.355
2012
34 ., 2 ., 18 ., 2 .
, , , , , , , , , , , , , ,
, :
;
;
.
, .
. 2
. 4
. 5
1 .. 6
2 .. 9
2.1 ( ) 9
2.2 ( ) 9
2.3 ( ) 10
2.3.1 D4 10
2.3.2 D3 17
3 .. 24
3.1 . 24
3.2 . 25
4 .. 27
. 33
.. 34
, , , .
. . .
, , .
:
k = 6 - ;
m = 4 - ;
n = 2 - ;
ki - , k- i- , , k = 1...6, i = 1...4;
Yij - , i-ro j- , , i = 1...4, j = 1...2;
Zkj - , k- j- , , k = 1...6, j = 1...2;
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k - k- , , k = 1...6;
Di - i-ro , , i = 1...3;
Bj - j- , , j = 1...2;
- 1 k- i- , ./,k=1...6, i=l...4;
- 1 i-ro j- , ./, i = 1...4, j = l...2;
- 1 k- j- , ./, k = 1...6,j = 1...2;
k, Di,Bj ; , , ; ki, Yij, Zkj .
( ) :
(1)
( ):
(2)
, , .
1. , j- , :
(3)
2. , i-ro , , :
(4)
3. , i- , :
(5)
4. , k- , :
(6)
(1) (2) (3), (4), (5), (6).
2.1 ( )
, . , , ( 1).
1 -
, | |||
B1 | B2 | ||
A1 | |||
A2 | |||
A3 | |||
A4 | |||
A5 | |||
A6 |
2.2 ( )
, . , , ( 2).
2
, | |||
B1 | B2 | ||
D1 | |||
D2 | |||
D3 | |||
D4 |
2.3 ( )
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, k (k = 1...6) Di (i = 3...4) . , Es (s = 1...9), .
k , Es, Di ; ( 3).
3 ,
A1 | A2 | A3 | A4 | E1 | E2 | E3 | E4 | E5 | E6 | E7 | E8 | E9 | D1 | D2 | D3 | D4 | ||
A1 | ||||||||||||||||||
A2 | ||||||||||||||||||
A3 | ||||||||||||||||||
A4 | ||||||||||||||||||
E1 | ||||||||||||||||||
E2 | ||||||||||||||||||
E3 | ||||||||||||||||||
E4 | ||||||||||||||||||
E5 | ||||||||||||||||||
E6 | ||||||||||||||||||
E7 | ||||||||||||||||||
E8 | ||||||||||||||||||
E9 | ||||||||||||||||||
D1 | ||||||||||||||||||
D2 | ||||||||||||||||||
D3 | ||||||||||||||||||
D4 |
2.3.1 D4
17 ( D4) 1 ( 1), 2 ( 2), 3 ( 3), 4 ( 4).
1). k=0.
( ) 17. j-o (j = 10, 12), 17 (.. ), 17; :
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7.
2) k=1.
L1i-j i- 17, j- , Li-j i- j- U0j 17:
L1i-j= Li-j+ U0j, i = 1, 2, 16, j = 1,2, 17, i ≠ 17, j ≠ i.
i- 17 :
U1j= min{L1i-j}.
4 17
3 | j | L3-j | U0j | L13-j | U13 |
3-10-17 | 10 | 20 | 33 | 53 | 53 |
4 | j | L4-j | U0j | L14-j | U14 |
4-10-17 | 10 | 11 | 33 | 44 | 44 |
8 | j | L8-j | U0j | L18-j | U18 |
8-12-17 | 12 | 12 | 9 | 21 | 21 |
10 | j | L10-j | U0j | L110-j | U110 |
10-17 | 15 | 33 | 33 | ||
11 | j | L11-j | U0j | L111-j | U111 |
11-10-17 | |||||
11-12-17 | 12 | 9 | 9 | 18 | 18 |
12 | j | L12-j | U0j | L112-j | U112 |
12-17 | 15 | 9 | 9 | ||
13 | j | L13-j | U0j | L113-j | U113 |
13-10-17 | |||||
13-12-17 | 12 | 15 | 9 | 24 | 24 |
17 U1j ( ) 7.
3) k = 2.
L2i-j i- 17, j- , Li-j i- j- U1j j- 17 :
L2i-j= Li-j+ U1j, i = 1, 2, 16, j = 1,2, 17,i ≠ 17,j ≠ i.
i- 17 :
U2j= min{L2i-j}.
5 17
1 | j | L1-j | U1j | L11-j | U21 |
1-8-12-17 | 8 | 16 | 21 | 37 | 37 |
2 | j | L2-j | U1j | L12-j | U22 |
2-8-12-17 | 8 | 9 | 21 | 30 | 30 |
3 | j | L3-j | U1j | L13-j | U23 |
3-10-17 | 10 | 20 | 33 | 53 | 53 |
4 | j | L4-j | U1j | L14-j | U24 |
4-10-17 | 10 | 11 | 33 | 44 | 44 |
6 | j | L6-j | U1j | L16-j | U26 |
6-11-12-17 | 11 | 12 | 18 | 30 | 30 |
7 | j | L7-j | U1j | L17-j | U27 |
7-8-12-17 | 8 | 11 | 21 | 32 | 32 |
7-11-12-17 | |||||
8 | j | L8-j | U1j | L18-j | U28 |
8-12-17 | 12 | 12 | 9 | 21 | 21 |
8-13-12-17 | |||||
9 | j | L9-j | U1j | L19-j | U29 |
9-3-10-17 | |||||
9-8-12-17 | 8 | 4 | 21 | 25 | 25 |
9-13-12-17 | |||||
10 | j | L10-j | U1j | L110-j | U210 |
10-17 | |||||
10-11-12-17 | 11 | 6 | 18 | 24 | 24 |
10-13-12-17 | |||||
11 | j | L11-j | U1j | L111-j | U211 |
11-12-17 | 12 | 9 | 9 | 18 | 18 |
11-10-17 | |||||
12 | j | L12-j | U1j | L112-j | U212 |
12-17 | 15 | 9 | 9 | ||
13 | j | L13-j | U1j | L113-j | U213 |
13-8-12-17 | |||||
13-10-17 | |||||
13-12-17 | 12 | 15 | 9 | 24 | 24 |
15 | j | L15-j | U0j | L115-j | U215 |
15-13-12-17 | 13 | 7 | 24 | 31 | 31 |
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17 U2j ( ) 7.
4). k=3.
L3i-j i- 17, j- , Li-j i- j- U2j j- 17 :
L3i-j= Li-j+ U2j, i = 1, 2, 16, j = 1,2, 17,i ≠ 17,j ≠ i.
i- 17 :
U3j= min{L3i-j}.
6 17
1 | j | L1-j | U2j | L11-j | U31 |
1-7-8-12-17 | |||||
1-8-12-17 | 8 | 16 | 21 | 37 | 37 |
2 | j | L2-j | U2j | L12-j | U32 |
2-8-12-17 | 8 | 9 | 21 | 30 | 30 |
2-9-8-12-17 | |||||
3 | j | L3-j | U2j | L13-j | U33 |
3-10-17 | |||||
3-9-8-12-17 | 9 | 9 | 25 | 34 | 34 |
4 | j | L4-j | U2j | L14-j | U34 |
4-10-17 | |||||
4-10-11-12-17 | 10 | 11 | 24 | 35 | 35 |
5 | j | L5-j | U2j | L15-j | U35 |
5-6-11-12-17 | 6 | 3 | 30 | 33 | 33 |
6 | j | L6-j | U2j | L16-j | U36 |
6-11-12-17 | 11 | 12 | 18 | 30 | 30 |
6-7-8-12-17 | |||||
7 | j | L7-j | U2j | L17-j | U37 |
7-8-12-17 | 8 | 11 | 21 | 32 | 32 |
7-1-8-12-17 | |||||
7-6-11-12-17 | |||||
7-11-12-17 | |||||
8 | j | L8-j | U2j | L18-j | U38 |
8-12-17 | 12 | 12 | 9 | 21 | 21 |
9 | j | L9-j | U2j | L19-j | U39 |
9-8-12-17 | 8 | 4 | 21 | 25 | 25 |
9-2-8-12-17 | |||||
9-3-10-17 | |||||
9-13-12-17 | |||||
10 | j | L10-j | U2j | L110-j | U310 |
10-11-12-17 | 11 | 6 | 18 | 24 | 24 |
10-13-12-17 | |||||
11 | j | L11-j | U2j | L111-j | U311 |
11-12-17 | 12 | 9 | 9 | 18 | 18 |
11-7-8-12-17 | |||||
12 | j | L12-j | U2j | L112-j | U312 |
12-17 | |||||
13 | j | L13-j | U2j | L113-j | U313 |
13-12-17 | 12 | 15 | 9 | 24 | 24 |
13-8-12-17 | |||||
13-9-8-12-17 | |||||
13-10-11-12-17 | |||||
15 | j | L15-j | U0j | L115-j | U215 |
15-13-12-17 | 13 | 7 | 24 | 31 | 31 |
17 U3j ( ) 7.
5) k=4.
L4i-j i-o 17, j- , , Li-j i- j- U3j j- 17 :
L4i-j= Li-j+ U3j, i = 1, 2, 16, j = 1,2, 17,i ≠ 17,j ≠ i.
i- 17 :
U4j= min{L4i-j}.
, U4j U3j . .
7 17 .
7 17
j | k=0 | k=1 | k=2 | |||
U0j | U1j | U2j | ||||
1-8-12-17 | ||||||
2-8-12-17 | ||||||
3-10-17 | 3-10-17 | |||||
4-10-17 | 4-10-17 | |||||
8-12-17 | ||||||
6-11-12-17 | ||||||
10-17 | 7-8-12-17 | |||||
11-12-17 | 8-12-17 | |||||
12-17 | 9-8-12-17 | |||||
10-17 | 13-12-17 | 10-11-12-17 | ||||
11-12-17 | ||||||
12-17 | 12-17 | |||||
13-12-17 | ||||||
14-11-12-17 | ||||||
15-13-12-17 |
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j | k=3 | k=4 | ||
U3j | U4j | |||
1-8-12-17 | 1-8-12-17 | |||
2-8-12-17 | 2-8-12-17 | |||
3-9-8-12-17 | 3-9-8-12-17 | |||
4-10-11-12-17 | 4-10-11-12-17 | |||
5-6-11-12-17 | 5-6-11-12-17 | |||
6-11-12-17 | 6-11-12-17 | |||
7-8-12-17 | 7-8-12-17 | |||
8-12-17 | 8-12-17 | |||
9-8-12-17 | 9-8-12-17 | |||
10-11-12-17 | 10-11-12-17 | |||
11-12-17 | 11-12-17 | |||
12-17 | 12-17 | |||
13-12-17 | 13-12-17 | |||
14-11-12-17 | 14-11-12-17 | |||
15-13-12-17 | 15-13-12-17 |
17 ( D4)
1 ( A1): 1-8-12-17(A1-E4-E8-D4); 37;
2 ( 2): 2-8-12-17(A2-E4-E8-D4); 30;
3 ( 3): 3-9-8-12-17(A3-E5-E4-E8-D4); 34;
4 ( 4): 4-10-11-12-17 (A4-E6-E7-E8-D4); 35.
2.3.2 D3
16 ( D3) 1 ( 1), 2 ( 2), 3 ( 3), 4 ( 4).
1). k=0.
( ) 16. j-o (j = 11, 13), 16 (.. ), Lj-16 16; :
;
12.
2) k=1.
L1i-j i- 16, j- , Li-j i- j- U0j 16:
L1i-j= Li-j+ U0j, i = 1, 2, 15, j = 1,2, 16, j ≠ i,j ≠ 16.
i- 16 :
U1j= min{L1i-j}.
8 16
6 | j | L6-j | U0j | L16-j | U16 |
6-11-16 | 11 | 12 | 12 | 24 | 24 |
7 | j | L7-j | U0j | L17-j | U17 |
7-11-16 | 11 | 40 | 12 | 52 | 52 |
8 | j | L8-j | U0j | L18-j | U18 |
8-13-16 | 13 | 10 | 22 | 32 | 32 |
9 | j | L9-j | U0j | L19-j | U19 |
9-13-16 | 13 | 9 | 22 | 31 | 31 |
10 | j | L10-j | U0j | L110-j | U110 |
10-11-16 | 11 | 6 | 12 | 18 | 18 |
10-13-16 | |||||
11 | j | L11-j | U0j | L111-j | U111 |
11-16 | 16 | 12 | 12 | ||
12 | j | L12-j | U0j | L112-j | U112 |
12-11-16 | 11 | 9 | 12 | 21 | 21 |
12-13-16 | |||||
13 | j | L13-j | U0j | L113-j | U113 |
13-16 | 16 | 22 | 22 | ||
14 | j | L14-j | U0j | L114-j | U114 |
15-13-16 | 13 | 7 | 22 | 29 | 29 |
16 U1j ( ) 12.
3) k = 2.
L2i-j i- 16, j- , Li-j i- j- U1j j- 16 :
L2i-j= Li-j+ U1j, i = 1, 2, 15, j = 1,2, 16, j ≠ i,j ≠ 16.
i- 16 :
U2j= min{L2i-j}.
9 16
1 | j | L1-j | U1j | L11-j | U21 |
1-7-11-16 | |||||
1-8-13-16 | 8 | 16 | 32 | 48 | 48 |
2 | j | L2-j | U1j | L12-j | U22 |
2-8-13-16 | 8 | 9 | 32 | 41 | 41 |
2-9-13-16 | |||||
3 | j | L3-j | U1j | L13-j | U23 |
3-9-13-16 | |||||
3-10-11-16 | 10 | 20 | 18 | 38 | 38 |
4 | j | L4-j | U1j | L14-j | U24 |
4-10-11-16 | 10 | 11 | 18 | 29 | 29 |
5 | j | L5-j | U1j | L15-j | U25 |
5-6-11-16 | 6 | 3 | 24 | 27 | 27 |
6 | j | L6-j | U1j | L16-j | U26 |
6-11-16 | 11 | 12 | 12 | 24 | 24 |
6-7-11-16 | |||||
7 | j | L7-j | U1j | L17-j | U27 |
7-11-16 | |||||
7-6-11-16 | 6 | 9 | 24 | 33 | 33 |
7-8-13-16 | |||||
8 | j | L8-j | U1j | L18-j | U28 |
8-13-16 | 13 | 10 | 22 | 32 | 32 |
8-7-11-16 | |||||
8-9-13-16 | |||||
8-12-11-16 | |||||
9 | j | L9-j | U1j | L19-j | U29 |
9-13-16 | 13 | 9 | 22 | 31 | 31 |
9-8-13-16 | |||||
10 | j | L10-j | U1j | L110-j | U210 |
10-11-16 | 11 | 6 | 12 | 18 | 18 |
11 | j | L11-j | U1j | L111-j | U211 |
11-16 | 16 | 12 | 12 | ||
12 | j | L12-j | U1j | L112-j | U212 |
12-11-16 | 11 | 9 | 12 | 21 | 21 |
12-8-13-16 | |||||
13 | j | L13-j | U1j | L113-j | U213 |
13-16 | |||||
13-10-11-16 | 10 | 2 | 18 | 20 | 20 |
13-12-11-16 | |||||
15 | j | L15-j | U1j | L115-j | U215 |
15-13-16 | 13 | 7 | 22 | 29 | 29 |
16 U2j ( ) 12.
4) k=3.
