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Домашня робота ТА 2

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На основании матрицы D2, вычислим последовательно все элементы матрицы D3. Для этого мы используем рекуррентное соотношение di,j3=min{ di,32+ d3,j2; di,j2}. d1,13=min{d1,32+d3,12d1,12}=min{∞+∞; 0}=0 d1,23=min{d1,32+d3,22d1,22}=min{∞+∞; ∞}=∞ d1,33=min{d1,32+d3,32d1,32}=min{∞+0; ∞}=∞ d1,43=min{d1,32+d3,42d1,42}=min{∞+20; ∞}=∞ d1,53=min{d1,32+d3,52d1,52}=min{∞+∞; ∞}=∞ d1,63=min{d1,32+d3,62d1,62}=min{∞+9; ∞}=∞ d1,73=min{d1,32+d3,72d1,72}=min{∞+∞; ∞}=∞ d1,83=min{d1,32+d3,82d1,82}=min{∞+∞; 28}=28 d2,13=min{d2,32+d3,12d2,12}=min{∞+∞; 14}=14 d2,23=min{d2,32+d3,22d2,22}=min{∞+∞; 0}=0 d2,33=min{d2,32+d3,32d2,32}=min{∞+0; ∞}=∞ d2,43=min{d2,32+d3,42d2,42}=min{∞+20; ∞}=∞ d2,53=min{d2,32+d3,52d2,52}=min{∞+∞; 31}=31 d2,63=min{d2,32+d3,62d2,62}=min{∞+9; ∞}=∞ d2,73=min{d2,32+d3,72d2,72}=min{∞+∞; ∞}=∞ d2,83=min{d2,32+d3,82d2,82}=min{∞+∞; 42}=42 d3,13=min{d3,32+d3,12d3,12}=min{0+∞; ∞}=∞ d3,23=min{d3,32+d3,22d3,22}=min{0+∞; ∞}=∞ d3,33=min{d3,32+d3,32d3,32}=min{0+0; 0}=0 d3,43=min{d3,32+d3,42d3,42}=min{0+20; 20}=20 d3,53=min{d3,32+d3,52d3,52}=min{0+∞; ∞}=∞ d3,63=min{d3,32+d3,62d3,62}=min{0+9; 9}=9 d3,73=min{d3,32+d3,72d3,72}=min{0+∞; ∞}=∞ d3,83=min{d3,32+d3,82d3,82}=min{0+∞; ∞}=∞ d4,13=min{d4,32+d3,12d4,12}=min{∞+∞; ∞}=∞ d4,23=min{d4,32+d3,22d4,22}=min{∞+∞; ∞}=∞ d4,33=min{d4,32+d3,32d4,32}=min{∞+0; ∞}=∞ d4,43=min{d4,32+d3,42d4,42}=min{∞+20; 0}=0 d4,53=min{d4,32+d3,52d4,52}=min{∞+∞; ∞}=∞ d4,63=min{d4,32+d3,62d4,62}=min{∞+9; ∞}=∞ d4,73=min{d4,32+d3,72d4,72}=min{∞+∞; 18}=18 d4,83=min{d4,32+d3,82d4,82}=min{∞+∞; 15}=15 d5,13=min{d5,32+d3,12d5,12}=min{∞+∞; ∞}=∞ d5,23=min{d5,32+d3,22d5,22}=min{∞+∞; ∞}=∞ d5,33=min{d5,32+d3,32d5,32}=min{∞+0; ∞}=∞ d5,43=min{d5,32+d3,42d5,42}=min{∞+20; ∞}=∞ d5,53=min{d5,32+d3,52d5,52}=min{∞+∞; 0}=0 d5,63=min{d5,32+d3,62d5,62}=min{∞+9; 22}=22 d5,73=min{d5,32+d3,72d5,72}=min{∞+∞; ∞}=∞ d5,83=min{d5,32+d3,82d5,82}=min{∞+∞; ∞}=∞ d6,13=min{d6,32+d3,12d6,12}=min{∞+∞; ∞}=∞ d6,23=min{d6,32+d3,22d6,22}=min{∞+∞; ∞}=∞ d6,33=min{d6,32+d3,32d6,32}=min{∞+0; ∞}=∞ d6,43=min{d6,32+d3,42d6,42}=min{∞+20; ∞}=∞ d6,53=min{d6,32+d3,52d6,52}=min{∞+∞; ∞}=∞ d6,63=min{d6,32+d3,62d6,62}=min{∞+9; 0}=0 d6,73=min{d6,32+d3,72d6,72}=min{∞+∞; 35}=35 d6,83=min{d6,32+d3,82d6,82}=min{∞+∞; ∞}=∞ d7,13=min{d7,32+d3,12d7,12}=min{∞+∞; ∞}=∞ d7,23=min{d7,32+d3,22d7,22}=min{∞+∞; ∞}=∞ d7,33=min{d7,32+d3,32d7,32}=min{∞+0; ∞}=∞ d7,43=min{d7,32+d3,42d7,42}=min{∞+20; ∞}=∞ d7,53=min{d7,32+d3,52d7,52}=min{∞+∞; ∞}=∞ d7,63=min{d7,32+d3,62d7,62}=min{∞+9; ∞}=∞ d7,73=min{d7,32+d3,72d7,72}=min{∞+∞; 0}=0 d7,83=min{d7,32+d3,82d7,82}=min{∞+∞; ∞}=∞ d8,13=min{d8,32+d3,12d8,12}=min{∞+∞; ∞}=∞ d8,23=min{d8,32+d3,22d8,22}=min{∞+∞; ∞}=∞ d8,33=min{d8,32+d3,32d8,32}=min{∞+0; ∞}=∞ d8,43=min{d8,32+d3,42d8,42}=min{∞+20; ∞}=∞ d8,53=min{d8,32+d3,52d8,52}=min{∞+∞; ∞}=∞ d8,63=min{d8,32+d3,62d8,62}=min{∞+9; ∞}=∞ d8,73=min{d8,32+d3,72d8,72}=min{∞+∞; ∞}=∞ d8,83=min{d8,32+d3,82d8,82}=min{∞+∞; 0}=0 Представим матрицу D3, включив в нее рассчитанные элементы.

