Gор(V,X)
???. 1
??????1 ??? ?????????????????? ????? G, ???????????????? ? ?????? Gор ???????? (????????????? ???????) :
?) ????????? ?????? V ? ????????? ????? X, G(V,X);
?) ?????? ?????????;
?) ??????? ?????????????;
?) ??????? ?????.
?) ??? ????? Gор ???????? ??????? ?????????.
????????? ?????? - ??. ??? 1
?) V={0,1,2,3,4,5,6,7,8,9}
X={{0,1},{0,2},{0,3},{1,2},{1,4},{1,5},{1,6},{1,7},{2,3},{2,5},{3,8},{3,9},{4,5},{4,6},{5,3},{5,6},{5,8},{6,9},{7,8},{7,9},{8,9}}
? ?????????? ????? ????? ???????????? ???????? ? ????????? ??????? ??????? ? ????.
?) ?0={1,2,3};
?1={0,2,4,5,6,7};
?2={0,1,3,5};
?3={0,2,5,8,9};
?4={1,5,6};
?5={1,2,3,4,6,8};
?6={1,4,5,9};
?7={1,8,9};
?8={1,3,5,7,9};
?9={3,6,7,8};
?) ????????? ?????? ? ????? ?????????????? ?. ?)
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?) ???????? ??????? ???????? ???????, ?.?. ??????? ????? ?????????????????? ????? ??????????? ???????????? ??????? ?????????.
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?) ??????? ????????? ??? ????? Gор.
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?????? 2 ????? ??????? D(G), ?????? R(G), ?????????? ??????? Z(G) ??? ????? G ; ??????? ???????, ?????????? ???????? ????? G.
D(G)=2
R(G)=2
Z(G)=10
??? ??????? ????? G(V,X) ???????? ????????.
?????? 3 ?????????????? ??????? ????? G, ????????? ?????????:
?) "?????? ? ???????";
?) "?????? ? ??????".
???????? ??????? - .
?)
?)
?????? 4 ????????? ???????? ????? ????? ????? ???????????? ???? ????? G. ???????? ??? ??????? ?? ????????? ?????????? ??????, ?????? ?? ???????? ??????? .
??? ?????????? ?????? - 14.
??? ??????? ??????: 000011000001111111.
?????? 5 ????????? ???????? ???????? ????? ????? ?????????? ????? ?? ??????? ????? G.
??? ?????????? ???? - 8.
?????? 6 ????????? ???????? ????? - ??????????, ????? ???????????? ????? ?? ?????????? ??????????? ??????????????? ???? {Gор , , w}. ??????? ?????? ???????????? ????.
?????????????????? ????????? ???? (?????????? ????? ???????? ??????????):
1-? ???
2-? ???
3-? ???
4-? ???
5-? ???
6-? ???
7-? ???
???????????? ?????:
??? ????? ?? ???????, ????? {6,9},{7,9},{3,9}, ???????? ??????? , ?????????, ? ?????????? ????? {8,9}, ?????????? ?? ??????? 8, ?? ????? ???????? ??????? ???????? ??????? ???????, ??? ??? ????????? ??? ?????, ???????? ??????? 8. ??????? ??????? - ???? ????????? ??? ?????????? ?????, ?? ??????? ???????????, ??? ???????? ????????? ????????????? ?????? ? ????.
???????????? ????? ? ???? ????? 12.
??????????? ?????? ???? ?? ????? ?????: {{0,1},{0,2},{0,3}}. ??? ?????????? ??????????? ????? 16
??????????? ?????? ???? ?? ?????????? ???????????: {{6,9}, {7,9}, {3,9}, {3,8}, {5,8}, {7,8}}. ??? ?????????? ??????????? ????? 12.
?????? 7 (?????? ? ??????????) ???????? ????????? ?????????????????? ?????? ????? G.
?) ??????? ? ????? G ???????? ????. ???? ??????? ???? ?? ??????????, ?? ? ????? G ???????? ?????????? ????? ????? ????? ???????, ????? ? ????? ????? ????? ???? ??????? ???????? ????.
?) ??????? ? ????? G ??????? ????. ???? ?????? ????? ?? ??????????, ?? ? ????? G ???????? ?????????? ????? ????? ????? ???????, ????? ? ????? ????? ????? ???? ??????? ??????? ????.
