- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Floyd's shortest path from A to E in example 1 : graph has 6 vertices; Floyd matrix has 36 entries. --- k=1 --- distances: [[1000000 1000000 1000000 1000000 1000000 1000000 1000000] [1000000 0 7 9 14 1000000 1000000] [1000000 7 0 10 21 15 1000000] [1000000 9 10 0 2 11 1000000] [1000000 14 21 2 0 1000000 9] [1000000 1000000 15 11 1000000 0 6] [1000000 1000000 1000000 1000000 9 6 0]] path_next: [[0 0 0 0 0 0 0] [0 1 2 3 4 5 6] [0 1 2 3 1 5 6] [0 1 2 3 4 5 6] [0 1 1 3 4 5 6] [0 1 2 3 4 5 6] [0 1 2 3 4 5 6]] --- k=2 --- distances: [[1000000 1000000 1000000 1000000 1000000 1000000 1000000] [1000000 0 7 9 14 22 1000000] [1000000 7 0 10 21 15 1000000] [1000000 9 10 0 2 11 1000000] [1000000 14 21 2 0 36 9] [1000000 22 15 11 36 0 6] [1000000 1000000 1000000 1000000 9 6 0]] path_next: [[0 0 0 0 0 0 0] [0 1 2 3 4 2 6] [0 1 2 3 1 5 6] [0 1 2 3 4 5 6] [0 1 1 3 4 1 6] [0 2 2 3 2 5 6] [0 1 2 3 4 5 6]] --- k=3 --- distances: [[1000000 1000000 1000000 1000000 1000000 1000000 1000000] [1000000 0 7 9 11 20 1000000] [1000000 7 0 10 12 15 1000000] [1000000 9 10 0 2 11 1000000] [1000000 11 12 2 0 13 9] [1000000 20 15 11 13 0 6] [1000000 1000000 1000000 1000000 9 6 0]] path_next: [[0 0 0 0 0 0 0] [0 1 2 3 3 3 6] [0 1 2 3 3 5 6] [0 1 2 3 4 5 6] [0 3 3 3 4 3 6] [0 3 2 3 3 5 6] [0 1 2 3 4 5 6]] --- k=4 --- distances: [[1000000 1000000 1000000 1000000 1000000 1000000 1000000] [1000000 0 7 9 11 20 20] [1000000 7 0 10 12 15 21] [1000000 9 10 0 2 11 11] [1000000 11 12 2 0 13 9] [1000000 20 15 11 13 0 6] [1000000 20 21 11 9 6 0]] path_next: [[0 0 0 0 0 0 0] [0 1 2 3 3 3 3] [0 1 2 3 3 5 3] [0 1 2 3 4 5 4] [0 3 3 3 4 3 6] [0 3 2 3 3 5 6] [0 4 4 4 4 5 6]] --- k=5 --- distances: [[1000000 1000000 1000000 1000000 1000000 1000000 1000000] [1000000 0 7 9 11 20 20] [1000000 7 0 10 12 15 21] [1000000 9 10 0 2 11 11] [1000000 11 12 2 0 13 9] [1000000 20 15 11 13 0 6] [1000000 20 21 11 9 6 0]] path_next: [[0 0 0 0 0 0 0] [0 1 2 3 3 3 3] [0 1 2 3 3 5 3] [0 1 2 3 4 5 4] [0 3 3 3 4 3 6] [0 3 2 3 3 5 6] [0 4 4 4 4 5 6]] --- k=6 --- distances: [[1000000 1000000 1000000 1000000 1000000 1000000 1000000] [1000000 0 7 9 11 20 20] [1000000 7 0 10 12 15 21] [1000000 9 10 0 2 11 11] [1000000 11 12 2 0 13 9] [1000000 20 15 11 13 0 6] [1000000 20 21 11 9 6 0]] path_next: [[0 0 0 0 0 0 0] [0 1 2 3 3 3 3] [0 1 2 3 3 5 3] [0 1 2 3 4 5 4] [0 3 3 3 4 3 6] [0 3 2 3 3 5 6] [0 4 4 4 4 5 6]] ['A', 'C', 'F', 'E'] graph { "A" -- "B" [label=7]; "A" -- "C" [label=9, penwidth=3]; "A" -- "F" [label=14]; "B" -- "C" [label=10]; "B" -- "D" [label=15]; "C" -- "F" [label=2, penwidth=3]; "C" -- "D" [label=11]; "D" -- "E" [label=6]; "E" -- "F" [label=9, penwidth=3]; } - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Floyd's