algorithm stringclasses 4
values | answer stringlengths 2 153 | explanation stringlengths 40 12.7k | id int64 0 173k | nedges int64 0 168 | nnodes int64 4 19 | question stringlengths 95 7.52k | task stringclasses 6
values | text_encoding stringclasses 9
values |
|---|---|---|---|---|---|---|---|---|
er | 1. | Because there is an edge from node 3 to node 0. | 0 | 6 | 5 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, and 4.
The edges in G are: (0, 1) (0, 3) (0, 4) (1, 3) (2, 3) (3, 4).
Q: What is the length of the shortest path from node 3 to node 0?
A: | shortest_path | adjacency |
er | 1. | Because there is an edge from node 0 to node 1. | 1 | 54 | 11 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
The edges in G are: (0, 1) (0, 2) (0, 3) (0, 4) (0, 5) (0, 6) (0, 7) (0, 8) (0, 9) (0, 10) (1, 2) (1, 3) (1, 4) (1, 6) (1, 7) (1, 8) (1, 9) (1, 10) (2, ... | shortest_path | adjacency |
er | There is no path from node 0 to node 5. | There is no path connecting node 0 to node 5 based on the graph description. | 2 | 2 | 8 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, and 7.
The edges in G are: (0, 4) (3, 6).
Q: What is the length of the shortest path from node 0 to node 5?
A: | shortest_path | adjacency |
er | There is no path from node 2 to node 3. | There is no path connecting node 2 to node 3 based on the graph description. | 3 | 19 | 19 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, and 18.
The edges in G are: (0, 18) (1, 12) (1, 13) (3, 12) (3, 15) (4, 17) (5, 10) (5, 14) (6, 10) (6, 12) (6, 13) (6, 14) (6, ... | shortest_path | adjacency |
er | 3. | Because there is an edge from node 2 to node 5, there is an edge from node 5 to node 0, and there is an edge from node 0 to node 1. | 4 | 4 | 6 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, and 5.
The edges in G are: (0, 1) (0, 5) (2, 5) (3, 5).
Q: What is the length of the shortest path from node 2 to node 1?
A: | shortest_path | adjacency |
er | There is no path from node 0 to node 4. | There is no path connecting node 0 to node 4 based on the graph description. | 5 | 3 | 5 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, and 4.
The edges in G are: (0, 2) (1, 2) (2, 3).
Q: What is the length of the shortest path from node 0 to node 4?
A: | shortest_path | adjacency |
er | 1. | Because there is an edge from node 0 to node 2. | 6 | 5 | 5 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, and 4.
The edges in G are: (0, 2) (0, 4) (1, 2) (2, 3) (2, 4).
Q: What is the length of the shortest path from node 0 to node 2?
A: | shortest_path | adjacency |
er | 1. | Because there is an edge from node 7 to node 4. | 7 | 17 | 8 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, and 7.
The edges in G are: (0, 1) (0, 5) (0, 6) (1, 2) (1, 3) (1, 4) (1, 5) (1, 7) (2, 3) (2, 4) (2, 5) (2, 6) (3, 4) (4, 5) (4, 6) (4, 7) (6, 7).
Q: What is the length ... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 7 to node 2. | 8 | 69 | 13 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
The edges in G are: (0, 2) (0, 3) (0, 5) (0, 6) (0, 7) (0, 8) (0, 9) (0, 10) (0, 12) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (1, 7) (1, 8) (1, 9) (1,... | shortest_path | adjacency |
er | 2. | Because there is an edge from node 2 to node 12, and there is an edge from node 12 to node 5. | 9 | 54 | 18 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, and 17.
The edges in G are: (0, 1) (0, 2) (0, 3) (0, 12) (0, 16) (0, 17) (1, 7) (1, 9) (1, 11) (1, 13) (2, 3) (2, 7) (2, 9) (2, 12) ... | shortest_path | adjacency |
er | 2. | Because there is an edge from node 1 to node 2, and there is an edge from node 2 to node 6. | 10 | 10 | 8 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, and 7.
The edges in G are: (0, 2) (0, 3) (0, 5) (1, 2) (1, 7) (2, 6) (2, 7) (3, 6) (3, 7) (4, 7).
Q: What is the length of the shortest path from node 1 to node 6?
A: | shortest_path | adjacency |
er | 1. | Because there is an edge from node 0 to node 8. | 11 | 81 | 16 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15.
The edges in G are: (0, 4) (0, 6) (0, 7) (0, 8) (0, 9) (0, 14) (0, 15) (1, 2) (1, 4) (1, 6) (1, 7) (1, 9) (1, 10) (1, 11) (1, 12) (1... | shortest_path | adjacency |
er | 2. | Because there is an edge from node 7 to node 6, and there is an edge from node 6 to node 3. | 12 | 28 | 15 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14.