????????? ?????????????????? ?????? ????? G:
(3,6,4,5,3,6,4,3,4,4)
?) ??? ????????????? ????????? ???? ????????? ?????? ??? ??????? ? ????????? ?????????, ??????? ?????????? ???????? ???? ?????, ?????? ????? ????????? 4 ? 7.
?????????? ???????? ????: 0,3,2,0,1,2,5,1,4,5,6,1,7,4,6,9,7,8,9,3,8,5,3.
????? ????????? ???? (??????????? ????? ???????? ?????????):
?) ?????????? ?????? ?) ????????? ????? {3,0}, ??????? ???????? ???? (??? ???? ???????? ??????? ????????????? ???????? ????? - ???????? ???????? ???? ??????). ????? {3,0} ???????, ??? ?? ???????????? ???????, ?? ??? ????????????? ????? ?????? ????? {0,7} ? {4,3} ?????? ????? ?????????.
?????????? ??????? ????: 0,3,2,0,1,2,5,1,4,5,6,1,7,4,6,9,7,8,9,3,8,5,3,0.
????? ???????? ????? (??????????? ????? ???????? ?????????):
?????? 8
?) ??????? ? ????? Gор ??????????? ????. ???? ????? ???? ?? ??????????, ?? ? ????? Gор ???????? ?????????? ??????????? ????? ????? ????? ???????, ????? ? ????? ????? ??????????? ???? ????? ???? ???????.
?) ??????? ? ????? Gор ??????????? ????. ???? ????? ???? ?? ??????????, ?? ? ????? Gор ???????? ?????????? ??????????? ????? ????? ????? ???????, ????? ? ????? ????? ??????????? ???? ????? ???? ???????.
?) ??????????? ???? (????? ? ?????????? ??????????? ???????? ?????????):
?) ??????????? ???? (????? ? ?????????? ??????????? ???????? ?????????):
?????? 9 (?????? ? ????????????) ??? ?????? ??????????????? ?????????????? ???? ? ????????? x1, x2,...xn.??? ???? xixj ????? ?????????? Vij ??????? ?????. ????????? ???????? ?????? ?????? ? ??????, ????? ??????????? ?????? ???????????? (?????????????) ????. ?????? ?? ???????????? ???????? ???????????? ??????? ?????? ? ?????? ?? ??????????? ????????, ?????????? ??????? ? ?????????? ,??? . ????????? ???????.
???????? ???????.
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??????? ? 14
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?????? ?? ???????? x2-x3:
??????? 23 =14+0=14
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??????? 23 =14+1=15
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?????????? ?? 23. ?????? ?? ???????? x3-x6:
??????? 23E36 =14+0=14
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??????? 2336 =14+6=20
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?????????? ?? 2336. ?????? ?? ???????? x4-x5:
??????? 23E3645 =14+0=14
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??????? 233645 =14+1=15
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?????????? ?? 233645. ?????? ?? ???????? x5-x1:
??????? 23364551 =14+1=15
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??????? 23364551 =14+6=20
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???????????? ????? ??????????? ??????: 2,3,6,4,5,1,2.
????????? ?????????:
?????? 10 (?????? ? ???????????) ??? ?????? ?????????? ???? Knn ? ????????? ?????? ???? x1, x2,...xn.? ????????? ?????? ???? y1, y2,...yn..??? ????? {xi,yj} ???????? ?????????? vij ??????? ?????. ????????? ?????????? ????????, ????? ??????????? ????????????? ???????????? (????????????? ????). ????????? ???????.
??????? ????? ??????????? ????? K55 :
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?????? ???? - ????????? ????? ?? ?????, ?. ?. ???? ??? ???? ?? ???? ????? ? ????????.
?????? ???? - ?????????? ??????? ?????????????.
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?????? ???? - ?????????? ????????????? ?????????????.
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????? ???? - ????????? ???????????? ????????? ?????.
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??????? ? ????????? ?????????. ??????? ?? ??????? ?????.