shortest path from A to E in example 2 : graph has 5 vertices; Floyd matrix has 25 entries. --- k=1 --- distances: [[1000000 1000000 1000000 1000000 1000000 1000000] [1000000 0 10 2 3 1000000] [1000000 10 0 4 5 6] [1000000 2 4 0 5 1000000] [1000000 3 5 5 0 1000000] [1000000 1000000 6 1000000 1000000 0]] path_next: [[0 0 0 0 0 0] [0 1 2 3 4 5] [0 1 2 3 4 5] [0 1 2 3 1 5] [0 1 2 1 4 5] [0 1 2 3 4 5]] --- k=2 --- distances: [[1000000 1000000 1000000 1000000 1000000 1000000] [1000000 0 10 2 3 16] [1000000 10 0 4 5 6] [1000000 2 4 0 5 10] [1000000 3 5 5 0 11] [1000000 16 6 10 11 0]] path_next: [[0 0 0 0 0 0] [0 1 2 3 4 2] [0 1 2 3 4 5] [0 1 2 3 1 2] [0 1 2 1 4 2] [0 2 2 2 2 5]] --- k=3 --- distances: [[1000000 1000000 1000000 1000000 1000000 1000000] [1000000 0 6 2 3 12] [1000000 6 0 4 5 6] [1000000 2 4 0 5 10] [1000000 3 5 5 0 11] [1000000 12 6 10 11 0]] path_next: [[0 0 0 0 0 0] [0 1 3 3 4 3] [0 3 2 3 4 5] [0 1 2 3 1 2] [0 1 2 1 4 2] [0 2 2 2 2 5]] --- k=4 --- distances: [[1000000 1000000 1000000 1000000 1000000 1000000] [1000000 0 6 2 3 12] [1000000 6 0 4 5 6] [1000000 2 4 0 5 10] [1000000 3 5 5 0 11] [1000000 12 6 10 11 0]] path_next: [[0 0 0 0 0 0] [0 1 3 3 4 3] [0 3 2 3 4 5] [0 1 2 3 1 2] [0 1 2 1 4 2] [0 2 2 2 2 5]] --- k=5 --- distances: [[1000000 1000000 1000000 1000000 1000000 1000000] [1000000 0 6 2 3 12] [1000000 6 0 4 5 6] [1000000 2 4 0 5 10] [1000000 3 5 5 0 11] [1000000 12 6 10 11 0]] path_next: [[0 0 0 0 0 0] [0 1 3 3 4 3] [0 3 2 3 4 5] [0 1 2 3 1 2] [0 1 2 1 4 2] [0 2 2 2 2 5]] ['A', 'C', 'B', 'E'] graph { "A" -- "B" [label=10]; "A" -- "C" [label=2, penwidth=3]; "A" -- "D" [label=3]; "B" -- "C" [label=4, penwidth=3]; "B" -- "D" [label=5]; "B" -- "E" [label=6, penwidth=3]; } - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Floyd's shortest path from 5,0 to 5,10 in grid 10 x 10 : graph has 103 vertices; Floyd matrix has 10609 entries. ['5,0', '5,1', '6,1', '6,2', '7,2', '8,2', '8,3', '8,4', '8,5', '8,6', '8,7', '7,7', '6,7', '5,7', '5,8', '5,9', '5,10'] graph { "0,0" -- "0,1" [label=6]; "0,0" -- "1,0" [label=6]; "0,1" -- "0,2" [label=7]; "0,1" -- "1,1" [label=7]; "1,0" -- "1,1" [label=5]; "1,0" -- "2,0" [label=7]; "0,2" -- "0,3" [label=7]; "0,2" -- "1,2" [label=6]; "1,1" -- "1,2" [label=5]; "1,1" -- "2,1" [label=6]; "0,3" -- "0,4" [label=5]; "0,3" -- "1,3" [label=6]; "1,2" -- "1,3" [label=7]; "1,2" -- "2,2" [label=7]; "0,4" -- "0,5" [label=6]; "0,4" -- "1,4" [label=5]; "1,3" -- "1,4" [label=6]; "1,3" -- "2,3" [label=7]; "0,5" -- "0,6" [label=5]; "0,5" -- "1,5" [label=6]; "1,4" -- "1,5" [label=6]; "0,6" -- "0,7" [label=5]; "0,6" -- "1,6" [label=7]; "1,5" -- "1,6" [label=6]; "0,7" -- "0,8" [label=7]; "0,7" -- "1,7" [label=6]; "1,