D3=

0

28

14

0

31

42

0

20

9

0

18

15

0

22

0

35

0

0

На основании матрицы D3, вычислим последовательно все элементы матрицы D4. Для этого мы используем рекуррентное соотношение di,j4=min{ di,43+ d4,j3; di,j3}. d1,14=min{d1,43+d4,13d1,13}=min{∞+∞; 0}=0 d1,24=min{d1,43+d4,23d1,23}=min{∞+∞; ∞}=∞ d1,34=min{d1,43+d4,33d1,33}=min{∞+∞; ∞}=∞ d1,44=min{d1,43+d4,43d1,43}=min{∞+0; ∞}=∞ d1,54=min{d1,43+d4,53d1,53}=min{∞+∞; ∞}=∞ d1,64=min{d1,43+d4,63d1,63}=min{∞+∞; ∞}=∞ d1,74=min{d1,43+d4,73d1,73}=min{∞+18; ∞}=∞ d1,84=min{d1,43+d4,83d1,83}=min{∞+15; 28}=28 d2,14=min{d2,43+d4,13d2,13}=min{∞+∞; 14}=14 d2,24=min{d2,43+d4,23d2,23}=min{∞+∞; 0}=0 d2,34=min{d2,43+d4,33d2,33}=min{∞+∞; ∞}=∞ d2,44=min{d2,43+d4,43d2,43}=min{∞+0; ∞}=∞ d2,54=min{d2,43+d4,53d2,53}=min{∞+∞; 31}=31 d2,64=min{d2,43+d4,63d2,63}=min{∞+∞; ∞}=∞ d2,74=min{d2,43+d4,73d2,73}=min{∞+18; ∞}=∞ d2,84=min{d2,43+d4,83d2,83}=min{∞+15; 42}=42 d3,14=min{d3,43+d4,13d3,13}=min{20+∞; ∞}=∞ d3,24=min{d3,43+d4,23d3,23}=min{20+∞; ∞}=∞ d3,34=min{d3,43+d4,33d3,33}=min{20+∞; 0}=0 d3,44=min{d3,43+d4,43d3,43}=min{20+0; 20}=20 d3,54=min{d3,43+d4,53d3,53}=min{20+∞; ∞}=∞ d3,64=min{d3,43+d4,63d3,63}=min{20+∞; 9}=9 d3,74=min{d3,43+d4,73d3,73}=min{20+18; ∞}=38 d3,84=min{d3,43+d4,83d3,83}=min{20+15; ∞}=35 d4,14=min{d4,43+d4,13d4,13}=min{0+∞; ∞}=∞ d4,24=min{d4,43+d4,23d4,23}=min{0+∞; ∞}=∞ d4,34=min{d4,43+d4,33d4,33}=min{0+∞; ∞}=∞ d4,44=min{d4,43+d4,43d4,43}=min{0+0; 0}=0 d4,54=min{d4,43+d4,53d4,53}=min{0+∞; ∞}=∞ d4,64=min{d4,43+d4,63d4,63}=min{0+∞; ∞}=∞ d4,74=min{d4,43+d4,73d4,73}=min{0+18; 18}=18 d4,84=min{d4,43+d4,83d4,83}=min{0+15; 15}=15 d5,14=min{d5,43+d4,13d5,13}=min{∞+∞; ∞}=∞ d5,24=min{d5,43+d4,23d5,23}=min{∞+∞; ∞}=∞ d5,34=min{d5,43+d4,33d5,33}=min{∞+∞; ∞}=∞ d5,44=min{d5,43+d4,43d5,43}=min{∞+0; ∞}=∞ d5,54=min{d5,43+d4,53d5,53}=min{∞+∞; 0}=0 d5,64=min{d5,43+d4,63d5,63}=min{∞+∞; 22}=22 d5,74=min{d5,43+d4,73d5,73}=min{∞+18; ∞}=∞ d5,84=min{d5,43+d4,83d5,83}=min{∞+15; ∞}=∞ d6,14=min{d6,43+d4,13d6,13}=min{∞+∞; ∞}=∞ d6,24=min{d6,43+d4,23d6,23}=min{∞+∞; ∞}=∞ d6,34=min{d6,43+d4,33d6,33}=min{∞+∞; ∞}=∞ d6,44=min{d6,43+d4,43d6,43}=min{∞+0; ∞}=∞ d6,54=min{d6,43+d4,53d6,53}=min{∞+∞; ∞}=∞ d6,64=min{d6,43+d4,63d6,63}=min{∞+∞; 0}=0 d6,74=min{d6,43+d4,73d6,73}=min{∞+18; 35}=35 d6,84=min{d6,43+d4,83d6,83}=min{∞+15; ∞}=∞ d7,14=min{d7,43+d4,13d7,13}=min{∞+∞; ∞}=∞ d7,24=min{d7,43+d4,23d7,23}=min{∞+∞; ∞}=∞ d7,34=min{d7,43+d4,33d7,33}=min{∞+∞; ∞}=∞ d7,44=min{d7,43+d4,43d7,43}=min{∞+0; ∞}=∞ d7,54=min{d7,43+d4,53d7,53}=min{∞+∞; ∞}=∞ d7,64=min{d7,43+d4,63d7,63}=min{∞+∞; ∞}=∞ d7,74=min{d7,43+d4,73d7,73}=min{∞+18; 0}=0 d7,84=min{d7,43+d4,83d7,83}=min{∞+15; ∞}=∞ d8,14=min{d8,43+d4,13d8,13}=min{∞+∞; ∞}=∞ d8,24=min{d8,43+d4,23d8,23}=min{∞+∞; ∞}=∞ d8,34=min{d8,43+d4,33d8,33}=min{∞+∞; ∞}=∞ d8,44=min{d8,43+d4,43d8,43}=min{∞+0; ∞}=∞ d8,54=min{d8,43+d4,53d8,53}=min{∞+∞; ∞}=∞ d8,64=min{d8,43+d4,63d8,63}=min{∞+∞; ∞}=∞ d8,74=min{d8,43+d4,73d8,73}=min{∞+18; ∞}=∞ d8,84=min{d8,43+d4,83d8,83}=min{∞+15; 0}=0 Представим матрицу D4, включив в нее рассчитанные элементы.

D4=

0

28

14

0

31

42

0

20

9

38

35

0

18

15

0

22

0

35

0

0

На основании матрицы D4, вычислим последовательно все элементы матрицы D5. Для этого мы используем рекуррентное соотношение di,j5=min{ di,54+ d5,j4; di,j4}. d1,15=min{d1,54+d5,14d1,14}=min{∞+∞; 0}=0 d1,25=min{d1,54+d5,24d1,24}=min{∞+∞; ∞}=∞ d1,35=min{d1,54+d5,34d1,34}=min{∞+∞; ∞}=∞ d1,45=min{d1,54+d5,44d1,44}=min{∞+∞; ∞}=∞ d1,55=min{d1,54+d5,54d1,54}=min{∞+0; ∞}=∞ d1,65=min{d1,54+d5,64d1,64}=min{∞+22; ∞}=∞ d1,75=min{d1,54+d5,74d1,74}=min{∞+∞; ∞}=∞ d1,85=min{d1,54+d5,84d1,84}=min{∞+∞; 28}=28 d2,15=min{d2,54+d5,14d2,14}=min{31+∞; 14}=14 d2,25=min{d2,54+d5,24d2,24}=min{31+∞; 0}=0 d2,35=min{d2,54+d5,34d2,34}=min{31+∞; ∞}=∞ d2,45=min{d2,54+d5,44d2,44}=min{31+∞; ∞}=∞ d2,55=min{d2,54+d5,54d2,54}=min{31+0; 31}=31 d2,65=min{d2,54+d5,64d2,64}=min{31+22; ∞}=53 d2,75=min{d2,54+d5,74d2,74}=min{31+∞; ∞}=∞ d2,85=min{d2,54+d5,84d2,84}=min{31+∞; 42}=42 d3,15=min{d3,54+d5,14d3,14}=min{∞+∞; ∞}=∞ d3,25=min{d3,54+d5,24d3,24}=min{∞+∞; ∞}=∞ d3,35=min{d3,54+d5,34d3,34}=min{∞+∞; 0}=0 d3,45=min{d3,54+d5,44d3,44}=min{∞+∞; 20}=20 d3,55=min{d3,54+d5,54d3,54}=min{∞+0; ∞}=∞ d3,65=min{d3,54+d5,64d3,64}=min{∞+22; 9}=9 d3,75=min{d3,54+d5,74d3,74}=min{∞+∞; 38}=38 d3,85=min{d3,54+d5,84d3,84}=min{∞+∞; 35}=35 d4,15=min{d4,54+d5,14d4,14}=min{∞+∞; ∞}=∞ d4,25=min{d4,54+d5,24d4,24}=min{∞+∞; ∞}=∞ d4,35=min{d4,54+d5,34d4,34}=min{∞+∞; ∞}=∞ d4,45=min{d4,54+d5,44d4,44}=min{∞+∞; 0}=0 d4,55=min{d4,54+d5,54d4,54}=min{∞+0; ∞}=∞ d4,65=min{d4,54+d5,64d4,64}=min{∞+22; ∞}=∞ d4,75=min{d4,54+d5,74d4,74}=min{∞+∞; 18}=18 d4,85=min{d4,54+d5,84d4,84}=min{∞+∞; 15}=15 d5,15=min{d5,54+d5,14d5,14}=min{0+∞; ∞}=∞ d5,25=min{d5,54+d5,24d5,24}=min{0+∞; ∞}=∞ d5,35=min{d5,54+d5,34d5,34}=min{0+∞; ∞}=∞ d5,45=min{d5,54+d5,44d5,44}=min{0+∞; ∞}=∞ d5,55=min{d5,54+d5,54d5,54}=min{0+0; 0}=0 d5,65=min{d5,54+d5,64d5,64}=min{0+22; 22}=22 d5,75=min{d5,54+d5,74d5,74}=min{0+∞; ∞}=∞ d5,85=min{d5,54+d5,84d5,84}=min{0+∞; ∞}=∞ d6,15=min{d6,54+d5,14d6,14}=min{∞+∞; ∞}=∞ d6,25=min{d6,54+d5,24d6,24}=min{∞+∞; ∞}=∞ d6,35=min{d6,54+d5,34d6,34}=min{∞+∞; ∞}=∞ d6,45=min{d6,54+d5,44d6,44}=min{∞+∞; ∞}=∞ d6,55=min{d6,54+d5,54d6,54}=min{∞+0; ∞}=∞ d6,65=min{d6,54+d5,64d6,64}=min{∞+22; 0}=0 d6,75=min{d6,54+d5,74d6,74}=min{∞+∞; 35}=35 d6,85=min{d6,54+d5,84d6,84}=min{∞+∞; ∞}=∞ d7,15=min{d7,54+d5,14d7,14}=min{∞+∞; ∞}=∞ d7,25=min{d7,54+d5,24d7,24}=min{∞+∞; ∞}=∞ d7,35=min{d7,54+d5,34d7,34}=min{∞+∞; ∞}=∞ d7,45=min{d7,54+d5,44d7,44}=min{∞+∞; ∞}=∞ d7,55=min{d7,54+d5,54d7,54}=min{∞+0; ∞}=∞ d7,65=min{d7,54+d5,64d7,64}=min{∞+22; ∞}=∞ d7,75=min{d7,54+d5,74d7,74}=min{∞+∞; 0}=0 d7,85=min{d7,54+d5,84d7,84}=min{∞+∞; ∞}=∞ d8,15=min{d8,54+d5,14d8,14}=min{∞+∞; ∞}=∞ d8,25=min{d8,54+d5,24d8,24}=min{∞+∞; ∞}=∞ d8,35=min{d8,54+d5,34d8,34}=min{∞+∞; ∞}=∞ d8,45=min{d8,54+d5,44d8,44}=min{∞+∞; ∞}=∞ d8,55=min{d8,54+d5,54d8,54}=min{∞+0; ∞}=∞ d8,65=min{d8,54+d5,64d8,64}=min{∞+22; ∞}=∞ d8,75=min{d8,54+d5,74d8,74}=min{∞+∞; ∞}=∞ d8,85=min{d8,54+d5,84d8,84}=min{∞+∞; 0}=0 Представим матрицу D5, включив в нее рассчитанные элементы.

