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Created November 16, 2015 17:22
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tables.tex
\begin{tabular}{ll}
\toprule
{} & $T_{ij}$ \\
\midrule
0 & T(1, 2)=6 \\
1 & T(4, 7)=80 \\
2 & T(1, 3)=2 \\
3 & T(10, 11)=16 \\
4 & T(12, 14)=4 \\
5 & T(3, 13)=32 \\
6 & T(6, 9)=8 \\
7 & T(1, 4)=9 \\
8 & T(8, 9)=40 \\
9 & T(14, 15)=16 \\
10 & T(2, 5)=7 \\
11 & T(6, 8)=16 \\
12 & T(0, 1)=5 \\
13 & T(9, 10)=0 \\
14 & T(12, 15)=2 \\
15 & T(4, 6)=16 \\
16 & T(13, 14)=24 \\
17 & T(5, 12)=7 \\
18 & T(3, 6)=0 \\
19 & T(9, 11)=4 \\
20 & T(7, 10)=8 \\
21 & T(11, 15)=8 \\
22 & T(3, 5)=4 \\
23 & T(15, 16)=3 \\
\bottomrule
\end{tabular}
\begin{tabular}{llll}
\toprule
{} & $R_i$ & $t^n_j$ & $t^p_i$ \\
\midrule
0 & $t_{16} = 129 - 129 = 0$ & $t^{p}_{16} = max(0) = 0$ & $t^{p}_{0} = max(0) = 0$ \\
1 & $t_{15} = 126 - 126 = 0$ & $t^{n}_{15} = min([129 - 3]) = 126$ & $t^{p}_{1} = max([0 + 5]) = 5$ \\
2 & $t_{14} = 110 - 63 = 47$ & $t^{n}_{14} = min([126 - 16]) = 110$ & $t^{p}_{2} = max([5 + 6]) = 11$ \\
3 & $t_{13} = 86 - 39 = 47$ & $t^{n}_{13} = min([110 - 24]) = 86$ & $t^{p}_{3} = max([5 + 2]) = 7$ \\
4 & $t_{12} = 106 - 25 = 81$ & $t^{n}_{12} = min([110 - 4, 126 - 2]) = 106$ & $t^{p}_{4} = max([5 + 9]) = 14$ \\
5 & $t_{11} = 118 - 118 = 0$ & $t^{n}_{11} = min([126 - 8]) = 118$ & $t^{p}_{5} = max([11 + 7, 7 + 4]) = 18$ \\
6 & $t_{10} = 102 - 102 = 0$ & $t^{n}_{10} = min([118 - 16]) = 102$ & $t^{p}_{6} = max([7 + 0, 14 + 16]) = 30$ \\
7 & $t_{9} = 102 - 86 = 16$ & $t^{n}_{9} = min([102 - 0, 118 - 4]) = 102$ & $t^{p}_{7} = max([14 + 80]) = 94$ \\
8 & $t_{8} = 62 - 46 = 16$ & $t^{n}_{8} = min([102 - 40]) = 62$ & $t^{p}_{8} = max([30 + 16]) = 46$ \\
9 & $t_{7} = 94 - 94 = 0$ & $t^{n}_{7} = min([102 - 8]) = 94$ & $t^{p}_{9} = max([46 + 40, 30 + 8]) = 86$ \\
10 & $t_{6} = 46 - 30 = 16$ & $t^{n}_{6} = min([62 - 16, 102 - 8]) = 46$ & $t^{p}_{10} = max([86 + 0, 94 + 8]) = 102$ \\
11 & $t_{5} = 99 - 18 = 81$ & $t^{n}_{5} = min([106 - 7]) = 99$ & $t^{p}_{11} = max([86 + 4, 102 + 16]) = 118$ \\
12 & $t_{4} = 14 - 14 = 0$ & $t^{n}_{4} = min([46 - 16, 94 - 80]) = 14$ & $t^{p}_{12} = max([18 + 7]) = 25$ \\
13 & $t_{3} = 46 - 7 = 39$ & $t^{n}_{3} = min([86 - 32, 46 - 0, 99 - 4]) = 46$ & $t^{p}_{13} = max([7 + 32]) = 39$ \\
14 & $t_{2} = 92 - 11 = 81$ & $t^{n}_{2} = min([99 - 7]) = 92$ & $t^{p}_{14} = max([25 + 4, 39 + 24]) = 63$ \\
15 & $t_{1} = 5 - 5 = 0$ & $t^{n}_{1} = min([92 - 6, 46 - 2, 14 - 9]) = 5$ & $t^{p}_{15} = max([118 + 8, 25 + 2, 63 + 16]) ... \\
16 & $t_{0} = 0 - 0 = 0$ & $t^{n}_{0} = min([5 - 5]) = 0$ & $t^{p}_{16} = max([126 + 3]) = 129$ \\
\bottomrule
\end{tabular}
\begin{tabular}{lllll}
\toprule
{} & $R^{\textup{CB}}$ & $R^{''}$ & $R^{'}$ & $R^{n}$ \\
\midrule
0 & $R^{\textup{св}}(0, 1) = 5 - 0 - 5= 0$ & $R^{''}(0, 1) = 5 - 0 - 5= 0$ & $R^{'}(0, 1) = 5 - 0 - 5= 0$ & $R^{n}(0, 1) = 5 - 0 - 5= 0$ \\
1 & $R^{\textup{св}}(1, 2) = 11 - 5 - 6= 0$ & $R^{''}(1, 2) = 11 - 5 - 6= 0$ & $R^{'}(1, 2) = 92 - 5 - 6= 81$ & $R^{n}(1, 2) = 92 - 5 - 6= 81$ \\
2 & $R^{\textup{св}}(1, 3) = 7 - 5 - 2= 0$ & $R^{''}(1, 3) = 7 - 5 - 2= 0$ & $R^{'}(1, 3) = 46 - 5 - 2= 39$ & $R^{n}(1, 3) = 46 - 5 - 2= 39$ \\
3 & $R^{\textup{св}}(1, 4) = 14 - 5 - 9= 0$ & $R^{''}(1, 4) = 14 - 5 - 9= 0$ & $R^{'}(1, 4) = 14 - 5 - 9= 0$ & $R^{n}(1, 4) = 14 - 5 - 9= 0$ \\
4 & $R^{\textup{св}}(2, 5) = 18 - 92 - 7= -81$ & $R^{''}(2, 5) = 18 - 11 - 7= 0$ & $R^{'}(2, 5) = 99 - 92 - 7= 0$ & $R^{n}(2, 5) = 99 - 11 - 7= 81$ \\
5 & $R^{\textup{св}}(3, 13) = 39 - 46 - 32= -39$ & $R^{''}(3, 13) = 39 - 7 - 32= 0$ & $R^{'}(3, 13) = 86 - 46 - 32= 8$ & $R^{n}(3, 13) = 86 - 7 - 32= 47$ \\
6 & $R^{\textup{св}}(3, 6) = 30 - 46 - 0= -16$ & $R^{''}(3, 6) = 30 - 7 - 0= 23$ & $R^{'}(3, 6) = 46 - 46 - 0= 0$ & $R^{n}(3, 6) = 46 - 7 - 0= 39$ \\
7 & $R^{\textup{св}}(3, 5) = 18 - 46 - 4= -32$ & $R^{''}(3, 5) = 18 - 7 - 4= 7$ & $R^{'}(3, 5) = 99 - 46 - 4= 49$ & $R^{n}(3, 5) = 99 - 7 - 4= 88$ \\
8 & $R^{\textup{св}}(4, 6) = 30 - 14 - 16= 0$ & $R^{''}(4, 6) = 30 - 14 - 16= 0$ & $R^{'}(4, 6) = 46 - 14 - 16= 16$ & $R^{n}(4, 6) = 46 - 14 - 16= 16$ \\
9 & $R^{\textup{св}}(4, 7) = 94 - 14 - 80= 0$ & $R^{''}(4, 7) = 94 - 14 - 80= 0$ & $R^{'}(4, 7) = 94 - 14 - 80= 0$ & $R^{n}(4, 7) = 94 - 14 - 80= 0$ \\
10 & $R^{\textup{св}}(5, 12) = 25 - 99 - 7= -81$ & $R^{''}(5, 12) = 25 - 18 - 7= 0$ & $R^{'}(5, 12) = 106 - 99 - 7= 0$ & $R^{n}(5, 12) = 106 - 18 - 7= 81$ \\