6" -- "1,7" [label=7]; "0,8" -- "0,9" [label=6]; "0,8" -- "1,8" [label=5]; "1,7" -- "1,8" [label=7]; "1,7" -- "2,7" [label=6]; "0,9" -- "1,9" [label=6]; "1,8" -- "1,9" [label=5]; "1,8" -- "2,8" [label=6]; "0,10" -- "0,9" [label=6]; "0,10" -- "1,10" [label=7]; "1,9" -- "2,9" [label=6]; "1,10" -- "1,9" [label=7]; "1,10" -- "2,10" [label=5]; "2,0" -- "2,1" [label=7]; "2,0" -- "3,0" [label=7]; "2,1" -- "2,2" [label=6]; "2,1" -- "3,1" [label=7]; "2,2" -- "2,3" [label=6]; "2,2" -- "3,2" [label=5]; "2,3" -- "3,3" [label=7]; "2,7" -- "2,8" [label=6]; "2,7" -- "3,7" [label=6]; "2,8" -- "2,9" [label=5]; "2,8" -- "3,8" [label=5]; "2,9" -- "3,9" [label=6]; "2,10" -- "2,9" [label=6]; "2,10" -- "3,10" [label=6]; "3,0" -- "3,1" [label=7]; "3,0" -- "4,0" [label=5]; "3,1" -- "3,2" [label=7]; "3,1" -- "4,1" [label=7]; "3,2" -- "3,3" [label=7]; "3,2" -- "4,2" [label=6]; "3,3" -- "4,3" [label=7]; "3,7" -- "3,8" [label=5]; "3,7" -- "4,7" [label=7]; "3,8" -- "3,9" [label=7]; "3,8" -- "4,8" [label=5]; "3,9" -- "4,9" [label=5]; "3,10" -- "3,9" [label=6]; "3,10" -- "4,10" [label=7]; "4,0" -- "4,1" [label=5]; "4,0" -- "5,0" [label=5]; "4,1" -- "4,2" [label=7]; "4,1" -- "5,1" [label=5]; "4,2" -- "4,3" [label=5]; "4,2" -- "5,2" [label=5]; "4,3" -- "5,3" [label=6]; "4,7" -- "4,8" [label=6]; "4,7" -- "5,7" [label=6]; "4,8" -- "4,9" [label=5]; "4,8" -- "5,8" [label=5]; "4,9" -- "5,9" [label=6]; "4,10" -- "4,9" [label=7]; "4,10" -- "5,10" [label=6]; "5,0" -- "5,1" [label=5, penwidth=3]; "5,0" -- "6,0" [label=5]; "5,1" -- "5,2" [label=6]; "5,1" -- "6,1" [label=5, penwidth=3]; "5,2" -- "5,3" [label=6]; "5,2" -- "6,2" [label=7]; "5,3" -- "6,3" [label=7]; "5,7" -- "5,8" [label=6, penwidth=3]; "5,7" -- "6,7" [label=5, penwidth=3]; "5,8" -- "5,9" [label=5, penwidth=3]; "5,8" -- "6,8" [label=7]; "5,9" -- "6,9" [label=7]; "5,10" -- "5,9" [label=7, penwidth=3]; "5,10" -- "6,10" [label=6]; "6,0" -- "6,1" [label=6]; "6,0" -- "7,0" [label=5]; "6,1" -- "6,2" [label=5, penwidth=3]; "6,1" -- "7,1" [label=6]; "6,2" -- "6,3" [label=5]; "6,2" -- "7,2" [label=6, penwidth=3]; "6,3" -- "7,3" [label=7]; "6,7" -- "6,8" [label=7]; "6,7" -- "7,7" [label=5, penwidth=3]; "6,8" -- "6,9" [label=5]; "6,8" -- "7,8" [label=5]; "6,9" -- "7,9" [label=5]; "6,10" -- "6,9" [label=6]; "6,10" -- "7,10" [label=6]; "7,0" -- "7,1" [label=7]; "7,0" -- "8,0" [label=5]; "7,1" -- "7,2" [label=5]; "7,1" -- "8,1" [label=5]; "7,2" -- "7,3" [label=6]; "7,2" -- "8,2" [label=5, penwidth=3]; "7,3" -- "8,3" [label=6]; "7,7" -- "7,8" [label=6]; "7,7" -- "8,7" [label=5, penwidth=3]; "7,8" -- "7,9" [label=5]; "7,8" -- "8,8" [label=5]; "7,9" -- "8,9" [label=7]; "7,10" -- "7,9" [label=5]; "7,10" -- "8,10" [label=5]; "8,0" -- "8,1" [label=6]; "8,0" -- "9,0" [label=