?????? ?????????????:
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|
4 |
3 |
5 |
0 |
2 |
|
3 |
|
|
|
|
|
?????? ?????????????:
|
y1 |
y2 |
y3 |
y4 |
y5 |
|
x1 |
5 |
|
0 |
|
|
|
x2 |
0 |
4 |
6 |
5 |
3 |
|
x3 |
2 |
0 |
2 |
1 |
1 |
|
x4 |
2 |
7 |
6 |
5 |
3 |
|
x5 |
|
4 |
3 |
5 |
0 |
|
|
|
|
|
|
|
|
???????????? ?????????????:
|
y1 |
y2 |
y3 |
y4 |
y5 |
|
x1 |
5 |
|
0 |
|
|
X |
x2 |
0 |
4 |
6 |
5 |
3 |
X |
x3 |
2 |
0 |
2 |
1 |
1 |
X |
x4 |
2 |
7 |
6 |
5 |
3 |
|
x5 |
|
4 |
3 |
5 |
0 |
X |
|
X |
X |
X |
|
X |
|
??????????? ?????:
|
y1 |
y2 |
y3 |
y4 |
y5 |
|
x1 |
5 |
|
0 |
|
|
|
x2 |
0 |
4 |
6 |
5 |
3 |
|
x3 |
2 |
0 |
2 |
1 |
1 |
|
x4 |
2 |
7 |
6 |
5 |
3 |
1 |
x5 |
|
4 |
3 |
5 |
0 |
|
|
|
|
|
|
|
|
???????????? ?????:
|
y1 |
y2 |
y3 |
y4 |
y5 |
|
x1 |
5 |
|
0 |
|
|
|
x2 |
0 |
4 |
6 |
5 |
3 |
|
x3 |
2 |
0 |
2 |
1 |
1 |
|
x4 |
0 |
5 |
4 |
3 |
1 |
1 |
x5 |
|
4 |
3 |
5 |
0 |
|
|
|
|
|
|
|
|
?????? ?????????????:
|
y1 |
y2 |
y3 |
y4 |
y5 |
|
x1 |
5 |
|
0 |
|
|
|
x2 |
0 |
4 |
6 |
5 |
3 |
|
x3 |
2 |
0 |
2 |
1 |
1 |
|
x4 |
|
5 |
4 |
3 |
1 |
1 |
x5 |
|
4 |
3 |
5 |
0 |
|
|
|
|
|
|
|
|
???????????? ?????????????:
|
y1 |
y2 |
y3 |
y4 |
y5 |
|
x1 |
5 |
|
0 |
|
|
X |
x2 |
0 |
4 |
6 |
5 |
3 |
X |
x3 |
2 |
0 |
2 |
1 |
1 |
X |
x4 |
|
5 |
4 |
3 |
1 |
|
x5 |
|
4 |
3 |
5 |
0 |
X |
|
X |
X |
X |
|
X |
|
??????????? ?????:
|
y1 |
y2 |
y3 |
y4 |
y5 |
|
x1 |
5 |
|
0 |
|
|
|
x2 |
0 |
4 |
6 |
5 |
3 |
3 |
x3 |
2 |
0 |
2 |
1 |
1 |
|
x4 |
|
5 |
4 |
3 |
1 |
1 |
x5 |
|
4 |
3 |
5 |
0 |
|
|
2 |
|
|
|
|
|
???????????? ?????:
|
y1 |
y2 |
y3 |
y4 |
y5 |
|
x1 |
6 |
|
0 |
|
|
|
x2 |
0 |
3 |
5 |
4 |
2 |
3 |
x3 |
3 |
0 |
2 |
1 |
1 |
|
x4 |
|
4 |
3 |
2 |
0 |
1 |
x5 |
1 |
4 |
3 |
5 |
0 |
|
|
2 |
|
|
|
|
|
?????? ?????????????:
|
y1 |
y2 |
y3 |
y4 |
y5 |
|
x1 |
6 |
|
0 |
|
|
|
x2 |
0 |
3 |
5 |
4 |
2 |
3 |
x3 |
3 |
0 |
2 |
1 |
1 |
|
x4 |
|
4 |
3 |
2 |
|
1 |
x5 |
1 |
4 |
3 |
5 |
0 |
|
|
2 |
|
|
|
|
|
???????????? ?????????????:
|
y1 |
y2 |
y3 |
y4 |
y5 |
|
x1 |
6 |
|
0 |
|
|
X |
x2 |
0 |
3 |
5 |
4 |
2 |
X |
x3 |
3 |
0 |
2 |
1 |
1 |
X |
x4 |
|
4 |
3 |
2 |
|
|
x5 |
1 |
4 |
3 |
5 |
0 |
X |
|
X |
X |
X |
|
X |
|
??????????? ?????:
|
y1 |
y2 |
y3 |
y4 |
y5 |
|
x1 |
6 |
|
0 |
|
|
|
x2 |
0 |
3 |
5 |
4 |
2 |
4 |
x3 |
3 |
0 |
2 |
1 |
1 |
|
x4 |
|
4 |
3 |
2 |
|
1 |
x5 |
1 |
4 |
3 |
5 |
0 |
5 |
|
2 |
|
|
|
3 |
|
? ?????????? ?????:
|
y1 |
y2 |
y3 |
y4 |
y5 |
|
x1 |
6 |
|
0 |
|
|
|
x2 |
0 |
1 |
3 |
2 |
2 |
4 |
x3 |
3 |
0 |
2 |
1 |
1 |
|
x4 |
|
2 |
1 |
0 |
|
1 |
x5 |
1 |
4 |
3 |
5 |
0 |
5 |
|
2 |
|
|
|
3 |
|
???????? ????