11 & $R^{\textup{св}}(6, 8) = 46 - 46 - 16= -16$ & $R^{''}(6, 8) = 46 - 30 - 16= 0$ & $R^{'}(6, 8) = 62 - 46 - 16= 0$ & $R^{n}(6, 8) = 62 - 30 - 16= 16$ \\
12 & $R^{\textup{св}}(6, 9) = 86 - 46 - 8= 32$ & $R^{''}(6, 9) = 86 - 30 - 8= 48$ & $R^{'}(6, 9) = 102 - 46 - 8= 48$ & $R^{n}(6, 9) = 102 - 30 - 8= 64$ \\
13 & $R^{\textup{св}}(7, 10) = 102 - 94 - 8= 0$ & $R^{''}(7, 10) = 102 - 94 - 8= 0$ & $R^{'}(7, 10) = 102 - 94 - 8= 0$ & $R^{n}(7, 10) = 102 - 94 - 8= 0$ \\
14 & $R^{\textup{св}}(8, 9) = 86 - 62 - 40= -16$ & $R^{''}(8, 9) = 86 - 46 - 40= 0$ & $R^{'}(8, 9) = 102 - 62 - 40= 0$ & $R^{n}(8, 9) = 102 - 46 - 40= 16$ \\
15 & $R^{\textup{св}}(9, 10) = 102 - 102 - 0= 0$ & $R^{''}(9, 10) = 102 - 86 - 0= 16$ & $R^{'}(9, 10) = 102 - 102 - 0= 0$ & $R^{n}(9, 10) = 102 - 86 - 0= 16$ \\
16 & $R^{\textup{св}}(9, 11) = 118 - 102 - 4= 12$ & $R^{''}(9, 11) = 118 - 86 - 4= 28$ & $R^{'}(9, 11) = 118 - 102 - 4= 12$ & $R^{n}(9, 11) = 118 - 86 - 4= 28$ \\
17 & $R^{\textup{св}}(10, 11) = 118 - 102 - 16= 0$ & $R^{''}(10, 11) = 118 - 102 - 16= 0$ & $R^{'}(10, 11) = 118 - 102 - 16= 0$ & $R^{n}(10, 11) = 118 - 102 - 16= 0$ \\
18 & $R^{\textup{св}}(11, 15) = 126 - 118 - 8= 0$ & $R^{''}(11, 15) = 126 - 118 - 8= 0$ & $R^{'}(11, 15) = 126 - 118 - 8= 0$ & $R^{n}(11, 15) = 126 - 118 - 8= 0$ \\
19 & $R^{\textup{св}}(12, 14) = 63 - 106 - 4= -47$ & $R^{''}(12, 14) = 63 - 25 - 4= 34$ & $R^{'}(12, 14) = 110 - 106 - 4= 0$ & $R^{n}(12, 14) = 110 - 25 - 4= 81$ \\
20 & $R^{\textup{св}}(12, 15) = 126 - 106 - 2= 18$ & $R^{''}(12, 15) = 126 - 25 - 2= 99$ & $R^{'}(12, 15) = 126 - 106 - 2= 18$ & $R^{n}(12, 15) = 126 - 25 - 2= 99$ \\
21 & $R^{\textup{св}}(13, 14) = 63 - 86 - 24= -47$ & $R^{''}(13, 14) = 63 - 39 - 24= 0$ & $R^{'}(13, 14) = 110 - 86 - 24= 0$ & $R^{n}(13, 14) = 110 - 39 - 24= 47$ \\
22 & $R^{\textup{св}}(14, 15) = 126 - 110 - 16= 0$ & $R^{''}(14, 15) = 126 - 63 - 16= 47$ & $R^{'}(14, 15) = 126 - 110 - 16= 0$ & $R^{n}(14, 15) = 126 - 63 - 16= 47$ \\
23 & $R^{\textup{св}}(15, 16) = 129 - 126 - 3= 0$ & $R^{''}(15, 16) = 129 - 126 - 3= 0$ & $R^{'}(15, 16) = 129 - 126 - 3= 0$ & $R^{n}(15, 16) = 129 - 126 - 3= 0$ \\
\bottomrule
\end{tabular}
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