D5=

0

28

14

0

31

53

42

0

20

9

38

35

0

18

15

0

22

0

35

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На основании матрицы D5, вычислим последовательно все элементы матрицы D6. Для этого мы используем рекуррентное соотношение di,j6=min{ di,65+ d6,j5; di,j5}. d1,16=min{d1,65+d6,15d1,15}=min{∞+∞; 0}=0 d1,26=min{d1,65+d6,25d1,25}=min{∞+∞; ∞}=∞ d1,36=min{d1,65+d6,35d1,35}=min{∞+∞; ∞}=∞ d1,46=min{d1,65+d6,45d1,45}=min{∞+∞; ∞}=∞ d1,56=min{d1,65+d6,55d1,55}=min{∞+∞; ∞}=∞ d1,66=min{d1,65+d6,65d1,65}=min{∞+0; ∞}=∞ d1,76=min{d1,65+d6,75d1,75}=min{∞+35; ∞}=∞ d1,86=min{d1,65+d6,85d1,85}=min{∞+∞; 28}=28 d2,16=min{d2,65+d6,15d2,15}=min{53+∞; 14}=14 d2,26=min{d2,65+d6,25d2,25}=min{53+∞; 0}=0 d2,36=min{d2,65+d6,35d2,35}=min{53+∞; ∞}=∞ d2,46=min{d2,65+d6,45d2,45}=min{53+∞; ∞}=∞ d2,56=min{d2,65+d6,55d2,55}=min{53+∞; 31}=31 d2,66=min{d2,65+d6,65d2,65}=min{53+0; 53}=53 d2,76=min{d2,65+d6,75d2,75}=min{53+35; ∞}=88 d2,86=min{d2,65+d6,85d2,85}=min{53+∞; 42}=42 d3,16=min{d3,65+d6,15d3,15}=min{9+∞; ∞}=∞ d3,26=min{d3,65+d6,25d3,25}=min{9+∞; ∞}=∞ d3,36=min{d3,65+d6,35d3,35}=min{9+∞; 0}=0 d3,46=min{d3,65+d6,45d3,45}=min{9+∞; 20}=20 d3,56=min{d3,65+d6,55d3,55}=min{9+∞; ∞}=∞ d3,66=min{d3,65+d6,65d3,65}=min{9+0; 9}=9 d3,76=min{d3,65+d6,75d3,75}=min{9+35; 38}=38 d3,86=min{d3,65+d6,85d3,85}=min{9+∞; 35}=35 d4,16=min{d4,65+d6,15d4,15}=min{∞+∞; ∞}=∞ d4,26=min{d4,65+d6,25d4,25}=min{∞+∞; ∞}=∞ d4,36=min{d4,65+d6,35d4,35}=min{∞+∞; ∞}=∞ d4,46=min{d4,65+d6,45d4,45}=min{∞+∞; 0}=0 d4,56=min{d4,65+d6,55d4,55}=min{∞+∞; ∞}=∞ d4,66=min{d4,65+d6,65d4,65}=min{∞+0; ∞}=∞ d4,76=min{d4,65+d6,75d4,75}=min{∞+35; 18}=18 d4,86=min{d4,65+d6,85d4,85}=min{∞+∞; 15}=15 d5,16=min{d5,65+d6,15d5,15}=min{22+∞; ∞}=∞ d5,26=min{d5,65+d6,25d5,25}=min{22+∞; ∞}=∞ d5,36=min{d5,65+d6,35d5,35}=min{22+∞; ∞}=∞ d5,46=min{d5,65+d6,45d5,45}=min{22+∞; ∞}=∞ d5,56=min{d5,65+d6,55d5,55}=min{22+∞; 0}=0 d5,66=min{d5,65+d6,65d5,65}=min{22+0; 22}=22 d5,76=min{d5,65+d6,75d5,75}=min{22+35; ∞}=57 d5,86=min{d5,65+d6,85d5,85}=min{22+∞; ∞}=∞ d6,16=min{d6,65+d6,15d6,15}=min{0+∞; ∞}=∞ d6,26=min{d6,65+d6,25d6,25}=min{0+∞; ∞}=∞ d6,36=min{d6,65+d6,35d6,35}=min{0+∞; ∞}=∞ d6,46=min{d6,65+d6,45d6,45}=min{0+∞; ∞}=∞ d6,56=min{d6,65+d6,55d6,55}=min{0+∞; ∞}=∞ d6,66=min{d6,65+d6,65d6,65}=min{0+0; 0}=0 d6,76=min{d6,65+d6,75d6,75}=min{0+35; 35}=35 d6,86=min{d6,65+d6,85d6,85}=min{0+∞; ∞}=∞ d7,16=min{d7,65+d6,15d7,15}=min{∞+∞; ∞}=∞ d7,26=min{d7,65+d6,25d7,25}=min{∞+∞; ∞}=∞ d7,36=min{d7,65+d6,35d7,35}=min{∞+∞; ∞}=∞ d7,46=min{d7,65+d6,45d7,45}=min{∞+∞; ∞}=∞ d7,56=min{d7,65+d6,55d7,55}=min{∞+∞; ∞}=∞ d7,66=min{d7,65+d6,65d7,65}=min{∞+0; ∞}=∞ d7,76=min{d7,65+d6,75d7,75}=min{∞+35; 0}=0 d7,86=min{d7,65+d6,85d7,85}=min{∞+∞; ∞}=∞ d8,16=min{d8,65+d6,15d8,15}=min{∞+∞; ∞}=∞ d8,26=min{d8,65+d6,25d8,25}=min{∞+∞; ∞}=∞ d8,36=min{d8,65+d6,35d8,35}=min{∞+∞; ∞}=∞ d8,46=min{d8,65+d6,45d8,45}=min{∞+∞; ∞}=∞ d8,56=min{d8,65+d6,55d8,55}=min{∞+∞; ∞}=∞ d8,66=min{d8,65+d6,65d8,65}=min{∞+0; ∞}=∞ d8,76=min{d8,65+d6,75d8,75}=min{∞+35; ∞}=∞ d8,86=min{d8,65+d6,85d8,85}=min{∞+∞; 0}=0 Представим матрицу D6, включив в нее рассчитанные элементы.

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