5]; "8,1" -- "8,2" [label=5]; "8,1" -- "9,1" [label=7]; "8,2" -- "8,3" [label=6, penwidth=3]; "8,2" -- "9,2" [label=7]; "8,3" -- "8,4" [label=6, penwidth=3]; "8,3" -- "9,3" [label=5]; "8,7" -- "8,8" [label=6]; "8,7" -- "9,7" [label=6]; "8,8" -- "8,9" [label=7]; "8,8" -- "9,8" [label=5]; "8,9" -- "9,9" [label=5]; "8,10" -- "8,9" [label=5]; "8,10" -- "9,10" [label=6]; "9,0" -- "9,1" [label=7]; "9,1" -- "9,2" [label=6]; "9,2" -- "9,3" [label=6]; "8,4" -- "8,5" [label=5, penwidth=3]; "8,4" -- "9,4" [label=6]; "9,3" -- "9,4" [label=5]; "8,5" -- "8,6" [label=5, penwidth=3]; "8,5" -- "9,5" [label=7]; "9,4" -- "9,5" [label=6]; "8,6" -- "8,7" [label=7, penwidth=3]; "8,6" -- "9,6" [label=5]; "9,5" -- "9,6" [label=7]; "9,6" -- "9,7" [label=6]; "9,7" -- "9,8" [label=6]; "9,8" -- "9,9" [label=7]; "9,10" -- "9,9" [label=5]; "10,0" -- "9,0" [label=5]; "10,0" -- "10,1" [label=5]; "10,1" -- "9,1" [label=7]; "10,1" -- "10,2" [label=6]; "10,2" -- "9,2" [label=5]; "10,2" -- "10,3" [label=6]; "10,3" -- "9,3" [label=7]; "10,3" -- "10,4" [label=6]; "10,4" -- "9,4" [label=6]; "10,4" -- "10,5" [label=5]; "10,5" -- "9,5" [label=6]; "10,5" -- "10,6" [label=7]; "10,6" -- "9,6" [label=6]; "10,6" -- "10,7" [label=7]; "10,7" -- "9,7" [label=7]; "10,7" -- "10,8" [label=6]; "10,8" -- "9,8" [label=7]; "10,8" -- "10,9" [label=6]; "10,9" -- "9,9" [label=5]; "10,10" -- "9,10" [label=5]; "10,10" -- "10,9" [label=7]; } - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Floyd's shortest path from 7,0 to 7,15 in grid 15 x 15 : graph has 229 vertices; Floyd matrix has 52441 entries. ['7,0', '6,0', '6,1', '6,2', '6,3', '5,3', '4,3', '3,3', '2,3', '2,4', '2,5', '2,6', '2,7', '2,8', '2,9', '3,9', '4,9', '5,9', '5,10', '5,11', '6,11', '6,12', '6,13', '6,14', '7,14', '7,15'] graph { "0,0" -- "0,1" [label=7]; "0,0" -- "1,0" [label=8]; "0,1" -- "0,2" [label=10]; "0,1" -- "1,1" [label=10]; "1,0" -- "1,1" [label=10]; "1,0" -- "2,0" [label=10]; "0,2" -- "0,3" [label=7]; "0,2" -- "1,2" [label=8]; "1,1" -- "1,2" [label=9]; "1,1" -- "2,1" [label=9]; "0,3" -- "0,4" [label=8]; "0,3" -- "1,3" [label=7]; "1,2" -- "1,3" [label=9]; "1,2" -- "2,2" [label=7]; "0,4" -- "0,5" [label=8]; "0,4" -- "1,4" [label=7]; "1,3" -- "1,4" [label=10]; "1,3" -- "2,3" [label=7]; "0,5" -- "0,6" [label=10]; "0,5" -- "1,5" [label=9]; "1,4" -- "1,5" [label=10]; "1,4" -- "2,4" [label=10]; "0,6" -- "0,7" [label=10]; "0,6" -- "1,6" [label=9]; "1,5" -- "1,6" [label=10]; "1,5" -- "2,5" [label=10]; "0,7" -- "0,8" [label=7]; "0,7" -- "1,7" [label=8]; "1,6" -- "1,7" [label=10]; "1,6" -- "2,6" [label=7]; "0,8" -- "0,9" [label=10]; "0,8" -- "1,8" [label=10]; "1,7" -- "1,8" [label=7]; "1,7" -- "2,7" [label=7]; "0,9" -- "1,9" [label=8]; "1,8" -- "1,9" [label=7]; "1,8" -- "2,8" [label=8]; "0,10" -- "0,9" [label=8]; "0,10" -- "0,11" [label=7]; "0,10" -- "1,10" [label=8]; "1,9" -- "2,9" [label=8]; "0,11" -- "0,12" [label=8]; "0,11" -- "1,11" [label=7]; "1,10" -- "1,9" [label=9]; "1,10" -- "1,11" [label=8]; "1,10" -- "2,10" [label=9]; "0,12" -- "0,13" [label=10]; "0,12" -- "1,12" [label=8]; "1,11" -- "1,12" [label=8]; "1,11" -- "2,11" [label=9]; "0,13" -- "0,14" [label=8]; "0,13" -- "1,13" [label=10]; "1,12" -- "1,13" [label=8]; "1,12" -- "2,12" [label=10]; "0,14" -- "0,15" [label=8]; "0,14" -- "1,14" [label=7]; "1,13" -- "1,14" [label=10]; "1,13" -- "2,13" [label=9]; "0,15" -- "1,15" [label=7]; "1,14" -- "1,15" [label=9]; "1,14" -- "2,14" [label=10]; "1,15" -- "2,15" [label=10]; "2,0" -- "2,1" [label=8]; "2,0" -- "3,0" [label=10]; "2,1" -- "2,2" [label=10]; "2,1" -- "3,1" [label=7]; "2,2" -- "2,3" [label=10]; "2,2" -- "3,2" [label=8]; "2,3" -- "2,4" [label=7, penwidth=3]; "2,3" -- "3,3" [label=7, penwidth=3]; "2,4" -- "2,5" [label=9, penwidth=3]; "2,4" -- "3,4" [label=10]; "2,5" -- "2,6" [label=8, penwidth=3]; "2,5" -- "3,5" [label=9]; "2,6" -- "2,7" [label=8, penwidth=3]; "2,7" -- "2,8" [label=9, penwidth=3]; "2,8" -- "2,9" [label=8, penwidth=3]; "2,9" -- "3,9" [label=7, penwidth=3]; "2,10" -- "2,9" [label=7]; "2,10" -- "2,11" [label=8]; "2,10" -- "3,10" [label=9]; "2,11" -- "2,12" [label=9]; "2,11" -- "3,11" [label=7]; "2,12" -- "2,13" [label=8]; "2,12" -- "3,12" [label=8]; "2,13" -- "2,14" [label=10]; "2,13" -- "3,13" [label=9]; "2,14" -- "2,15" [label=7]; "2,14" -- "3,14" [label=8]; "2,15" -- "3,15" [label=10]; "3,0" -- "3,1" [label=8]; "3,0" -- "4,0" [label=7]; "3,1" -- "3,2" [label=8]; "3,1" -- "4,1" [label=9]; "3,2" -- "3,3" [label=10]; "3,2" -- "4,2" [label=9]; "3,3" -- "3,4" [label=9]; "3,3" -- "4,3" [label=7, penwidth=3]; "3,4" -- "3,5" [label=9]; "3,4" -- "4,4" [label=9]; "3,5" -- "4,5" [label=7]; "3,9" -- "4,9" [label=7, penwidth=3]; "3,10" -- "3,9" [label=8]; "3,10" -- "3,11" [label=7]; "3,10" -- "4,10" [label=9]; "3,11" -- "3,12" [label=7]; "3,11" -- "4,11" [label=10]; "3,12" -- "3,13" [label=10]; "3,12" -- "4,12" [label=7]; "3,13" -- "3,14" [label=8]; "3,13" -- "4,13" [label=8]; "3,14" -- "3,15" [label=10]; "3,14" -- "4,14" [label=9]; "3,15" -- "4,15" [label=7]; "4,0" -- "4,1" [label=9]; "4,0" -- "5,0" [label=9]; "4,1" -- "4,2" [label=9]; "4,1" -- "5,1" [label=10]; "4,2" -- "4,3" [label=9]; "4,2" -- "5,2" [label=10]; "4,3" -- "4,4" [label=7]; "4,3" -- "5,3" [label=8, penwidth=3]; "4,4" -- "4,5" [label=10]; "4,4" -- "5,4" [label=10]; "4,5" -- "5,5" [label=10]; "4,9" -- "5,9" [label=7, penwidth=3]; "4,10" -- "4,9" [label=9]; "4,10" -- "4,11" [label=9]; "4,10" -- "5,10" [label=9]; "4,11" -- "4,12" [label=9]; "4,11" -- "5,11" [label=9]; "4,12" -- "4,13" [label=9]; "4,12" -- "5,12" [label=8]; "4,13" -- "4,14" [label=10]; "4,13" -- "5,13" [label=8]; "4,14" -- "4,15" [label=7]; "4,14" -- "5,14" [label=9]; "4,15" -- "5,15" [label=10]; "5,0" -- "5,1" [label=9]; "5,0" -- "6,0" [label=9]; "5,1" -- "5,2" [label=9]; "5,1" -- "6,1" [label=9]; "5,2" -- "5,3" [label=8]; "5,2" -- "6,2" [label=7]; "5,3" -- "5,4" [label=10]; "5,3" -- "6,3" [label=7, penwidth=3]; "5,4" -- "5,5" [label=9]; "5,4" -- "6,4" [label=10]; "5,5" -- "6,5" [label=8]; "5,9" -- "6,9" [label=7]; "5,10" -- "5,9" [label=7, penwidth=3]; "5,10" -- "5,11" [label=7, penwidth=3]; "5,10" -- "6,10" [label=9]; "5,11" -- "5,12" [label=10]; "5,11" -- "6,11" [label=7, penwidth=3]; "5,12" -- "5,13" [label=7]; "5,12" -- "6,12" [label=9]; "5,13" -- "5,14" [label=7]; "5,13" -- "6,13" [label=10]; "5,14" -- "5,15" [label=7]; "5,14" -- "6,14" [label=8]; "5,15" -- "6,15" [label=9]; "6,0" -- "6,1" [label=7, penwidth=3]; "6,0" -- "7,0" [label=10, penwidth=3]; "6,1" -- "6,2" [label=7, penwidth=3]; "6,1" -- "7,1" [label=10]; "6,2" -- "6,3" [label=7, penwidth=3]; "6,2" -- "7,2" [label=8]; "6,3" -- "6,4" [label=9]; "6,3" -- "7,3" [label=7]; "6,4" -- "6,5" [label=7]; "6,4" -- "7,4" [label=7]; "6,5" -- "7,5" [label=8]; "6,9" -- "7,9" [label=8]; "6,10" -- "6,9" [label=8]; "6,10" -- "6,11" [label=8]; "6,10" -- "7,10" [label=7]; "6,11" -- "6,12" [label=8, penwidth=3]; "6,11" -- "7,11" [label=10]; "6,12" -- "6,13" [label=7, penwidth=3]; "6,12" -- "7,12" [label=7]; "6,13" -- "6,14" [label=7, penwidth=3]; "6,13" -- "7,13" [label=10]; "6,14" -- "6,15" [label=9]; "6,14" -- "7,14" [label=8, penwidth=3]; "6,15" -- "7,15" [label=9]; "7,0" -- "7,1" [label=9]; "7,0" -- "8,0" [label=8]; "7,1" -- "7,2" [label=8]; "7,1" -- "8,1" [label=7]; "7,2" -- "7,3" [label=8]; "7,2" -- "8,2" [label=10]; "7,3" -- "7,4" [label=9]; "7,3" -- "8,3" [label=10]; "7,4" -- "7,5" [label=9]; "7,4" -- "8,4" [label=10]; "7,5" -- "8,5" [label=10]; "7,9" -- "8,9" [label=8]; "7,10" -- "7,9" [label=10]; "7,10" -- "7,11" [label=9]; "7,10" -- "8,10" [label=7]; "7,11" -- "7,12" [label=8]; "7,11" -- "8,11" [label=7]; "7,12" -- "7,13" [label=10]; "7,12" -- "8,12" [label=8]; "7,13" -- "7,14" [label=8]; "7,13" -- "8,13" [label=7]; "7,14" -- "7,15" [label=8, penwidth=3]; "7,14" -- "8,14" [label=10]; "7,15" -- "8,15" [label=8]; "8,0" -- "8,1" [label=9]; "8,0" -- "9,0" [label=9]; "8,1" -- "8,2" [label=7]; "8,1" -- "9,1" [label=7]; "8,2" -- "8,3" [label=7]; "8,2" -- "9,2" [label=9]; "8,3" -- "8,4" [label=10]; "8,3" -- "9,3" [label=9]; "8,4" -- "8,5" [label=10]; "8,4" -- "9,4" [label=10]; "8,5" -- "9,5" [label=7]; "8,9" -- "9,9" [label=10]; "8,10" -- "8,9" [label=10]; "8,10" -- "8,11" [label=8]; "8,10" -- "9,10" [label=8]; "8