L3i-j i- 16, j- , Li-j i- j- U2j j- 16 :
L3i-j= Li-j+ U2j, i = 1, 2, 15, j = 1,2, 16, j ≠ i,j ≠ 16.
i- 16 :
U3j= min{L3i-j}.
10 16
1 | j | L1-j | U2j | L11-j | U31 |
1-8-13-16 | |||||
1-7-6-11-16 | 7 | 5 | 33 | 38 | 38 |
2 | j | L2-j | U2j | L12-j | U32 |
2-8-13-16 | 8 | 9 | 32 | 41 | 41 |
3 | j | L3-j | U2j | L13-j | U33 |
3-10-11-16 | 10 | 20 | 18 | 38 | 38 |
4 | j | L4-j | U2j | L14-j | U34 |
4-10-11-16 | 10 | 11 | 18 | 29 | 29 |
5 | j | L5-j | U2j | L15-j | U35 |
5-6-11-16 | 6 | 3 | 24 | 27 | 27 |
6 | j | L6-j | U2j | L16-j | U36 |
6-11-16 | 11 | 12 | 12 | 24 | 24 |
7 | j | L7-j | U2j | L17-j | U37 |
7-1-8-13-16 | |||||
7-6-11-16 | 6 | 9 | 24 | 33 | 33 |
8 | j | L8-j | U2j | L18-j | U38 |
8-13-16 | |||||
8-7-6-11-16 | |||||
8-13-10-11-16 | 13 | 10 | 20 | 30 | 30 |
9 | j | L9-j | U2j | L19-j | U39 |
9-13-16 | |||||
9-2-8-13-16 | |||||
9-3-10-11-16 | |||||
9-13-10-11-16 | 13 | 9 | 20 | 29 | 29 |
10 | j | L10-j | U2j | L110-j | U310 |
10-11-16 | 11 | 6 | 12 | 18 | 18 |
11 | j | L11-j | U2j | L111-j | U311 |
11-16 | 16 | 12 | 12 | ||
12 | j | L12-j | U2j | L112-j | U312 |
12-11-16 | 11 | 9 | 12 | 21 | 21 |
12-13-10-11-16 | |||||
13 | j | L13-j | U2j | L113-j | U313 |
13-10-11-16 | 10 | 2 | 18 | 20 | 20 |
15 | j | L15-j | U2j | L115-j | U315 |
15-13-16 | |||||
15-13-10-11-16 | 13 | 7 | 20 | 27 | 27 |
16 U3j ( ) 12.
5) k=4.
L4i-j i-o 16, j- , , Li-j i- j- U3j j- 16 :
L4i-j= Li-j+ U3j, i = 1, 2, 15, j = 1,2, 16, j ≠ i,j ≠ 16.
i- 16 :
U4j= min{L4i-j}
11 16
1 | j | L1-j | U2j | L11-j | U31 |
1-7-6-11-16 | 7 | 5 | 33 | 38 | 38 |
2 | j | L2-j | U2j | L12-j | U32 |
2-8-13-16 | |||||
2-8-13-10-11-16 | 8 | 9 | 30 | 39 | 39 |
3 | j | L3-j | U2j | L13-j | U33 |
3-10-11-16 | 10 | 20 | 18 | 38 | 38 |
4 | j | L4-j | U2j | L14-j | U34 |
4-10-11-16 | 10 | 11 | 18 | 29 | 29 |
5 | j | L5-j | U2j | L15-j | U35 |
5-6-11-16 | 6 | 3 | 24 | 27 | 27 |
6 | j | L6-j | U2j | L16-j |