52 ???? ????? ????? ?????? ???????? ?????? ??????
??? ???
D C B A
A TO D A TO C A TO B 0 A
B TO D B TO C 0 0 B
C TO D 0 0 0 C
0 D TO C 0 0 D
???? ??????? ?? ???????? ???? C ???????
int COSTNN
53???????? ??????? ?????? ????? (Distance
Matrix)
- ?????? ??? ???? ????? ?? ???? ????????
- ??? ?????? J ???? ?? ??????
- DISTANCEJ
- ???? ??????? ?? ???????? ???? C ???????
- int DISTANCENN
54???????? ??????? ??????
??????? (Path Matrix)
?????? ??????? ???? ??? ??? ?? ???? ??????? ???
?? path j ????? ??? ?????? ??????? ????????
????? j ?? ???? ??????? ???? ??????? ?? ????????
???? C ??????? int PATHN
55???????? ??????? ?????? ???????
(Include Matrix)
??? ?????? ?????? ?????? ????? ??? ???????
???????? ? ??? ?? ??? ???? ????? (????????) ???
???? ??????? ????? ??? ?????? ?? ????? ??????????
???? ?? ???? ????????
56??? ???? ???? ?? ?? ?????? ??? j ??? ????
??????? Included ????? True ???? ??????? ??
???????? ???? C ??????? bool
INCLUDEN
57??? ???????? ???????? ?????? ???? ???????
Const int N50 Typedef bool Boolean Type N
Int cost NN Int DISTANCE N Int PATH
N Bool INCLUDE N Void SHORTPATH ( int
SOURCE ) Boolean Type Included Int I , j
ReadMat ()
58Initialize ( SOURCE ) Do FINDMIN (J)
INCLUDEJ true For
(i0iltN i) If ( ! INCLUDEDJ
) UPDATE ( I, J ) PRINT () While
ALL( Included ) PrintPath ()
59?????? ????????? ?? ???????? ????????
- ?????? ReadMAT
- ??? ??? ?? ???? ??? ??????
- ????? ?????? ????? ??????
60???? ????? ??? ??? ????? ??? ????? ?????? 0 ??
?????? ???
???? ??? ???? ?????? (Vi ,Vi) ?? ?? ????
??????. ????? ??? ?? ???? ????.
61- ???? Initialize
- ??? ??? ?? ??? ?????? ????? ????? ??????????
- INCLUDE SOURCE ???? ?? ???????
- ??? ???? ????? true INCLUDE i ???
- ?????? ???????? ????? false
62- ?????? FINDMIN
- ??? ???? ???? ???? ??????? ?? ???? ???????
- ??? ?????? J
- ????? ???? ?????? J ??? ???? ???????
- ??? ??? ????? ???? Included j
- ????? ?????? ?????? true
63??????? ??? ??? ??? ????? ???? ??????? ?? ????
??????? ??? ???? j ???? ??????? ???? ??
????????? Distance Matrix
64- ?????? UPDATE
- ?????? ?????? ???????? Distance Matrix
- ????????? Path Matrix ?? ???? ????? ???? ???
- i ??? ?? (INCLUDE i false)
- ???? ??? ???? ???? ??????? ????????
- ??? ?????? ??? ??????
65??? ??? ?????? ???? ??? ?????? ??? ??????
???????? ?? ???? ???????
66- ?????? ALL
- ? ?????? ????? ??????
- ? ???? ?????? true ????? ???? ??? ????
- ??????? ?? ???????? Include Matrix
- ????? true
- ????? ??? ?????? ?????? false ???? ???
67- ?????? SHORT PATH
- ??????? ????? ??? ?? ??????
- ??????? ?????? ???????
- ???????? ??? ???? ??????? ???? ???? ??????
- ??????? ??? ??????? ???? ???? ????
- ??? ????? ??? ?????? ??? ????? ???? ???????
?????? ??? ?????
68- ???? ??????? PRINT
- ?????? ??? ??????
- ?????? ??? ???????????
- DISTANSE , INCLUDE , PATH
- ??? ?? ???? ?? ????? ??????????
69- ?????? PRINTPATH
- ?????? ??? ???????
- ?????? ???? ??????? ??? ???? ??????
- ????? ?????? ????????
70?????? ???? ??????? ??? ?????? ???????? ????????
????????
???????? ?????? ????? ?????? ??????? ?? ?????
?????? ??? ??? ???? ??????? ?? ?????? 1???
??????3
715 4 3 2 1
200 310 2985 800 0 1
0 612 410 0 800 2
0 1421 0 410 2985 3
400 0 1421 612 310 4
0 400 0 0 200 5
72???????
- ??? ?? ??? ???? ???? ?? ?????? (?)
- ??? ??????(?) ??? ???? ??????
- ?? ???? ? ??????? ? ????? ?? ??????? .
73- ??? ??? ???????? ??? ?????? Initialize
- ???? ??? ????? ??????? ??????? ?? ???
- ???? ???? ??? ?????? ?? ?????? ??? ????
- ???? ????? ????? ?? ??? C ????? ???
- ??? ?????? ?????? MAXINT ??? ?????
- 32767 .
74?? ??????
???? ???????? ???????? ?????? ??? ?????? ??????
? ???? ????? ??? ????? ?? ???????? cost ???? ????
?????? ????? cost 2,3 ?????? 410 ???? ???? ??
??? ?????? ???? ??? ??? ???????? 2 ? 3 ?? 410
75??? ??? ??? ??????? ??????? initialize ?????
???? ????? ?????????? ????????? Distance
?Path ? Included ??? ???
76- ????
- ??????? ???????? DISTANCE ??? ???
- ??? ?????? 1 ?? ???? ??????? ??? ?????? ?????
- ?? DISTANCE 1 ????? ???
- ??? ?????? 2 ?? ???? ???????
- ?? DISTANCE 2 ????? 800
77- ??? ?????? 3 ?? ???? ???????
- ?? DISTANCE 3 ????? 2985
- ??? ?????? 4 ?? ???? ???????
- ?? DISTANCE 4 ????? 310
- ??? ?????? 5 ?? ???? ???????
- ?? DISTANCE 5 ????? 200
78????? ???? ???????? DISTANCE ??? ???
Distance 0 800 2985 310 200
79 ????? ??????? ???????? PATH ??? ???? ????
??????? ?? ??? ???? ???? ?? ????? ???? ???????
??? ?????? ?????? . ????? ???? ???????
????????PATH ?????? ?????? 1(?? ???? ???????)
???????? PATH1 ??? ????? ????? ???? . Path
0 1 1 1 1
80????? ??????? ???????? INCLUDE ??? ??? ????
??????? ????? false ???????? ???? ??????INCLUDE
1 ??? ?? ?????? 1 ???? ???? ????????????
????? true???? ???? ?? ?????? 1 ????? ?? ????
?? ???? ??????? .
81 ????? ???? ??? ????? ?????????? ?????????
DISTANCE ? INCLUDE ? PATH ??? ???
?????? 1 2 3 4 5
Distance 0 800 2985 310 200
Path 0 1 1 1 1
Include true false false false false
82 ??? ??????? ??????? ?? ????? ?????????? ???
????? ??????? ????????? ?????? ???? ???? ???
????????? ????? ???? ??????? ?? ???? ??????? ???
???? ??? ????????? ?????? ???? ?? ????? ????
???????? ??????? ???????? ?? ???? ???????
83???? ??? ?? ?????? ??????? ?? ?????????? ?????
????????? ??????? ??? ????????? ??????
???? ?? ??? ?????? 5 ?? ?????? 1 ?? ????? ??
????? ?????? ?????? ??? ?????? 5 ????? ?? ????
??? ???? ???????
84????? ???? INCLUDE 5 ?????? ?????? true ?????
?????? 1 ?????? ?????? ???? ???? ?????? ??? ???
??? ?????? ?? ?????????? ????? ??????? ?? ????
??????? (??? ??????1) ?????? ??? ?????? ??????
??? ???? ??????? ???????? PATH ??? ??
85 ????? ???? ??????? ???????? ??????
??????? ??? ?????? 5 ??? ???
?????? 1 2 3 4 5
Distance 200 1000 1821 400 0
Path 5 1 4 5 0
Include true false false true true
86???? ?????? ????? ????? ?? ?????? 5 ??? ?????? 3
?? ???? ?????? 2
?????? 1 2 3 4 5
Distance 200 1000 1410 400 0
Path 5 1 2 5 0
Include true true false true true
87 ????? ??? ???
?????? 1 2 3 4 5
Distance 200 1000 1410 400 0
Path 5 1 2 5 0
Include true true true true true
88???????
?? ????? ?????? 2 ?????? ???? ????? ???????? ??
????????? ?????? ????? ?? ??????? ?????? ??????
?? ????????? ?????? ?? (false , 1 , 800) ????
???? ?? ??? ???? ??????? ?? ?????? 1 ??? ?????? 2
??? ??? ?????? ?? 800
89??? ???? ?????? 1 ?? ?????? ???? ?? ?????????
?????? ??? ?????? 2 ?? ?????? 1 ????? ??????
false ?? ?????? 2 ?? ???? ???? ???????? ??????
???? ??????? ??? ??? ??????
90 ?????? ??????? ???? ?????? ??? ?????? 3 ??? ??
?????? 1 ?????? ?????? ??? ????? 2985 ?? ?? ????
?????? 2 ?????? ??? ????? 800 ?? ?????? 1 ?? ??
???? ?????? 4 ?????? ?????? ?? ??? ?????? ??
310
91???? ?? 310 ???? ?? 800 ???? ???? ?????? 4 ???
???? ??????? ????? ???? ???? DISTANCE 3
????? ( 3101421 1731 )
92 ??? ???? ??????? PATH 4 1 ?? ?? ??????
??? ?????? 3 ?? ???? ?????? 4 ???? ?? PATH 4
1 ?? ?? ?????? ??? 4 ?? ???? ?????? 1 ( ????
??????? ) ???? ??? ??? ?????? ?????? 4 ??????
??? ?????? 3
93????? ??????? ?????? ?????? ????????
INCLUDE ?????? ?????? true ?? ?? ???????
????????? ?????? ??? ???
94?????? 1 2 3 4 5
Distance 0 800 1731 310 200
Path 0 1 4 1 1
Include true false false true true
95???? ?? ??? ??? ???????? INCLUDE ??? ?????? ????
???????? (??? ?? ???? ???? ?????? false) ???
????? ????? ?????????? ??? ???? ???? ??? ?????
??? ???????? ?????? ?????? true
96???? ?? ?????? ??????? ?? ?????????? ?????? ??
??? ????? ?? 1 ??? 2 ??? 3 ???? ?? ??? ????? ??
?????? 1 ??? 4 ?????? ???? ???? ??? ??????? ??
1 ??? 3 ????? 800410 1210
97??? ??? ?? ????? ?????? ????? ?? 1 ??? 4 ?? ???
3 ????? ??? ????? ????????? ??????? ???
????????? ?? ???? ??????? UPDATE
98??? ??? ??? ????????? ?? ??? ?????? ????? ????
???? PATH 3 ?? 4 ??? 2 ?????? DISTANCE3 ??
1731??? 1210 ?????? ???? INCLUDE 2 ?? false
??? true
99??? ???? ?? ?????? 2 ?? ???? ???? ???????? ?????
???? ??????? ????????? ??????
?????? 1 2 3 4 5
Distance 0 800 1210 310 200
Path 0 1 2 1 1
Include true true true false true
100??? ???????? ??????? ??? ???? ??????? ????
?????? ??? ?????? 3 ( ?? ???? ??????? ) ???
????? ??PATH 3 2 ?? ?? ?????? ??? 3 ?? ??
2 ??? ?? ????? ?????? ??? 2 ??? ?????? ??? ??
??? 1 ??? PATH 2 1
101???? ?? 1 ?? ???? ??????? ??? ???? ??????? ?? 1
??? 2 ??? 3 ??????? ???? ??? ?????
?????? ???????? DISTANCE ??????? DISTANCE 3
?????? (1210) ??? ??? ?????
102?????? 1 2 3 4 5
Distance 0 800 1210 310 200
Path 0 1 2 1 1
Include true true true true true
103?????? ?????????? ???? ?????? ??????? ?????
??????
104????? ???? ????? ???? ?????? ??? ?????? 1 ?
?????? 3
??????????
1210 410800 3 2 1
2985 3 1
3233 1421612800 3 4 2 1
1731 1421310 3 4 1
2021 1421400200 3 4 5 1
1622 410612400200 3 2 4 5 1
1332 410612310 3 2 4 1
105?????? ??????
???? ???? ????? ???? ?????????? ??? ?????? 1 ?
?????? 3 ???? ?? ????? ?? ?????? 1 ??? ?????? 2
??? ?????? 3 ?? ???? ??????? ?????? ?? ?????
???? ??????? ??? ??? ??????? ?? ?? ??????
?????????? 1 2 3 800 410
1210
106??????? ???????
???????? ????? Floyd
??? ???????? ????? ?????? ??? ???????? Dijkstra
??? ???? ??? ?????????? ??? ???? ?????? ????
??????? ??? ?????? ???????? ?? ?????? ??????
107?? ???? ?????? ???? ??? ?????? ????? ?????
??????? ?????? ??????? ??????? ????? ?????
?????? ????? ?? ???? ????? ?????? ?? ??? ????
??????? ?? ???????? ??? ??? ??????? ??? ?? ??????
?????? ????? ???? ?????? ????? ??????? ???????
??? ?? ??? ???? ??????? ????? ??? ?????????? ??
O(n3)
108- ????? ??? ?????????? ??? ???? ??????? ???
- ?????? ????? ?????? (Adjacency Matrix Cost)
- ?? ????? ?????.
- ?????? ??????? (Path Matrix)
- ????? ??? ???????? ??? ????? ??????? ??????
????? ????????? ????? ??????? ?? ??? ?????? - I ? J ????? ??? ??? ? PATH IJ
109- ?????? P
- ??? ????? ???????? ?? ????? ?????????? ???
???
??? ?? ??? COST IJ ?????? ????? ?
COSTIJPIJ ??? ???? JI ( ?? ????? ?????