,11" -- "8,12" [label=7]; "8,11" -- "9,11" [label=8]; "8,12" -- "8,13" [label=8]; "8,12" -- "9,12" [label=9]; "8,13" -- "8,14" [label=9]; "8,13" -- "9,13" [label=10]; "8,14" -- "8,15" [label=8]; "8,14" -- "9,14" [label=8]; "8,15" -- "9,15" [label=7]; "9,0" -- "9,1" [label=8]; "9,1" -- "9,2" [label=8]; "9,2" -- "9,3" [label=8]; "9,3" -- "9,4" [label=9]; "9,4" -- "9,5" [label=8]; "9,10" -- "9,9" [label=10]; "9,10" -- "9,11" [label=8]; "9,11" -- "9,12" [label=9]; "9,12" -- "9,13" [label=10]; "9,13" -- "9,14" [label=10]; "9,14" -- "9,15" [label=9]; "10,0" -- "9,0" [label=10]; "10,0" -- "10,1" [label=8]; "10,0" -- "11,0" [label=9]; "10,1" -- "9,1" [label=7]; "10,1" -- "10,2" [label=10]; "10,1" -- "11,1" [label=8]; "10,2" -- "9,2" [label=10]; "10,2" -- "10,3" [label=10]; "10,2" -- "11,2" [label=9]; "10,3" -- "9,3" [label=9]; "10,3" -- "10,4" [label=8]; "10,3" -- "11,3" [label=9]; "10,4" -- "9,4" [label=9]; "10,4" -- "10,5" [label=10]; "10,4" -- "11,4" [label=9]; "10,5" -- "9,5" [label=7]; "10,5" -- "11,5" [label=9]; "10,9" -- "9,9" [label=8]; "10,9" -- "11,9" [label=8]; "10,10" -- "9,10" [label=8]; "10,10" -- "10,9" [label=8]; "10,10" -- "10,11" [label=7]; "10,10" -- "11,10" [label=7]; "10,11" -- "9,11" [label=7]; "10,11" -- "10,12" [label=7]; "10,11" -- "11,11" [label=10]; "10,12" -- "9,12" [label=10]; "10,12" -- "10,13" [label=8]; "10,12" -- "11,12" [label=8]; "10,13" -- "9,13" [label=7]; "10,13" -- "10,14" [label=7]; "10,13" -- "11,13" [label=9]; "10,14" -- "9,14" [label=8]; "10,14" -- "10,15" [label=7]; "10,14" -- "11,14" [label=9]; "10,15" -- "9,15" [label=7]; "10,15" -- "11,15" [label=7]; "11,0" -- "11,1" [label=7]; "11,0" -- "12,0" [label=10]; "11,1" -- "11,2" [label=10]; "11,1" -- "12,1" [label=10]; "11,2" -- "11,3" [label=7]; "11,2" -- "12,2" [label=9]; "11,3" -- "11,4" [label=9]; "11,3" -- "12,3" [label=10]; "11,4" -- "11,5" [label=10]; "11,4" -- "12,4" [label=9]; "11,5" -- "12,5" [label=7]; "11,9" -- "12,9" [label=9]; "11,10" -- "11,9" [label=9]; "11,10" -- "11,11" [label=9]; "11,10" -- "12,10" [label=9]; "11,11" -- "11,12" [label=8]; "11,11" -- "12,11" [label=10]; "11,12" -- "11,13" [label=8]; "11,12" -- "12,12" [label=8]; "11,13" -- "11,14" [label=10]; "11,13" -- "12,13" [label=10]; "11,14" -- "11,15" [label=9]; "11,14" -- "12,14" [label=10]; "11,15" -- "12,15" [label=8]; "12,0" -- "12,1" [label=7]; "12,0" -- "13,0" [label=8]; "12,1" -- "12,2" [label=10]; "12,1" -- "13,1" [label=9]; "12,2" -- "12,3" [label=7]; "12,2" -- "13,2" [label=9]; "12,3" -- "12,4" [label=10]; "12,3" -- "13,3" [label=8]; "12,4" -- "12,5" [label=8]; "12,4" -- "13,4" [label=7]; "12,5" -- "12,6" [label=9]; "12,5" -- "13,5" [label=9]; "12,9" -- "13,9" [label=9]; "12,10" -- "12,9" [label=8]; "12,10" -- "12,11" [label=10]; "12,10" -- "13,10" [label=10]; "12,11" -- "12,12" [label=10]; "12,11" -- "13,11" [label=9]; "12,12" -- "12,13" [label=8]; "12,12" -- "13,12" [label=10]; "12,13" -- "12,14" [label=9]; "12,13" -- "13,13" [label=8]; "12,14" -- "12,15" [label=7]; "12,14" -- "13,14" [label=9]; "12,15" -- "13,15" [label=7]; "13,0" -- "13,1" [label=9]; "13,0" -- "14,0" [label=10]; "13,1" -- "13,2" [label=10]; "13,1" -- "14,1" [label=8]; "13,2" -- "13,3" [label=9]; "13,2" -- "14,2" [label=8]; "13,3" -- "13,4" [label=7]; "13,3" -- "14,3" [label=9]; "13,4" -- "13,5" [label=7]; "13,4" -- "14,4" [label=9]; "12,6" -- "12,7" [label=10]; "12,6" -- "13,6" [label=7]; "13,5" -- "13,6" [label=7]; "13,5" -- "14,5" [label=9]; "12,7" -- "12,8" [label=10]; "12,7" -- "13,7" [label=7]; "13,6" -- "13,7" [label=8]; "13,6" -- "14,6" [label=10]; "12,8" -- "12,9" [label=10]; "12,8" -- "13,8" [label=8]; "13,7" -- "13,8" [label=7]; "13,7" -- "14,7" [label=8]; "13,8" -- "13,9" [label=9]; "13,8" -- "14,8" [label=7]; "13,9" -- "14,9" [label=9]; "13,10" -- "13,9" [label=8]; "13,10" -- "13,11" [label=9]; "13,10" -- "14,10" [label=10]; "13,11" -- "13,12" [label=7]; "13,11" -- "14,11" [label=8]; "13,12" -- "13,13" [label=10]; "13,12" -- "14,12" [label=9]; "13,13" -- "13,14" [label=9]; "13,13" -- "14,13" [label=7]; "13,14" -- "13,15" [label=7]; "13,14" -- "14,14" [label=7]; "13,15" -- "14,15" [label=8]; "14,0" -- "14,1" [label=10]; "14,0" -- "15,0" [label=7]; "14,1" -- "14,2" [label=8]; "14,1" -- "15,1" [label=7]; "14,2" -- "14,3" [label=8]; "14,2" -- "15,2" [label=8]; "14,3" -- "14,4" [label=7]; "14,3" -- "15,3" [label=8]; "14,4" -- "14,5" [label=8]; "14,4" -- "15,4" [label=8]; "14,5" -- "14,6" [label=8]; "14,5" -- "15,5" [label=7]; "14,6" -- "14,7" [label=8]; "14,6" -- "15,6" [label=8]; "14,7" -- "14,8" [label=9]; "14,7" -- "15,7" [label=7]; "14,8" -- "14,9" [label=7]; "14,8" -- "15,8" [label=8]; "14,9" -- "15,9" [label=8]; "14,10" -- "14,9" [label=7]; "14,10" -- "14,11" [label=9]; "14,10" -- "15,10" [label=10]; "14,11" -- "14,12" [label=8]; "14,11" -- "15,11" [label=9]; "14,12" -- "14,13" [label=10]; "14,12" -- "15,12" [label=7]; "14,13" -- "14,14" [label=9]; "14,13" -- "15,13" [label=10]; "14,14" -- "14,15" [label=9]; "14,14" -- "15,14" [label=7]; "14,15" -- "15,15" [label=9]; "15,0" -- "15,1" [label=10]; "15,1" -- "15,2" [label=9]; "15,2" -- "15,3" [label=8]; "15,3" -- "15,4" [label=7]; "15,4" -- "15,5" [label=10]; "15,5" -- "15,6" [label=9]; "15,6" -- "15,7" [label=9]; "15,7" -- "15,8" [label=8]; "15,8" -- "15,9" [label=9]; "15,10" -- "15,9" [label=7]; "15,10" -- "15,11" [label=10]; "15,11" -- "15,12" [label=7]; "15,12" -- "15,13" [label=9]; "15,13" -- "15,14" [label=9]; "15,14" -- "15,15" [label=8]; }