The edges in G are: (0, 1) (0, 9) (0, 11) (0, 12) (1, 12) (1, 13) (1, 14) (2, 12) (3, 4) (3, 5) (3, 6) (3, 12) (4, 5) (4, 8) (4, 9) (4, ... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 1 to node 10. | 13 | 55 | 12 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11.
The edges in G are: (0, 1) (0, 2) (0, 3) (0, 4) (0, 5) (0, 6) (0, 7) (0, 8) (0, 9) (0, 10) (0, 11) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (1, 8) (1, 9) ... | shortest_path | adjacency |
er | 3. | Because there is an edge from node 14 to node 2, there is an edge from node 2 to node 0, and there is an edge from node 0 to node 1. | 14 | 27 | 16 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15.
The edges in G are: (0, 1) (0, 2) (0, 6) (0, 9) (0, 11) (1, 6) (1, 7) (2, 3) (2, 4) (2, 6) (2, 12) (2, 14) (2, 15) (4, 6) (4, 8) (4,... | shortest_path | adjacency |
er | 4. | Because there is an edge from node 2 to node 0, there is an edge from node 0 to node 11, there is an edge from node 11 to node 8, and there is an edge from node 8 to node 16. | 15 | 17 | 19 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, and 18.
The edges in G are: (0, 2) (0, 11) (1, 5) (2, 14) (2, 15) (2, 18) (3, 4) (3, 12) (5, 10) (5, 13) (6, 7) (6, 12) (7, 17) ... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 9 to node 0. | 16 | 36 | 10 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
The edges in G are: (0, 1) (0, 2) (0, 3) (0, 4) (0, 5) (0, 7) (0, 8) (0, 9) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (1, 8) (2, 3) (2, 4) (2, 5) (2, 6) (2, 7) (2,... | shortest_path | adjacency |
er | 3. | Because there is an edge from node 2 to node 6, there is an edge from node 6 to node 3, and there is an edge from node 3 to node 4. | 17 | 9 | 7 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, and 6.
The edges in G are: (0, 1) (0, 5) (1, 3) (1, 5) (2, 6) (3, 4) (3, 5) (3, 6) (4, 5).
Q: What is the length of the shortest path from node 2 to node 4?
A: | shortest_path | adjacency |
er | 2. | Because there is an edge from node 1 to node 0, and there is an edge from node 0 to node 10. | 18 | 57 | 12 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11.
The edges in G are: (0, 1) (0, 2) (0, 4) (0, 5) (0, 7) (0, 8) (0, 9) (0, 10) (0, 11) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (1, 8) (1, 9) (1, 11) (2, 3)... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 4 to node 7. | 19 | 72 | 13 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
The edges in G are: (0, 1) (0, 2) (0, 3) (0, 4) (0, 5) (0, 6) (0, 7) (0, 8) (0, 9) (0, 10) (0, 11) (0, 12) (1, 4) (1, 5) (1, 6) (1, 7) (1, 8) (1... | shortest_path | adjacency |
er | 2. | Because there is an edge from node 5 to node 0, and there is an edge from node 0 to node 4. | 20 | 50 | 13 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
The edges in G are: (0, 2) (0, 4) (0, 5) (0, 6) (0, 7) (0, 9) (0, 12) (1, 3) (1, 4) (1, 5) (1, 6) (1, 8) (1, 10) (1, 12) (2, 3) (2, 4) (2, 5) (2... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 7 to node 10. | 21 | 44 | 16 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15.
The edges in G are: (0, 1) (0, 7) (0, 8) (0, 9) (0, 12) (0, 13) (0, 15) (1, 13) (1, 14) (2, 4) (2, 7) (2, 10) (2, 11) (2, 12) (3, 5)... | shortest_path | adjacency |
er | There is no path from node 3 to node 7. | There is no path connecting node 3 to node 7 based on the graph description. | 22 | 2 | 8 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, and 7.
The edges in G are: (0, 4) (0, 6).
Q: What is the length of the shortest path from node 3 to node 7?
A: | shortest_path | adjacency |
er | There is no path from node 16 to node 0. | There is no path connecting node 16 to node 0 based on the graph description. | 23 | 23 | 18 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, and 17.
The edges in G are: (0, 2) (0, 12) (0, 15) (1, 15) (1, 17) (2, 8) (2, 12) (3, 4) (3, 9) (4, 15) (4, 17) (6, 12) (6, 17) (7, ... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 4 to node 0. | 24 | 2 | 6 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, and 5.
The edges in G are: (0, 4) (3, 4).
Q: What is the length of the shortest path from node 4 to node 0?
A: | shortest_path | adjacency |
er | 2. | Because there is an edge from node 0 to node 11, and there is an edge from node 11 to node 5. | 25 | 28 | 16 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15.
The edges in G are: (0, 6) (0, 9) (0, 11) (1, 2) (1, 5) (1, 7) (1, 8) (1, 11) (2, 6) (2, 12) (3, 4) (4, 5) (4, 6) (4, 9) (4, 15) (5,... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 2 to node 7. | 26 | 21 | 9 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, and 8.
The edges in G are: (0, 1) (0, 2) (0, 5) (0, 6) (0, 7) (0, 8) (1, 2) (1, 4) (1, 5) (1, 6) (2, 7) (2, 8) (3, 4) (3, 7) (3, 8) (4, 5) (4, 7) (5, 6) (5, 7) (5, 8)... | shortest_path | adjacency |
er | 2. | Because there is an edge from node 12 to node 0, and there is an edge from node 0 to node 5. | 27 | 52 | 18 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, and 17.
The edges in G are: (0, 5) (0, 8) (0, 9) (0, 11) (0, 12) (0, 13) (0, 14) (1, 2) (1, 9) (1, 10) (1, 11) (1, 13) (1, 14) (1, 1... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 0 to node 1. | 28 | 38 | 12 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11.
The edges in G are: (0, 1) (0, 3) (0, 4) (0, 5) (0, 6) (0, 8) (0, 9) (0, 11) (1, 4) (1, 6) (1, 8) (2, 4) (2, 5) (2, 6) (2, 8) (2, 9) (2, 11) (3, 5) ... | shortest_path | adjacency |
er | There is no path from node 4 to node 3. | There is no path connecting node 4 to node 3 based on the graph description. | 29 | 1 | 7 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, and 6.
The edges in G are: (4, 6).
Q: What is the length of the shortest path from node 4 to node 3?
A: | shortest_path | adjacency |
er | 1. | Because there is an edge from node 2 to node 1. | 30 | 26 | 10 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
The edges in G are: (0, 2) (0, 3) (0, 4) (0, 5) (0, 7) (0, 8) (0, 9) (1, 2) (1, 8) (2, 3) (2, 4) (2, 7) (2, 8) (3, 4) (3, 6) (3, 7) (4, 5) (4, 7) (4, 8) (4,... | shortest_path | adjacency |
er | 2. | Because there is an edge from node 4 to node 0, and there is an edge from node 0 to node 1. | 31 | 9 | 6 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, and 5.
The edges in G are: (0, 1) (0, 2) (0, 3) (0, 4) (1, 2) (2, 3) (2, 4) (2, 5) (4, 5).
Q: What is the length of the shortest path from node 4 to node 1?
A: | shortest_path | adjacency |
er | 1. | Because there is an edge from node 4 to node 0. | 32 | 76 | 17 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16.
The edges in G are: (0, 1) (0, 2) (0, 4) (0, 5) (0, 6) (0, 9) (0, 10) (0, 11) (0, 12) (0, 14) (1, 5) (1, 6) (1, 8) (1, 9) (1, 11... | shortest_path | adjacency |
er | 2. | Because there is an edge from node 11 to node 8, and there is an edge from node 8 to node 3. | 33 | 49 | 18 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, and 17.
The edges in G are: (0, 6) (0, 7) (0, 8) (0, 9) (0, 10) (0, 11) (0, 12) (1, 2) (1, 3) (1, 5) (1, 9) (1, 12) (1, 13) (1, 14) ... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 4 to node 1. | 34 | 11 | 6 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, and 5.
The edges in G are: (0, 1) (0, 2) (0, 3) (0, 5) (1, 3) (1, 4) (1, 5) (2, 3) (2, 4) (2, 5) (4, 5).
Q: What is the length of the shortest path from node 4 to node 1?
A: | shortest_path | adjacency |
er | 1. | Because there is an edge from node 10 to node 4. | 35 | 66 | 12 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11.
The edges in G are: (0, 1) (0, 2) (0, 3) (0, 4) (0, 5) (0, 6) (0, 7) (0, 8) (0, 9) (0, 10) (0, 11) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (1, 7) (1, 8) ... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 7 to node 0. | 36 | 66 | 14 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and 13.
The edges in G are: (0, 1) (0, 3) (0, 4) (0, 7) (0, 8) (0, 9) (0, 10) (0, 11) (1, 2) (1, 3) (1, 4) (1, 6) (1, 7) (1, 8) (1, 9) (1, 10) (1, 1... | shortest_path | adjacency |
er | There is no path from node 3 to node 2. | There is no path connecting node 3 to node 2 based on the graph description. | 37 | 4 | 7 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, and 6.
The edges in G are: (0, 5) (1, 4) (2, 6) (4, 5).
Q: What is the length of the shortest path from node 3 to node 2?
A: | shortest_path | adjacency |
er | 2. | Because there is an edge from node 10 to node 7, and there is an edge from node 7 to node 0. | 38 | 28 | 13 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
The edges in G are: (0, 7) (0, 8) (0, 9) (0, 12) (1, 2) (1, 6) (1, 7) (1, 11) (2, 3) (2, 5) (2, 6) (2, 8) (2, 9) (2, 10) (3, 5) (3, 6) (3, 7) (3... | shortest_path | adjacency |
er | There is no path from node 2 to node 7. | There is no path connecting node 2 to node 7 based on the graph description. | 39 | 6 | 8 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, and 7.
The edges in G are: (0, 1) (0, 4) (1, 4) (3, 4) (5, 6) (5, 7).
Q: What is the length of the shortest path from node 2 to node 7?
A: | shortest_path | adjacency |
er | 1. | Because there is an edge from node 2 to node 4. | 40 | 21 | 10 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
The edges in G are: (0, 2) (0, 3) (0, 5) (1, 2) (1, 7) (2, 4) (2, 5) (2, 6) (2, 7) (2, 9) (3, 4) (3, 7) (3, 8) (3, 9) (4, 7) (4, 8) (4, 9) (5, 8) (6, 8) (6,... | shortest_path | adjacency |
er | 2. | Because there is an edge from node 2 to node 0, and there is an edge from node 0 to node 7. | 41 | 19 | 13 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
The edges in G are: (0, 1) (0, 2) (0, 7) (0, 10) (1, 7) (3, 5) (3, 10) (4, 5) (4, 8) (4, 9) (4, 10) (5, 6) (5, 8) (5, 10) (5, 11) (6, 8) (7, 10)... | shortest_path | adjacency |
er | 2. | Because there is an edge from node 0 to node 5, and there is an edge from node 5 to node 6. | 42 | 10 | 9 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, and 8.
The edges in G are: (0, 5) (1, 6) (2, 3) (2, 6) (3, 6) (3, 8) (4, 5) (4, 7) (5, 6) (7, 8).
Q: What is the length of the shortest path from node 0 to node 6?
A:... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 6 to node 2. | 43 | 4 | 7 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, and 6.
The edges in G are: (0, 1) (0, 2) (2, 6) (4, 6).
Q: What is the length of the shortest path from node 6 to node 2?
A: | shortest_path | adjacency |
er | 2. | Because there is an edge from node 7 to node 8, and there is an edge from node 8 to node 5. | 44 | 33 | 13 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
The edges in G are: (0, 7) (0, 10) (0, 12) (1, 2) (1, 3) (1, 11) (2, 3) (2, 5) (2, 9) (2, 10) (3, 5) (3, 6) (3, 9) (3, 11) (3, 12) (4, 10) (4, 1... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 4 to node 3. | 45 | 6 | 7 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, and 6.
The edges in G are: (0, 3) (1, 2) (1, 3) (2, 5) (3, 4) (4, 6).
Q: What is the length of the shortest path from node 4 to node 3?
A: | shortest_path | adjacency |
er | 2. | Because there is an edge from node 7 to node 12, and there is an edge from node 12 to node 0. | 46 | 14 | 13 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
The edges in G are: (0, 12) (1, 8) (1, 9) (2, 4) (2, 5) (2, 11) (3, 10) (4, 7) (5, 7) (5, 8) (6, 7) (6, 11) (7, 12) (8, 12).
Q: What is the leng... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 6 to node 3. | 47 | 12 | 7 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, and 6.
The edges in G are: (0, 2) (0, 5) (0, 6) (1, 2) (1, 3) (1, 6) (2, 4) (2, 6) (3, 5) (3, 6) (4, 5) (4, 6).
Q: What is the length of the shortest path from node 6 to no... | shortest_path | adjacency |
er | There is no path from node 13 to node 9. | There is no path connecting node 13 to node 9 based on the graph description. | 48 | 11 | 14 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and 13.
The edges in G are: (1, 3) (1, 4) (1, 6) (1, 12) (2, 4) (2, 6) (2, 12) (3, 12) (4, 11) (8, 12) (10, 13).
Q: What is the length of the shorte... | shortest_path | adjacency |
er | There is no path from node 1 to node 3. | There is no path connecting node 1 to node 3 based on the graph description. | 49 | 2 | 6 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, and 5.
The edges in G are: (0, 5) (2, 4).
Q: What is the length of the shortest path from node 1 to node 3?
A: | shortest_path | adjacency |
er | There is no path from node 5 to node 4. | There is no path connecting node 5 to node 4 based on the graph description. | 50 | 2 | 7 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, and 6.
The edges in G are: (2, 3) (2, 4).
Q: What is the length of the shortest path from node 5 to node 4?
A: | shortest_path | adjacency |
er | 2. | Because there is an edge from node 14 to node 11, and there is an edge from node 11 to node 9. | 51 | 51 | 17 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16.
The edges in G are: (0, 1) (0, 4) (0, 5) (0, 7) (0, 11) (0, 16) (1, 8) (1, 9) (1, 10) (1, 11) (1, 13) (2, 12) (2, 13) (2, 14) (3... | shortest_path | adjacency |
er | There is no path from node 8 to node 1. | There is no path connecting node 8 to node 1 based on the graph description. | 52 | 4 | 16 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15.
The edges in G are: (2, 9) (5, 8) (7, 9) (9, 11).
Q: What is the length of the shortest path from node 8 to node 1?
A: | shortest_path | adjacency |
er | There is no path from node 1 to node 3. | There is no path connecting node 1 to node 3 based on the graph description. | 53 | 0 | 5 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, and 4..
Q: What is the length of the shortest path from node 1 to node 3?
A: | shortest_path | adjacency |
er | 1. | Because there is an edge from node 13 to node 12. | 54 | 119 | 16 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15.
The edges in G are: (0, 1) (0, 2) (0, 3) (0, 4) (0, 5) (0, 6) (0, 7) (0, 8) (0, 9) (0, 10) (0, 11) (0, 12) (0, 13) (0, 14) (0, 15) (... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 3 to node 16. | 55 | 129 | 17 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16.
The edges in G are: (0, 1) (0, 2) (0, 3) (0, 4) (0, 5) (0, 6) (0, 8) (0, 9) (0, 10) (0, 11) (0, 12) (0, 14) (0, 15) (1, 2) (1, 3... | shortest_path | adjacency |
er | There is no path from node 7 to node 6. | There is no path connecting node 7 to node 6 based on the graph description. | 56 | 9 | 11 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
The edges in G are: (0, 4) (1, 3) (2, 6) (3, 9) (4, 9) (5, 7) (5, 9) (6, 10) (7, 8).
Q: What is the length of the shortest path from node 7 to node 6?
A... | shortest_path | adjacency |
er | 2. | Because there is an edge from node 8 to node 1, and there is an edge from node 1 to node 6. | 57 | 49 | 18 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, and 17.
The edges in G are: (0, 1) (0, 7) (0, 11) (0, 15) (1, 3) (1, 4) (1, 5) (1, 6) (1, 8) (1, 16) (2, 3) (2, 4) (2, 9) (2, 15) (3... | shortest_path | adjacency |
er | There is no path from node 2 to node 0. | There is no path connecting node 2 to node 0 based on the graph description. | 58 | 8 | 6 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, and 5.
The edges in G are: (1, 2) (1, 3) (2, 3) (2, 4) (2, 5) (3, 4) (3, 5) (4, 5).
Q: What is the length of the shortest path from node 2 to node 0?
A: | shortest_path | adjacency |
er | 2. | Because there is an edge from node 11 to node 2, and there is an edge from node 2 to node 12. | 59 | 50 | 13 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
The edges in G are: (0, 1) (0, 3) (0, 4) (0, 5) (0, 7) (0, 8) (0, 10) (0, 12) (1, 2) (1, 4) (1, 7) (1, 8) (1, 10) (1, 11) (2, 3) (2, 4) (2, 6) (... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 5 to node 8. | 60 | 152 | 19 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, and 18.
The edges in G are: (0, 1) (0, 2) (0, 4) (0, 5) (0, 6) (0, 7) (0, 8) (0, 9) (0, 10) (0, 11) (0, 12) (0, 13) (0, 14) (0, ... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 4 to node 13. | 61 | 119 | 16 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15.
The edges in G are: (0, 1) (0, 2) (0, 3) (0, 4) (0, 5) (0, 6) (0, 7) (0, 8) (0, 9) (0, 10) (0, 11) (0, 12) (0, 13) (0, 14) (0, 15) (... | shortest_path | adjacency |
er | 2. | Because there is an edge from node 10 to node 0, and there is an edge from node 0 to node 12. | 62 | 94 | 16 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15.
The edges in G are: (0, 1) (0, 2) (0, 3) (0, 4) (0, 5) (0, 6) (0, 7) (0, 10) (0, 11) (0, 12) (0, 15) (1, 2) (1, 3) (1, 4) (1, 5) (1,... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 7 to node 1. | 63 | 20 | 9 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, and 8.
The edges in G are: (0, 1) (0, 3) (0, 4) (0, 5) (0, 6) (0, 7) (0, 8) (1, 4) (1, 7) (1, 8) (2, 4) (2, 5) (2, 7) (2, 8) (3, 7) (4, 6) (4, 7) (4, 8) (5, 6) (5, 7)... | shortest_path | adjacency |
er | There is no path from node 2 to node 6. | There is no path connecting node 2 to node 6 based on the graph description. | 64 | 10 | 16 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15.
The edges in G are: (0, 5) (0, 14) (1, 3) (1, 6) (2, 10) (3, 13) (6, 12) (7, 13) (7, 15) (12, 14).
Q: What is the length of the shor... | shortest_path | adjacency |
er | 2. | Because there is an edge from node 3 to node 2, and there is an edge from node 2 to node 0. | 65 | 24 | 13 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
The edges in G are: (0, 2) (0, 4) (0, 5) (0, 6) (0, 11) (1, 3) (1, 7) (1, 8) (2, 3) (2, 7) (2, 8) (3, 4) (4, 8) (4, 9) (4, 10) (4, 11) (4, 12) (... | shortest_path | adjacency |
er | There is no path from node 2 to node 0. | There is no path connecting node 2 to node 0 based on the graph description. | 66 | 0 | 6 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, and 5..
Q: What is the length of the shortest path from node 2 to node 0?
A: | shortest_path | adjacency |
er | 2. | Because there is an edge from node 7 to node 6, and there is an edge from node 6 to node 16. | 67 | 65 | 19 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, and 18.
The edges in G are: (0, 2) (0, 4) (0, 5) (0, 6) (0, 9) (0, 11) (0, 12) (0, 13) (0, 14) (0, 18) (1, 2) (1, 4) (1, 5) (1, ... | shortest_path | adjacency |
er | 2. | Because there is an edge from node 13 to node 8, and there is an edge from node 8 to node 1. | 68 | 24 | 14 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and 13.
The edges in G are: (0, 1) (0, 5) (1, 5) (1, 7) (1, 8) (3, 5) (3, 6) (3, 8) (4, 5) (4, 7) (4, 11) (4, 13) (5, 6) (5, 11) (6, 8) (6, 13) (7, ... | shortest_path | adjacency |
er | There is no path from node 12 to node 11. | There is no path connecting node 12 to node 11 based on the graph description. | 69 | 4 | 14 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and 13.
The edges in G are: (1, 11) (1, 13) (7, 12) (8, 11).
Q: What is the length of the shortest path from node 12 to node 11?
A: | shortest_path | adjacency |
er | 1. | Because there is an edge from node 10 to node 9. | 70 | 112 | 19 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, and 18.
The edges in G are: (0, 4) (0, 5) (0, 6) (0, 7) (0, 8) (0, 10) (0, 11) (0, 14) (0, 16) (0, 17) (1, 3) (1, 4) (1, 5) (1, ... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 7 to node 1. | 71 | 73 | 13 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
The edges in G are: (0, 1) (0, 2) (0, 3) (0, 4) (0, 6) (0, 7) (0, 8) (0, 9) (0, 10) (0, 11) (0, 12) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (1, 7) (1... | shortest_path | adjacency |
er | 2. | Because there is an edge from node 18 to node 1, and there is an edge from node 1 to node 8. | 72 | 93 | 19 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, and 18.
The edges in G are: (0, 1) (0, 3) (0, 4) (0, 6) (0, 8) (0, 11) (0, 13) (0, 14) (0, 15) (0, 16) (1, 3) (1, 7) (1, 8) (1, ... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 1 to node 6. | 73 | 26 | 10 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
The edges in G are: (0, 1) (0, 4) (0, 5) (0, 7) (0, 8) (0, 9) (1, 2) (1, 4) (1, 5) (1, 6) (1, 9) (2, 4) (2, 6) (2, 7) (3, 4) (3, 5) (3, 6) (4, 5) (4, 6) (4,... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 6 to node 3. | 74 | 114 | 19 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, and 18.
The edges in G are: (0, 1) (0, 3) (0, 4) (0, 7) (0, 9) (0, 10) (0, 11) (0, 12) (0, 14) (0, 15) (0, 16) (0, 17) (1, 2) (1... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 6 to node 3. | 75 | 35 | 13 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
The edges in G are: (0, 2) (0, 3) (0, 7) (0, 12) (1, 2) (1, 4) (1, 6) (1, 7) (1, 8) (1, 9) (1, 10) (1, 11) (2, 3) (2, 4) (2, 9) (2, 10) (2, 12) ... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 14 to node 16. | 76 | 32 | 19 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, and 18.
The edges in G are: (0, 2) (0, 5) (0, 6) (0, 14) (1, 3) (1, 6) (1, 9) (1, 18) (2, 8) (2, 11) (2, 13) (2, 15) (3, 7) (3, ... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 7 to node 13. | 77 | 91 | 16 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15.
The edges in G are: (0, 2) (0, 3) (0, 4) (0, 5) (0, 6) (0, 7) (0, 10) (0, 11) (0, 12) (0, 13) (0, 14) (0, 15) (1, 3) (1, 5) (1, 8) (... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 5 to node 3. | 78 | 33 | 12 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11.
The edges in G are: (0, 1) (0, 4) (0, 5) (0, 6) (0, 9) (0, 11) (1, 2) (1, 5) (1, 7) (1, 9) (2, 4) (2, 6) (2, 10) (2, 11) (3, 5) (3, 6) (3, 7) (3, 9)... | shortest_path | adjacency |
er | There is no path from node 4 to node 3. | There is no path connecting node 4 to node 3 based on the graph description. | 79 | 2 | 5 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, and 4.
The edges in G are: (1, 2) (2, 3).
Q: What is the length of the shortest path from node 4 to node 3?
A: | shortest_path | adjacency |
er | 2. | Because there is an edge from node 2 to node 0, and there is an edge from node 0 to node 9. | 80 | 42 | 12 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11.
The edges in G are: (0, 2) (0, 3) (0, 4) (0, 6) (0, 9) (0, 10) (1, 2) (1, 5) (1, 6) (1, 7) (1, 9) (1, 11) (2, 5) (2, 7) (2, 10) (2, 11) (3, 4) (3, 5... | shortest_path | adjacency |
er | There is no path from node 1 to node 2. | There is no path connecting node 1 to node 2 based on the graph description. | 81 | 2 | 7 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, and 6.
The edges in G are: (0, 1) (5, 6).
Q: What is the length of the shortest path from node 1 to node 2?
A: | shortest_path | adjacency |
er | There is no path from node 0 to node 2. | There is no path connecting node 0 to node 2 based on the graph description. | 82 | 0 | 5 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, and 4..
Q: What is the length of the shortest path from node 0 to node 2?
A: | shortest_path | adjacency |
er | 2. | Because there is an edge from node 8 to node 3, and there is an edge from node 3 to node 2. | 83 | 21 | 10 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
The edges in G are: (0, 1) (0, 2) (0, 4) (0, 5) (0, 6) (0, 9) (1, 4) (1, 6) (1, 8) (2, 3) (2, 4) (2, 9) (3, 8) (3, 9) (4, 5) (4, 6) (4, 8) (5, 7) (6, 7) (7,... | shortest_path | adjacency |
er | 3. | Because there is an edge from node 7 to node 1, there is an edge from node 1 to node 2, and there is an edge from node 2 to node 8. | 84 | 19 | 12 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11.
The edges in G are: (0, 2) (0, 3) (1, 2) (1, 3) (1, 7) (1, 9) (2, 3) (2, 6) (2, 8) (3, 11) (4, 5) (5, 8) (5, 9) (5, 11) (6, 9) (6, 10) (7, 9) (7, 10... | shortest_path | adjacency |
er | 2. | Because there is an edge from node 3 to node 5, and there is an edge from node 5 to node 2. | 85 | 14 | 7 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, and 6.
The edges in G are: (0, 1) (0, 5) (0, 6) (1, 2) (1, 4) (1, 5) (1, 6) (2, 4) (2, 5) (2, 6) (3, 5) (4, 5) (4, 6) (5, 6).
Q: What is the length of the shortest path fro... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 2 to node 14. | 86 | 86 | 15 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, and 14.
The edges in G are: (0, 2) (0, 4) (0, 6) (0, 7) (0, 9) (0, 10) (0, 11) (0, 12) (0, 13) (0, 14) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (1, 7)... | shortest_path | adjacency |
er | 2. | Because there is an edge from node 1 to node 0, and there is an edge from node 0 to node 9. | 87 | 43 | 16 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15.
The edges in G are: (0, 1) (0, 2) (0, 4) (0, 5) (0, 8) (0, 9) (1, 4) (1, 13) (1, 15) (2, 7) (2, 10) (2, 12) (2, 15) (3, 4) (3, 8) (3... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 5 to node 4. | 88 | 102 | 17 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, and 16.
The edges in G are: (0, 2) (0, 4) (0, 5) (0, 6) (0, 8) (0, 9) (0, 10) (0, 12) (0, 13) (0, 15) (0, 16) (1, 2) (1, 3) (1, 4) (1, 5... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 4 to node 0. | 89 | 10 | 5 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, and 4.
The edges in G are: (0, 1) (0, 2) (0, 3) (0, 4) (1, 2) (1, 3) (1, 4) (2, 3) (2, 4) (3, 4).
Q: What is the length of the shortest path from node 4 to node 0?
A: | shortest_path | adjacency |
er | 1. | Because there is an edge from node 2 to node 1. | 90 | 9 | 5 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, and 4.
The edges in G are: (0, 1) (0, 2) (0, 3) (0, 4) (1, 2) (1, 3) (1, 4) (2, 3) (3, 4).
Q: What is the length of the shortest path from node 2 to node 1?
A: | shortest_path | adjacency |
er | 1. | Because there is an edge from node 0 to node 10. | 91 | 66 | 16 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, and 15.
The edges in G are: (0, 1) (0, 2) (0, 4) (0, 6) (0, 9) (0, 10) (0, 11) (0, 12) (0, 14) (0, 15) (1, 2) (1, 7) (1, 10) (1, 11) (1, 12)... | shortest_path | adjacency |
er | 2. | Because there is an edge from node 1 to node 5, and there is an edge from node 5 to node 2. | 92 | 21 | 18 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, and 17.
The edges in G are: (0, 8) (1, 5) (1, 11) (2, 3) (2, 5) (2, 8) (3, 8) (3, 14) (4, 7) (4, 9) (4, 12) (4, 13) (6, 8) (6, 11) (... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 6 to node 1. | 93 | 8 | 7 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, and 6.
The edges in G are: (0, 1) (0, 2) (0, 4) (1, 4) (1, 5) (1, 6) (3, 4) (3, 6).
Q: What is the length of the shortest path from node 6 to node 1?
A: | shortest_path | adjacency |
er | 1. | Because there is an edge from node 3 to node 0. | 94 | 63 | 13 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
The edges in G are: (0, 1) (0, 2) (0, 3) (0, 4) (0, 5) (0, 6) (0, 7) (0, 8) (0, 10) (0, 11) (0, 12) (1, 2) (1, 3) (1, 5) (1, 6) (1, 8) (1, 9) (1... | shortest_path | adjacency |
er | 2. | Because there is an edge from node 6 to node 0, and there is an edge from node 0 to node 12. | 95 | 52 | 13 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12.
The edges in G are: (0, 1) (0, 2) (0, 3) (0, 4) (0, 5) (0, 6) (0, 7) (0, 9) (0, 10) (0, 11) (0, 12) (1, 2) (1, 4) (1, 5) (1, 6) (1, 10) (1, 11) ... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 10 to node 6. | 96 | 118 | 19 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, and 18.
The edges in G are: (0, 1) (0, 3) (0, 4) (0, 5) (0, 6) (0, 7) (0, 8) (0, 10) (0, 12) (0, 13) (0, 14) (0, 15) (0, 16) (0,... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 6 to node 4. | 97 | 31 | 10 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
The edges in G are: (0, 1) (0, 4) (0, 6) (0, 8) (0, 9) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6) (1, 7) (1, 8) (1, 9) (2, 3) (2, 4) (2, 5) (2, 8) (2, 9) (3, 5) (3,... | shortest_path | adjacency |
er | 1. | Because there is an edge from node 17 to node 9. | 98 | 142 | 19 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, and 18.
The edges in G are: (0, 1) (0, 2) (0, 3) (0, 5) (0, 6) (0, 7) (0, 8) (0, 9) (0, 10) (0, 11) (0, 12) (0, 13) (0, 14) (0, ... | shortest_path | adjacency |
er | 2. | Because there is an edge from node 6 to node 1, and there is an edge from node 1 to node 2. | 99 | 16 | 8 | In an undirected graph, (i,j) means that node i and node j are connected with an undirected edge. G describes a graph among nodes 0, 1, 2, 3, 4, 5, 6, and 7.
The edges in G are: (0, 1) (0, 2) (1, 2) (1, 3) (1, 5) (1, 6) (1, 7) (2, 4) (3, 4) (3, 5) (3, 6) (3, 7) (4, 6) (4, 7) (5, 6) (5, 7).
Q: What is the length of the ... | shortest_path | adjacency |
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