) ????? ??? ??? ??????? ?????? MAXINT ?? ?? ??
?????
110???? ?? ?????????? ??????? ?? ?????? ????????
??? ??? ?????? K ???? ??? PIJ
MINIMUM(PIKPKJ,PIJ ) ???? ?????
???? ??? ???? ??????? ?? ?????? I ??? ?????? J
??? ?????? ???? ?? ???? ????? ???? ?? J ??? ???
?? ???? ?????? ????? ??? N-1
111 ???? ?????? ???? ??????? ?????? ?????? ?? ?????
???????? ???????? ????? Floyd
?????
112?????
???? ??? ?????? ????? ??????
- ??????? ???????? ??? ????? ??????? ??????
??????. - ????? 8 ??? ??? ??? ???? ?? ???? ?????.
- ??? ?? ??? ???? ?????? ?????
- 5 (A,B,C,D,E)
113???? ??? 5 ??????? ((P1, P2, P3, P4, P5
E D C B A
18 8 10 23 8 A
8 48 10 8 23 B
7 19 8 10 10 C
20 8 19 48 8 D
8 20 7 8 18 E
114??????? ???????? P1
- ???? ??? ?????? ????? ????? ????? ??????
- ??? ????? ?????? ?? ????? ????? ??????
- ????? ?? ??? ???? ???????.
- ??? ??? ??????? ??? ?? ?????? ??? ?? ????
- ?????? ????? ???????.
115E D C B A
18 8 10 23 8 A
8 48 10 8 23 B
7 19 8 10 10 C
20 8 19 48 8 D
8 20 7 8 18 E
116- ??? ???? ????? ???????? ??????
- BB232346 is lt 8
- ?? ?????? ?? ?????? ???? ?? 8 ??? ?????? ??????
E D C B A
18 8 10 23 8 A
8 48 10 46 23 B
7 19 8 10 10 C
20 8 19 48 8 D
8 20 7 8 18 E
117- ???? ?????? ???? ????? ????????
- CB102333 is gt 10
- ?? ??? ??????? ??? ??? ?? ?????? ??? ???????????
E D C B A
18 8 10 23 8 A
8 48 10 46 23 B
7 19 8 10 10 C
20 8 19 48 8 D
8 20 7 8 18 E
118??????? ???????? ???????? P1
?????? ??? ???? ???? ????? ???? ???? ?????
????????? 8 ???? ?????? ??? ?? DB 823 ???
?? ????
119????? ?? ???? ????? ??? ?? ????? ?? ?????? ????
????? ?????? ?????? ????? ????? ????? ?????
??????? ??????
E D C B A
18 8 10 23 8 A
41 48 10 46 23 B
7 19 20 10 10 C
20 8 19 48 8 D
36 20 7 41 18 E
120??????? ???????? P2
???? ???? ??????? ?????? ????? ??????? ??? ??
??????? ???????
E D C B A
18 8 10 23 8 A
41 48 10 46 23 B
7 19 20 10 10 C
20 8 19 48 8 D
36 20 7 41 18 E
121??????? ???????? ???????? P2
???? ????? ???? ??? ?? ???????? ??????? ?????
E D C B A
18 71 10 23 46 A
41 48 10 46 23 B
7 19 20 10 10 C
20 96 19 48 71 D
36 20 7 41 18 E
122??????? ???????? P3
??????? ??????
E D C B A
18 71 10 23 46 A
41 48 10 46 23 B
7 19 20 10 10 C
20 96 19 48 71 D
36 20 7 41 18 E
123??????? ???????? ???????? P3
??????? ??????? ????? ?????? ?????? ???????
E D C B A
17 29 10 20 20 A
17 29 10 20 20 B
7 19 20 10 10 C
20 38 19 29 29 D
14 20 7 17 17 E
124??????? ???????? ???????? P4
??????? ???????? ??? ??????? ?? ????? ??? ?????
?? ??? ?? ?????? ???? ???? ??? ??????? ???? ????
E D C B A
17 29 10 20 20 A
17 29 10 20 20 B
7 19 20 10 10 C
20 38 19 29 29 D
14 20 7 17 17 E
125??????? ???????? ???????? P5
?? ??? ?????? ???? ???? ????? ????? ??? ???????
??????
E D C B A
17 29 10 20 20 A
17 29 10 20 20 B
7 19 14 10 10 C
20 38 19 29 29 D
14 20 7 17 17 E
126???????? ????????
??? P5 ???? ?????? ???? ??????? ??? ???????????
E D C B A
17 29 10 20 20 A
17 29 10 20 20 B
7 19 14 10 10 C
20 38 19 29 29 D
14 20 7 17 17 E
127???????? ????????
???? ??????? ???????? ??????? ?? ??? ????? ???
?????? ??????? ????? ??? ???