?????????? ????:
??? ?????????? ???????????? ????????????? = 12.
?????? 11 ?????? ?????? 10, ????????? ???????? ?????? ? ?????? (??????????? ??????? xi ? yj).
??????? ? (????????). ?????? - xi , ??????? - yj. =0
|
1 |
2 |
3 |
4 |
5 |
|
1 |
2 |
01 |
03 |
02 |
02 |
|
2 |
06 |
7 |
9 |
8 |
6 |
|
3 |
01 |
1 |
3 |
2 |
2 |
|
4 |
04 |
8 |
7 |
6 |
4 |
|
5 |
03 |
7 |
6 |
8 |
3 |
|
|
|
|
|
|
|
|
?????? ?? ???????? x2 - y1:
??????? ?21 =0+8=8
|
2 |
3 |
4 |
5 |
|
1 |
00 |
02 |
01 |
00 |
|
3 |
01 |
2 |
1 |
1 |
1 |
4 |
4 |
3 |
2 |
02 |
4 |
5 |
4 |
3 |
5 |
03 |
3 |
|
|
|
|
|
|
??????? 21 =0+6=6
|
1 |
2 |
3 |
4 |
5 |
|
1 |
2 |
01 |
03 |
02 |
00 |
|
2 |
|
1 |
3 |
2 |
01 |
6 |
3 |
01 |
1 |
3 |
2 |
2 |
|
4 |
04 |
8 |
7 |
6 |
4 |
|
5 |
03 |
7 |
6 |
8 |
3 |
|
|
|
|
|
|
|
|
?????????? ?? 21:
?????? ?? ???????? x4 - y1:
??????? 21?41 =6+4=10
|
2 |
3 |
4 |
5 |
|
1 |
00 |
02 |
01 |
00 |
|
2 |
1 |
3 |
2 |
01 |
|
3 |
01 |
2 |
1 |
1 |
1 |
5 |
4 |
3 |
5 |
03 |
3 |
|
|
|
|
|
|
??????? 2141 =6+4=10
|
1 |
2 |
3 |
4 |
5 |
|
1 |
2 |
01 |
03 |
02 |
00 |
|
2 |
|
1 |
3 |
2 |
01 |
|
3 |
01 |
1 |
3 |
2 |
2 |
|
4 |
|
4 |
3 |
2 |
02 |
4 |
5 |
03 |
7 |
6 |
8 |
3 |
|
|
|
|
|
|
|
|
?????????? ?? ?21:
?????? ?? ???????? x5 - y5:
??????? ?21?55 =8+2=10
|
2 |
3 |
4 |
|
1 |
00 |
01 |
00 |
|
3 |
01 |
2 |
1 |
|
4 |
2 |
1 |
01 |
2 |
|
|
|
|
|
??????? ?2155 =8+3=11
|
2 |
3 |
4 |
5 |
|
1 |
00 |
02 |
01 |
00 |
|
3 |
01 |
2 |
1 |
1 |
|
4 |
4 |
3 |
2 |
02 |
|
5 |
1 |
01 |
2 |
|
3 |
|
|
|
|
|
|
?????????? ?? ?21?55:
?????? ?? ???????? x3 - y2:
??????? ?21?55?32 =10+0=10
|
3 |
4 |
|
1 |
01 |
00 |
|
4 |
1 |
01 |
|
|
|
|
|
????? ??????? ????????: x1 - y3 ? x4 - y4. ??? ?? ???????? ??????.
? ????? ????? ??????????? ????????????? ? ??????????? ?????:
????????? ?????????: