Question:
In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 0 to node 4.
A: All the paths from node 0 to node 4 are:
0,1,4 with a total weight of 2 + 1 = 3,
0,2,3,4 with a total weight of 1 + 1 + 2 = 4.
The weight of path 0,1,4 is the smallest, so the shortest path from node 0 to node 4 is 0,1,4 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 4 and node 1 with weight 2,
an edge between node 2 and node 1 with weight 1,
an edge between node 3 and node 2 with weight 4,
an edge between node 2 and node 4 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 3 to node 1.
A: All the paths from node 3 to node 1 are:
3,2,1 with a total weight of 4 + 1 = 5,
3,2,4,1 with a total weight of 4 + 1 + 2 = 7,
3,4,1 with a total weight of 2 + 2 = 4,
3,4,2,1 with a total weight of 2 + 1 + 1 = 4,
3,0,4,1 with a total weight of 2 + 1 + 2 = 5,
3,0,2,1 with a total weight of 2 + 1 + 1 = 4,
3,4,2,4,1 with a total weight of 2 + 1 + 1 + 2 = 6.
The weight of path 3,4,1 is the smallest, so the shortest path from node 3 to node 1 is 3,4,1 with a total weight of 4.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 2 with weight 2,
an edge between node 1 and node 0 with weight 2,
an edge between node 5 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 3 and node 1 with weight 2,
an edge between node 5 and node 4 with weight 1.
Q: Give the shortest path from node 4 to node 2.
A: All the paths from node 4 to node 2 are:
4,5,1,0,2 with a total weight of 1 + 1 + 2 + 2 = 6,
4,5,1,2 with a total weight of 1 + 1 + 3 = 5.
The weight of path 4,5,1,2 is the smallest, so the shortest path from node 4 to node 2 is 4,5,1,2 with a total weight of 5.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 2 and node 1 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 3 and node 1 with weight 1,
an edge between node 5 and node 2 with weight 4,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 1.
Q: Give the shortest path from node 2 to node 0.
A: All the paths from node 2 to node 0 are:
2,1,0 with a total weight of 4 + 1 = 5,
2,5,1,0 with a total weight of 4 + 1 + 1 = 6,
2,3,1,0 with a total weight of 1 + 1 + 1 = 3.
The weight of path 2,3,1,0 is the smallest, so the shortest path from node 2 to node 0 is 2,3,1,0 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 4 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 4 and node 3 with weight 5,
an edge between node 6 and node 5 with weight 3,
an edge between node 3 and node 5 with weight 4.
Q: Give the shortest path from node 0 to node 5.
A: All the paths from node 0 to node 5 are:
0,2,6,5 with a total weight of 4 + 2 + 3 = 9,
0,1,2,6,5 with a total weight of 1 + 2 + 2 + 3 = 8,
0,4,6,5 with a total weight of 2 + 4 + 3 = 9,
0,4,3,5 with a total weight of 2 + 5 + 4 = 11.
The weight of path 0,1,2,6,5 is the smallest, so the shortest path from node 0 to node 5 is 0,1,2,6,5 with a total weight of 8.

In an undirected graph, the nodes are numbered from 0 to 16, and the edges are:
an edge between node 0 and node 12 with weight 8,
an edge between node 0 and node 7 with weight 6,
an edge between node 0 and node 9 with weight 4,
an edge between node 0 and node 11 with weight 10,
an edge between node 1 and node 11 with weight 8,
an edge between node 1 and node 16 with weight 10,
an edge between node 1 and node 6 with weight 5,
an edge between node 2 and node 5 with weight 2,
an edge between node 2 and node 12 with weight 2,
an edge between node 2 and node 7 with weight 9,
an edge between node 2 and node 4 with weight 8,
an edge between node 2 and node 9 with weight 10,
an edge between node 2 and node 10 with weight 2,
an edge between node 2 and node 14 with weight 1,
an edge between node 3 and node 8 with weight 4,
an edge between node 3 and node 7 with weight 3,
an edge between node 4 and node 10 with weight 1,
an edge between node 4 and node 13 with weight 9,
an edge between node 5 and node 14 with weight 2,
an edge between node 5 and node 6 with weight 9,
an edge between node 6 and node 15 with weight 4,
an edge between node 7 and node 10 with weight 4,
an edge between node 7 and node 16 with weight 1,
an edge between node 8 and node 10 with weight 8,
an edge between node 9 and node 10 with weight 3,
an edge between node 10 and node 12 with weight 2,
an edge between node 11 and node 15 with weight 7,
an edge between node 11 and node 12 with weight 4,
an edge between node 11 and node 13 with weight 1,
an edge between node 12 and node 14 with weight 6,
an edge between node 13 and node 15 with weight 2,
an edge between node 13 and node 14 with weight 9.
Q: Give the shortest path from node 12 to node 5.
A:

Answer: The shortest path from node 12 to node 5 is 12,2,5 with a total weight of 4


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 0 to node 4.
A: All the paths from node 0 to node 4 are:
0,1,4 with a total weight of 2 + 1 = 3,
0,2,3,4 with a total weight of 1 + 1 + 2 = 4.
The weight of path 0,1,4 is the smallest, so the shortest path from node 0 to node 4 is 0,1,4 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 4 and node 1 with weight 2,
an edge between node 2 and node 1 with weight 1,
an edge between node 3 and node 2 with weight 4,
an edge between node 2 and node 4 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 3 to node 1.
A: All the paths from node 3 to node 1 are:
3,2,1 with a total weight of 4 + 1 = 5,
3,2,4,1 with a total weight of 4 + 1 + 2 = 7,
3,4,1 with a total weight of 2 + 2 = 4,
3,4,2,1 with a total weight of 2 + 1 + 1 = 4,
3,0,4,1 with a total weight of 2 + 1 + 2 = 5,
3,0,2,1 with a total weight of 2 + 1 + 1 = 4,
3,4,2,4,1 with a total weight of 2 + 1 + 1 + 2 = 6.
The weight of path 3,4,1 is the smallest, so the shortest path from node 3 to node 1 is 3,4,1 with a total weight of 4.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 2 with weight 2,
an edge between node 1 and node 0 with weight 2,
an edge between node 5 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 3 and node 1 with weight 2,
an edge between node 5 and node 4 with weight 1.
Q: Give the shortest path from node 4 to node 2.
A: All the paths from node 4 to node 2 are:
4,5,1,0,2 with a total weight of 1 + 1 + 2 + 2 = 6,
4,5,1,2 with a total weight of 1 + 1 + 3 = 5.
The weight of path 4,5,1,2 is the smallest, so the shortest path from node 4 to node 2 is 4,5,1,2 with a total weight of 5.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 2 and node 1 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 3 and node 1 with weight 1,
an edge between node 5 and node 2 with weight 4,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 1.
Q: Give the shortest path from node 2 to node 0.
A: All the paths from node 2 to node 0 are:
2,1,0 with a total weight of 4 + 1 = 5,
2,5,1,0 with a total weight of 4 + 1 + 1 = 6,
2,3,1,0 with a total weight of 1 + 1 + 1 = 3.
The weight of path 2,3,1,0 is the smallest, so the shortest path from node 2 to node 0 is 2,3,1,0 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 4 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 4 and node 3 with weight 5,
an edge between node 6 and node 5 with weight 3,
an edge between node 3 and node 5 with weight 4.
Q: Give the shortest path from node 0 to node 5.
A: All the paths from node 0 to node 5 are:
0,2,6,5 with a total weight of 4 + 2 + 3 = 9,
0,1,2,6,5 with a total weight of 1 + 2 + 2 + 3 = 8,
0,4,6,5 with a total weight of 2 + 4 + 3 = 9,
0,4,3,5 with a total weight of 2 + 5 + 4 = 11.
The weight of path 0,1,2,6,5 is the smallest, so the shortest path from node 0 to node 5 is 0,1,2,6,5 with a total weight of 8.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 4 with weight 4,
an edge between node 0 and node 2 with weight 4,
an edge between node 1 and node 4 with weight 2,
an edge between node 1 and node 2 with weight 1,
an edge between node 2 and node 4 with weight 4,
an edge between node 2 and node 5 with weight 1,
an edge between node 2 and node 3 with weight 3,
an edge between node 3 and node 4 with weight 4,
an edge between node 4 and node 5 with weight 3.
Q: Give the shortest path from node 0 to node 5.
A:

Answer: The shortest path from node 0 to node 5 is 0,2,5 with a total weight of 5


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 0 to node 4.
A: All the paths from node 0 to node 4 are:
0,1,4 with a total weight of 2 + 1 = 3,
0,2,3,4 with a total weight of 1 + 1 + 2 = 4.
The weight of path 0,1,4 is the smallest, so the shortest path from node 0 to node 4 is 0,1,4 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 4 and node 1 with weight 2,
an edge between node 2 and node 1 with weight 1,
an edge between node 3 and node 2 with weight 4,
an edge between node 2 and node 4 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 3 to node 1.
A: All the paths from node 3 to node 1 are:
3,2,1 with a total weight of 4 + 1 = 5,
3,2,4,1 with a total weight of 4 + 1 + 2 = 7,
3,4,1 with a total weight of 2 + 2 = 4,
3,4,2,1 with a total weight of 2 + 1 + 1 = 4,
3,0,4,1 with a total weight of 2 + 1 + 2 = 5,
3,0,2,1 with a total weight of 2 + 1 + 1 = 4,
3,4,2,4,1 with a total weight of 2 + 1 + 1 + 2 = 6.
The weight of path 3,4,1 is the smallest, so the shortest path from node 3 to node 1 is 3,4,1 with a total weight of 4.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 2 with weight 2,
an edge between node 1 and node 0 with weight 2,
an edge between node 5 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 3 and node 1 with weight 2,
an edge between node 5 and node 4 with weight 1.
Q: Give the shortest path from node 4 to node 2.
A: All the paths from node 4 to node 2 are:
4,5,1,0,2 with a total weight of 1 + 1 + 2 + 2 = 6,
4,5,1,2 with a total weight of 1 + 1 + 3 = 5.
The weight of path 4,5,1,2 is the smallest, so the shortest path from node 4 to node 2 is 4,5,1,2 with a total weight of 5.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 2 and node 1 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 3 and node 1 with weight 1,
an edge between node 5 and node 2 with weight 4,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 1.
Q: Give the shortest path from node 2 to node 0.
A: All the paths from node 2 to node 0 are:
2,1,0 with a total weight of 4 + 1 = 5,
2,5,1,0 with a total weight of 4 + 1 + 1 = 6,
2,3,1,0 with a total weight of 1 + 1 + 1 = 3.
The weight of path 2,3,1,0 is the smallest, so the shortest path from node 2 to node 0 is 2,3,1,0 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 4 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 4 and node 3 with weight 5,
an edge between node 6 and node 5 with weight 3,
an edge between node 3 and node 5 with weight 4.
Q: Give the shortest path from node 0 to node 5.
A: All the paths from node 0 to node 5 are:
0,2,6,5 with a total weight of 4 + 2 + 3 = 9,
0,1,2,6,5 with a total weight of 1 + 2 + 2 + 3 = 8,
0,4,6,5 with a total weight of 2 + 4 + 3 = 9,
0,4,3,5 with a total weight of 2 + 5 + 4 = 11.
The weight of path 0,1,2,6,5 is the smallest, so the shortest path from node 0 to node 5 is 0,1,2,6,5 with a total weight of 8.

In an undirected graph, the nodes are numbered from 0 to 19, and the edges are:
an edge between node 0 and node 16 with weight 10,
an edge between node 0 and node 4 with weight 10,
an edge between node 0 and node 19 with weight 6,
an edge between node 0 and node 2 with weight 7,
an edge between node 1 and node 16 with weight 9,
an edge between node 1 and node 5 with weight 1,
an edge between node 1 and node 17 with weight 5,
an edge between node 2 and node 18 with weight 5,
an edge between node 2 and node 19 with weight 9,
an edge between node 3 and node 13 with weight 9,
an edge between node 3 and node 16 with weight 5,
an edge between node 3 and node 5 with weight 9,
an edge between node 3 and node 9 with weight 5,
an edge between node 3 and node 19 with weight 10,
an edge between node 3 and node 6 with weight 3,
an edge between node 4 and node 5 with weight 10,
an edge between node 5 and node 14 with weight 2,
an edge between node 5 and node 10 with weight 2,
an edge between node 5 and node 16 with weight 6,
an edge between node 6 and node 11 with weight 9,
an edge between node 7 and node 18 with weight 2,
an edge between node 7 and node 19 with weight 3,
an edge between node 8 and node 9 with weight 7,
an edge between node 9 and node 18 with weight 8,
an edge between node 10 and node 13 with weight 1,
an edge between node 10 and node 19 with weight 10,
an edge between node 11 and node 15 with weight 8,
an edge between node 11 and node 12 with weight 2,
an edge between node 12 and node 15 with weight 3,
an edge between node 12 and node 14 with weight 1,
an edge between node 12 and node 17 with weight 3,
an edge between node 13 and node 15 with weight 7,
an edge between node 13 and node 14 with weight 9,
an edge between node 14 and node 15 with weight 4,
an edge between node 14 and node 19 with weight 6,
an edge between node 15 and node 16 with weight 10,
an edge between node 17 and node 18 with weight 6.
Q: Give the shortest path from node 7 to node 11.
A:

Answer: The shortest path from node 7 to node 11 is 7,19,14,12,11 with a total weight of 12


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 0 to node 4.
A: All the paths from node 0 to node 4 are:
0,1,4 with a total weight of 2 + 1 = 3,
0,2,3,4 with a total weight of 1 + 1 + 2 = 4.
The weight of path 0,1,4 is the smallest, so the shortest path from node 0 to node 4 is 0,1,4 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 4 and node 1 with weight 2,
an edge between node 2 and node 1 with weight 1,
an edge between node 3 and node 2 with weight 4,
an edge between node 2 and node 4 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 3 to node 1.
A: All the paths from node 3 to node 1 are:
3,2,1 with a total weight of 4 + 1 = 5,
3,2,4,1 with a total weight of 4 + 1 + 2 = 7,
3,4,1 with a total weight of 2 + 2 = 4,
3,4,2,1 with a total weight of 2 + 1 + 1 = 4,
3,0,4,1 with a total weight of 2 + 1 + 2 = 5,
3,0,2,1 with a total weight of 2 + 1 + 1 = 4,
3,4,2,4,1 with a total weight of 2 + 1 + 1 + 2 = 6.
The weight of path 3,4,1 is the smallest, so the shortest path from node 3 to node 1 is 3,4,1 with a total weight of 4.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 2 with weight 2,
an edge between node 1 and node 0 with weight 2,
an edge between node 5 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 3 and node 1 with weight 2,
an edge between node 5 and node 4 with weight 1.
Q: Give the shortest path from node 4 to node 2.
A: All the paths from node 4 to node 2 are:
4,5,1,0,2 with a total weight of 1 + 1 + 2 + 2 = 6,
4,5,1,2 with a total weight of 1 + 1 + 3 = 5.
The weight of path 4,5,1,2 is the smallest, so the shortest path from node 4 to node 2 is 4,5,1,2 with a total weight of 5.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 2 and node 1 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 3 and node 1 with weight 1,
an edge between node 5 and node 2 with weight 4,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 1.
Q: Give the shortest path from node 2 to node 0.
A: All the paths from node 2 to node 0 are:
2,1,0 with a total weight of 4 + 1 = 5,
2,5,1,0 with a total weight of 4 + 1 + 1 = 6,
2,3,1,0 with a total weight of 1 + 1 + 1 = 3.
The weight of path 2,3,1,0 is the smallest, so the shortest path from node 2 to node 0 is 2,3,1,0 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 4 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 4 and node 3 with weight 5,
an edge between node 6 and node 5 with weight 3,
an edge between node 3 and node 5 with weight 4.
Q: Give the shortest path from node 0 to node 5.
A: All the paths from node 0 to node 5 are:
0,2,6,5 with a total weight of 4 + 2 + 3 = 9,
0,1,2,6,5 with a total weight of 1 + 2 + 2 + 3 = 8,
0,4,6,5 with a total weight of 2 + 4 + 3 = 9,
0,4,3,5 with a total weight of 2 + 5 + 4 = 11.
The weight of path 0,1,2,6,5 is the smallest, so the shortest path from node 0 to node 5 is 0,1,2,6,5 with a total weight of 8.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 3 with weight 1,
an edge between node 0 and node 4 with weight 4,
an edge between node 1 and node 2 with weight 2,
an edge between node 2 and node 3 with weight 4,
an edge between node 3 and node 5 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 1 to node 0.
A:

Answer: The shortest path from node 1 to node 0 is 1,2,3,0 with a total weight of 7


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 0 to node 4.
A: All the paths from node 0 to node 4 are:
0,1,4 with a total weight of 2 + 1 = 3,
0,2,3,4 with a total weight of 1 + 1 + 2 = 4.
The weight of path 0,1,4 is the smallest, so the shortest path from node 0 to node 4 is 0,1,4 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 4 and node 1 with weight 2,
an edge between node 2 and node 1 with weight 1,
an edge between node 3 and node 2 with weight 4,
an edge between node 2 and node 4 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 3 to node 1.
A: All the paths from node 3 to node 1 are:
3,2,1 with a total weight of 4 + 1 = 5,
3,2,4,1 with a total weight of 4 + 1 + 2 = 7,
3,4,1 with a total weight of 2 + 2 = 4,
3,4,2,1 with a total weight of 2 + 1 + 1 = 4,
3,0,4,1 with a total weight of 2 + 1 + 2 = 5,
3,0,2,1 with a total weight of 2 + 1 + 1 = 4,
3,4,2,4,1 with a total weight of 2 + 1 + 1 + 2 = 6.
The weight of path 3,4,1 is the smallest, so the shortest path from node 3 to node 1 is 3,4,1 with a total weight of 4.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 2 with weight 2,
an edge between node 1 and node 0 with weight 2,
an edge between node 5 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 3 and node 1 with weight 2,
an edge between node 5 and node 4 with weight 1.
Q: Give the shortest path from node 4 to node 2.
A: All the paths from node 4 to node 2 are:
4,5,1,0,2 with a total weight of 1 + 1 + 2 + 2 = 6,
4,5,1,2 with a total weight of 1 + 1 + 3 = 5.
The weight of path 4,5,1,2 is the smallest, so the shortest path from node 4 to node 2 is 4,5,1,2 with a total weight of 5.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 2 and node 1 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 3 and node 1 with weight 1,
an edge between node 5 and node 2 with weight 4,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 1.
Q: Give the shortest path from node 2 to node 0.
A: All the paths from node 2 to node 0 are:
2,1,0 with a total weight of 4 + 1 = 5,
2,5,1,0 with a total weight of 4 + 1 + 1 = 6,
2,3,1,0 with a total weight of 1 + 1 + 1 = 3.
The weight of path 2,3,1,0 is the smallest, so the shortest path from node 2 to node 0 is 2,3,1,0 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 4 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 4 and node 3 with weight 5,
an edge between node 6 and node 5 with weight 3,
an edge between node 3 and node 5 with weight 4.
Q: Give the shortest path from node 0 to node 5.
A: All the paths from node 0 to node 5 are:
0,2,6,5 with a total weight of 4 + 2 + 3 = 9,
0,1,2,6,5 with a total weight of 1 + 2 + 2 + 3 = 8,
0,4,6,5 with a total weight of 2 + 4 + 3 = 9,
0,4,3,5 with a total weight of 2 + 5 + 4 = 11.
The weight of path 0,1,2,6,5 is the smallest, so the shortest path from node 0 to node 5 is 0,1,2,6,5 with a total weight of 8.

In an undirected graph, the nodes are numbered from 0 to 11, and the edges are:
an edge between node 0 and node 4 with weight 6,
an edge between node 0 and node 11 with weight 3,
an edge between node 1 and node 8 with weight 10,
an edge between node 2 and node 5 with weight 5,
an edge between node 3 and node 11 with weight 5,
an edge between node 4 and node 10 with weight 3,
an edge between node 4 and node 8 with weight 10,
an edge between node 5 and node 7 with weight 6,
an edge between node 5 and node 11 with weight 3,
an edge between node 5 and node 6 with weight 1,
an edge between node 8 and node 11 with weight 7,
an edge between node 9 and node 11 with weight 8.
Q: Give the shortest path from node 7 to node 10.
A:

Answer: The shortest path from node 7 to node 10 is 7,5,11,0,4,10 with a total weight of 21


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 0 to node 4.
A: All the paths from node 0 to node 4 are:
0,1,4 with a total weight of 2 + 1 = 3,
0,2,3,4 with a total weight of 1 + 1 + 2 = 4.
The weight of path 0,1,4 is the smallest, so the shortest path from node 0 to node 4 is 0,1,4 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 4 and node 1 with weight 2,
an edge between node 2 and node 1 with weight 1,
an edge between node 3 and node 2 with weight 4,
an edge between node 2 and node 4 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 3 to node 1.
A: All the paths from node 3 to node 1 are:
3,2,1 with a total weight of 4 + 1 = 5,
3,2,4,1 with a total weight of 4 + 1 + 2 = 7,
3,4,1 with a total weight of 2 + 2 = 4,
3,4,2,1 with a total weight of 2 + 1 + 1 = 4,
3,0,4,1 with a total weight of 2 + 1 + 2 = 5,
3,0,2,1 with a total weight of 2 + 1 + 1 = 4,
3,4,2,4,1 with a total weight of 2 + 1 + 1 + 2 = 6.
The weight of path 3,4,1 is the smallest, so the shortest path from node 3 to node 1 is 3,4,1 with a total weight of 4.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 2 with weight 2,
an edge between node 1 and node 0 with weight 2,
an edge between node 5 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 3 and node 1 with weight 2,
an edge between node 5 and node 4 with weight 1.
Q: Give the shortest path from node 4 to node 2.
A: All the paths from node 4 to node 2 are:
4,5,1,0,2 with a total weight of 1 + 1 + 2 + 2 = 6,
4,5,1,2 with a total weight of 1 + 1 + 3 = 5.
The weight of path 4,5,1,2 is the smallest, so the shortest path from node 4 to node 2 is 4,5,1,2 with a total weight of 5.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 2 and node 1 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 3 and node 1 with weight 1,
an edge between node 5 and node 2 with weight 4,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 1.
Q: Give the shortest path from node 2 to node 0.
A: All the paths from node 2 to node 0 are:
2,1,0 with a total weight of 4 + 1 = 5,
2,5,1,0 with a total weight of 4 + 1 + 1 = 6,
2,3,1,0 with a total weight of 1 + 1 + 1 = 3.
The weight of path 2,3,1,0 is the smallest, so the shortest path from node 2 to node 0 is 2,3,1,0 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 4 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 4 and node 3 with weight 5,
an edge between node 6 and node 5 with weight 3,
an edge between node 3 and node 5 with weight 4.
Q: Give the shortest path from node 0 to node 5.
A: All the paths from node 0 to node 5 are:
0,2,6,5 with a total weight of 4 + 2 + 3 = 9,
0,1,2,6,5 with a total weight of 1 + 2 + 2 + 3 = 8,
0,4,6,5 with a total weight of 2 + 4 + 3 = 9,
0,4,3,5 with a total weight of 2 + 5 + 4 = 11.
The weight of path 0,1,2,6,5 is the smallest, so the shortest path from node 0 to node 5 is 0,1,2,6,5 with a total weight of 8.

In an undirected graph, the nodes are numbered from 0 to 10, and the edges are:
an edge between node 0 and node 9 with weight 2,
an edge between node 1 and node 5 with weight 7,
an edge between node 1 and node 6 with weight 1,
an edge between node 1 and node 10 with weight 10,
an edge between node 2 and node 3 with weight 8,
an edge between node 2 and node 10 with weight 5,
an edge between node 3 and node 4 with weight 10,
an edge between node 3 and node 8 with weight 6,
an edge between node 3 and node 6 with weight 4,
an edge between node 3 and node 10 with weight 9,
an edge between node 4 and node 7 with weight 4,
an edge between node 5 and node 9 with weight 7,
an edge between node 7 and node 8 with weight 6.
Q: Give the shortest path from node 8 to node 0.
A:

Answer: The shortest path from node 8 to node 0 is 8,3,6,1,5,9,0 with a total weight of 27


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 0 to node 4.
A: All the paths from node 0 to node 4 are:
0,1,4 with a total weight of 2 + 1 = 3,
0,2,3,4 with a total weight of 1 + 1 + 2 = 4.
The weight of path 0,1,4 is the smallest, so the shortest path from node 0 to node 4 is 0,1,4 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 4 and node 1 with weight 2,
an edge between node 2 and node 1 with weight 1,
an edge between node 3 and node 2 with weight 4,
an edge between node 2 and node 4 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 3 to node 1.
A: All the paths from node 3 to node 1 are:
3,2,1 with a total weight of 4 + 1 = 5,
3,2,4,1 with a total weight of 4 + 1 + 2 = 7,
3,4,1 with a total weight of 2 + 2 = 4,
3,4,2,1 with a total weight of 2 + 1 + 1 = 4,
3,0,4,1 with a total weight of 2 + 1 + 2 = 5,
3,0,2,1 with a total weight of 2 + 1 + 1 = 4,
3,4,2,4,1 with a total weight of 2 + 1 + 1 + 2 = 6.
The weight of path 3,4,1 is the smallest, so the shortest path from node 3 to node 1 is 3,4,1 with a total weight of 4.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 2 with weight 2,
an edge between node 1 and node 0 with weight 2,
an edge between node 5 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 3 and node 1 with weight 2,
an edge between node 5 and node 4 with weight 1.
Q: Give the shortest path from node 4 to node 2.
A: All the paths from node 4 to node 2 are:
4,5,1,0,2 with a total weight of 1 + 1 + 2 + 2 = 6,
4,5,1,2 with a total weight of 1 + 1 + 3 = 5.
The weight of path 4,5,1,2 is the smallest, so the shortest path from node 4 to node 2 is 4,5,1,2 with a total weight of 5.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 2 and node 1 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 3 and node 1 with weight 1,
an edge between node 5 and node 2 with weight 4,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 1.
Q: Give the shortest path from node 2 to node 0.
A: All the paths from node 2 to node 0 are:
2,1,0 with a total weight of 4 + 1 = 5,
2,5,1,0 with a total weight of 4 + 1 + 1 = 6,
2,3,1,0 with a total weight of 1 + 1 + 1 = 3.
The weight of path 2,3,1,0 is the smallest, so the shortest path from node 2 to node 0 is 2,3,1,0 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 4 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 4 and node 3 with weight 5,
an edge between node 6 and node 5 with weight 3,
an edge between node 3 and node 5 with weight 4.
Q: Give the shortest path from node 0 to node 5.
A: All the paths from node 0 to node 5 are:
0,2,6,5 with a total weight of 4 + 2 + 3 = 9,
0,1,2,6,5 with a total weight of 1 + 2 + 2 + 3 = 8,
0,4,6,5 with a total weight of 2 + 4 + 3 = 9,
0,4,3,5 with a total weight of 2 + 5 + 4 = 11.
The weight of path 0,1,2,6,5 is the smallest, so the shortest path from node 0 to node 5 is 0,1,2,6,5 with a total weight of 8.

In an undirected graph, the nodes are numbered from 0 to 12, and the edges are:
an edge between node 0 and node 5 with weight 2,
an edge between node 0 and node 6 with weight 5,
an edge between node 1 and node 2 with weight 4,
an edge between node 1 and node 11 with weight 6,
an edge between node 1 and node 9 with weight 1,
an edge between node 1 and node 8 with weight 5,
an edge between node 2 and node 3 with weight 7,
an edge between node 2 and node 12 with weight 4,
an edge between node 2 and node 8 with weight 8,
an edge between node 3 and node 10 with weight 10,
an edge between node 3 and node 12 with weight 9,
an edge between node 4 and node 7 with weight 3,
an edge between node 4 and node 8 with weight 2,
an edge between node 5 and node 11 with weight 3,
an edge between node 8 and node 11 with weight 7,
an edge between node 8 and node 12 with weight 4,
an edge between node 9 and node 11 with weight 6,
an edge between node 9 and node 12 with weight 9,
an edge between node 11 and node 12 with weight 3.
Q: Give the shortest path from node 10 to node 6.
A:

Answer: The shortest path from node 10 to node 6 is 10,3,12,11,5,0,6 with a total weight of 32


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 0 to node 4.
A: All the paths from node 0 to node 4 are:
0,1,4 with a total weight of 2 + 1 = 3,
0,2,3,4 with a total weight of 1 + 1 + 2 = 4.
The weight of path 0,1,4 is the smallest, so the shortest path from node 0 to node 4 is 0,1,4 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 4 and node 1 with weight 2,
an edge between node 2 and node 1 with weight 1,
an edge between node 3 and node 2 with weight 4,
an edge between node 2 and node 4 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 3 to node 1.
A: All the paths from node 3 to node 1 are:
3,2,1 with a total weight of 4 + 1 = 5,
3,2,4,1 with a total weight of 4 + 1 + 2 = 7,
3,4,1 with a total weight of 2 + 2 = 4,
3,4,2,1 with a total weight of 2 + 1 + 1 = 4,
3,0,4,1 with a total weight of 2 + 1 + 2 = 5,
3,0,2,1 with a total weight of 2 + 1 + 1 = 4,
3,4,2,4,1 with a total weight of 2 + 1 + 1 + 2 = 6.
The weight of path 3,4,1 is the smallest, so the shortest path from node 3 to node 1 is 3,4,1 with a total weight of 4.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 2 with weight 2,
an edge between node 1 and node 0 with weight 2,
an edge between node 5 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 3 and node 1 with weight 2,
an edge between node 5 and node 4 with weight 1.
Q: Give the shortest path from node 4 to node 2.
A: All the paths from node 4 to node 2 are:
4,5,1,0,2 with a total weight of 1 + 1 + 2 + 2 = 6,
4,5,1,2 with a total weight of 1 + 1 + 3 = 5.
The weight of path 4,5,1,2 is the smallest, so the shortest path from node 4 to node 2 is 4,5,1,2 with a total weight of 5.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 2 and node 1 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 3 and node 1 with weight 1,
an edge between node 5 and node 2 with weight 4,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 1.
Q: Give the shortest path from node 2 to node 0.
A: All the paths from node 2 to node 0 are:
2,1,0 with a total weight of 4 + 1 = 5,
2,5,1,0 with a total weight of 4 + 1 + 1 = 6,
2,3,1,0 with a total weight of 1 + 1 + 1 = 3.
The weight of path 2,3,1,0 is the smallest, so the shortest path from node 2 to node 0 is 2,3,1,0 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 4 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 4 and node 3 with weight 5,
an edge between node 6 and node 5 with weight 3,
an edge between node 3 and node 5 with weight 4.
Q: Give the shortest path from node 0 to node 5.
A: All the paths from node 0 to node 5 are:
0,2,6,5 with a total weight of 4 + 2 + 3 = 9,
0,1,2,6,5 with a total weight of 1 + 2 + 2 + 3 = 8,
0,4,6,5 with a total weight of 2 + 4 + 3 = 9,
0,4,3,5 with a total weight of 2 + 5 + 4 = 11.
The weight of path 0,1,2,6,5 is the smallest, so the shortest path from node 0 to node 5 is 0,1,2,6,5 with a total weight of 8.

In an undirected graph, the nodes are numbered from 0 to 7, and the edges are:
an edge between node 0 and node 5 with weight 3,
an edge between node 0 and node 3 with weight 4,
an edge between node 0 and node 7 with weight 2,
an edge between node 0 and node 6 with weight 4,
an edge between node 0 and node 1 with weight 2,
an edge between node 0 and node 4 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 1 and node 3 with weight 1,
an edge between node 1 and node 7 with weight 1,
an edge between node 1 and node 6 with weight 1,
an edge between node 1 and node 4 with weight 3,
an edge between node 1 and node 2 with weight 1,
an edge between node 2 and node 5 with weight 2,
an edge between node 2 and node 3 with weight 1,
an edge between node 2 and node 7 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 3 and node 5 with weight 4,
an edge between node 3 and node 7 with weight 3,
an edge between node 3 and node 6 with weight 1,
an edge between node 3 and node 4 with weight 1,
an edge between node 4 and node 5 with weight 3,
an edge between node 4 and node 7 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 5 and node 7 with weight 2,
an edge between node 5 and node 6 with weight 3.
Q: Give the shortest path from node 7 to node 6.
A:

Answer: The shortest path from node 7 to node 6 is 7,1,6 with a total weight of 2


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 0 to node 4.
A: All the paths from node 0 to node 4 are:
0,1,4 with a total weight of 2 + 1 = 3,
0,2,3,4 with a total weight of 1 + 1 + 2 = 4.
The weight of path 0,1,4 is the smallest, so the shortest path from node 0 to node 4 is 0,1,4 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 4 and node 1 with weight 2,
an edge between node 2 and node 1 with weight 1,
an edge between node 3 and node 2 with weight 4,
an edge between node 2 and node 4 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 3 to node 1.
A: All the paths from node 3 to node 1 are:
3,2,1 with a total weight of 4 + 1 = 5,
3,2,4,1 with a total weight of 4 + 1 + 2 = 7,
3,4,1 with a total weight of 2 + 2 = 4,
3,4,2,1 with a total weight of 2 + 1 + 1 = 4,
3,0,4,1 with a total weight of 2 + 1 + 2 = 5,
3,0,2,1 with a total weight of 2 + 1 + 1 = 4,
3,4,2,4,1 with a total weight of 2 + 1 + 1 + 2 = 6.
The weight of path 3,4,1 is the smallest, so the shortest path from node 3 to node 1 is 3,4,1 with a total weight of 4.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 2 with weight 2,
an edge between node 1 and node 0 with weight 2,
an edge between node 5 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 3 and node 1 with weight 2,
an edge between node 5 and node 4 with weight 1.
Q: Give the shortest path from node 4 to node 2.
A: All the paths from node 4 to node 2 are:
4,5,1,0,2 with a total weight of 1 + 1 + 2 + 2 = 6,
4,5,1,2 with a total weight of 1 + 1 + 3 = 5.
The weight of path 4,5,1,2 is the smallest, so the shortest path from node 4 to node 2 is 4,5,1,2 with a total weight of 5.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 2 and node 1 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 3 and node 1 with weight 1,
an edge between node 5 and node 2 with weight 4,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 1.
Q: Give the shortest path from node 2 to node 0.
A: All the paths from node 2 to node 0 are:
2,1,0 with a total weight of 4 + 1 = 5,
2,5,1,0 with a total weight of 4 + 1 + 1 = 6,
2,3,1,0 with a total weight of 1 + 1 + 1 = 3.
The weight of path 2,3,1,0 is the smallest, so the shortest path from node 2 to node 0 is 2,3,1,0 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 4 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 4 and node 3 with weight 5,
an edge between node 6 and node 5 with weight 3,
an edge between node 3 and node 5 with weight 4.
Q: Give the shortest path from node 0 to node 5.
A: All the paths from node 0 to node 5 are:
0,2,6,5 with a total weight of 4 + 2 + 3 = 9,
0,1,2,6,5 with a total weight of 1 + 2 + 2 + 3 = 8,
0,4,6,5 with a total weight of 2 + 4 + 3 = 9,
0,4,3,5 with a total weight of 2 + 5 + 4 = 11.
The weight of path 0,1,2,6,5 is the smallest, so the shortest path from node 0 to node 5 is 0,1,2,6,5 with a total weight of 8.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 4 with weight 2,
an edge between node 0 and node 1 with weight 4,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 3 with weight 3,
an edge between node 1 and node 4 with weight 2,
an edge between node 1 and node 3 with weight 3,
an edge between node 2 and node 4 with weight 3,
an edge between node 2 and node 3 with weight 4,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 1 to node 2.
A:

Answer: The shortest path from node 1 to node 2 is 1,4,2 with a total weight of 5


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 0 to node 4.
A: All the paths from node 0 to node 4 are:
0,1,4 with a total weight of 2 + 1 = 3,
0,2,3,4 with a total weight of 1 + 1 + 2 = 4.
The weight of path 0,1,4 is the smallest, so the shortest path from node 0 to node 4 is 0,1,4 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 4 and node 1 with weight 2,
an edge between node 2 and node 1 with weight 1,
an edge between node 3 and node 2 with weight 4,
an edge between node 2 and node 4 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 3 to node 1.
A: All the paths from node 3 to node 1 are:
3,2,1 with a total weight of 4 + 1 = 5,
3,2,4,1 with a total weight of 4 + 1 + 2 = 7,
3,4,1 with a total weight of 2 + 2 = 4,
3,4,2,1 with a total weight of 2 + 1 + 1 = 4,
3,0,4,1 with a total weight of 2 + 1 + 2 = 5,
3,0,2,1 with a total weight of 2 + 1 + 1 = 4,
3,4,2,4,1 with a total weight of 2 + 1 + 1 + 2 = 6.
The weight of path 3,4,1 is the smallest, so the shortest path from node 3 to node 1 is 3,4,1 with a total weight of 4.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 2 with weight 2,
an edge between node 1 and node 0 with weight 2,
an edge between node 5 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 3 and node 1 with weight 2,
an edge between node 5 and node 4 with weight 1.
Q: Give the shortest path from node 4 to node 2.
A: All the paths from node 4 to node 2 are:
4,5,1,0,2 with a total weight of 1 + 1 + 2 + 2 = 6,
4,5,1,2 with a total weight of 1 + 1 + 3 = 5.
The weight of path 4,5,1,2 is the smallest, so the shortest path from node 4 to node 2 is 4,5,1,2 with a total weight of 5.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 2 and node 1 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 3 and node 1 with weight 1,
an edge between node 5 and node 2 with weight 4,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 1.
Q: Give the shortest path from node 2 to node 0.
A: All the paths from node 2 to node 0 are:
2,1,0 with a total weight of 4 + 1 = 5,
2,5,1,0 with a total weight of 4 + 1 + 1 = 6,
2,3,1,0 with a total weight of 1 + 1 + 1 = 3.
The weight of path 2,3,1,0 is the smallest, so the shortest path from node 2 to node 0 is 2,3,1,0 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 4 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 4 and node 3 with weight 5,
an edge between node 6 and node 5 with weight 3,
an edge between node 3 and node 5 with weight 4.
Q: Give the shortest path from node 0 to node 5.
A: All the paths from node 0 to node 5 are:
0,2,6,5 with a total weight of 4 + 2 + 3 = 9,
0,1,2,6,5 with a total weight of 1 + 2 + 2 + 3 = 8,
0,4,6,5 with a total weight of 2 + 4 + 3 = 9,
0,4,3,5 with a total weight of 2 + 5 + 4 = 11.
The weight of path 0,1,2,6,5 is the smallest, so the shortest path from node 0 to node 5 is 0,1,2,6,5 with a total weight of 8.

In an undirected graph, the nodes are numbered from 0 to 11, and the edges are:
an edge between node 0 and node 1 with weight 8,
an edge between node 0 and node 3 with weight 1,
an edge between node 0 and node 6 with weight 4,
an edge between node 0 and node 2 with weight 5,
an edge between node 0 and node 9 with weight 2,
an edge between node 1 and node 8 with weight 3,
an edge between node 2 and node 8 with weight 10,
an edge between node 2 and node 7 with weight 8,
an edge between node 3 and node 10 with weight 6,
an edge between node 3 and node 8 with weight 1,
an edge between node 3 and node 7 with weight 1,
an edge between node 4 and node 5 with weight 2,
an edge between node 4 and node 7 with weight 3,
an edge between node 5 and node 11 with weight 10,
an edge between node 6 and node 8 with weight 10,
an edge between node 6 and node 9 with weight 4,
an edge between node 9 and node 11 with weight 8.
Q: Give the shortest path from node 5 to node 10.
A:

Answer: The shortest path from node 5 to node 10 is 5,4,7,3,10 with a total weight of 12


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 0 to node 4.
A: All the paths from node 0 to node 4 are:
0,1,4 with a total weight of 2 + 1 = 3,
0,2,3,4 with a total weight of 1 + 1 + 2 = 4.
The weight of path 0,1,4 is the smallest, so the shortest path from node 0 to node 4 is 0,1,4 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 4 and node 1 with weight 2,
an edge between node 2 and node 1 with weight 1,
an edge between node 3 and node 2 with weight 4,
an edge between node 2 and node 4 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 3 to node 1.
A: All the paths from node 3 to node 1 are:
3,2,1 with a total weight of 4 + 1 = 5,
3,2,4,1 with a total weight of 4 + 1 + 2 = 7,
3,4,1 with a total weight of 2 + 2 = 4,
3,4,2,1 with a total weight of 2 + 1 + 1 = 4,
3,0,4,1 with a total weight of 2 + 1 + 2 = 5,
3,0,2,1 with a total weight of 2 + 1 + 1 = 4,
3,4,2,4,1 with a total weight of 2 + 1 + 1 + 2 = 6.
The weight of path 3,4,1 is the smallest, so the shortest path from node 3 to node 1 is 3,4,1 with a total weight of 4.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 2 with weight 2,
an edge between node 1 and node 0 with weight 2,
an edge between node 5 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 3 and node 1 with weight 2,
an edge between node 5 and node 4 with weight 1.
Q: Give the shortest path from node 4 to node 2.
A: All the paths from node 4 to node 2 are:
4,5,1,0,2 with a total weight of 1 + 1 + 2 + 2 = 6,
4,5,1,2 with a total weight of 1 + 1 + 3 = 5.
The weight of path 4,5,1,2 is the smallest, so the shortest path from node 4 to node 2 is 4,5,1,2 with a total weight of 5.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 2 and node 1 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 3 and node 1 with weight 1,
an edge between node 5 and node 2 with weight 4,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 1.
Q: Give the shortest path from node 2 to node 0.
A: All the paths from node 2 to node 0 are:
2,1,0 with a total weight of 4 + 1 = 5,
2,5,1,0 with a total weight of 4 + 1 + 1 = 6,
2,3,1,0 with a total weight of 1 + 1 + 1 = 3.
The weight of path 2,3,1,0 is the smallest, so the shortest path from node 2 to node 0 is 2,3,1,0 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 4 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 4 and node 3 with weight 5,
an edge between node 6 and node 5 with weight 3,
an edge between node 3 and node 5 with weight 4.
Q: Give the shortest path from node 0 to node 5.
A: All the paths from node 0 to node 5 are:
0,2,6,5 with a total weight of 4 + 2 + 3 = 9,
0,1,2,6,5 with a total weight of 1 + 2 + 2 + 3 = 8,
0,4,6,5 with a total weight of 2 + 4 + 3 = 9,
0,4,3,5 with a total weight of 2 + 5 + 4 = 11.
The weight of path 0,1,2,6,5 is the smallest, so the shortest path from node 0 to node 5 is 0,1,2,6,5 with a total weight of 8.

In an undirected graph, the nodes are numbered from 0 to 15, and the edges are:
an edge between node 0 and node 9 with weight 7,
an edge between node 0 and node 15 with weight 4,
an edge between node 0 and node 14 with weight 3,
an edge between node 1 and node 10 with weight 3,
an edge between node 1 and node 11 with weight 1,
an edge between node 2 and node 15 with weight 8,
an edge between node 2 and node 13 with weight 7,
an edge between node 3 and node 5 with weight 2,
an edge between node 3 and node 15 with weight 6,
an edge between node 3 and node 10 with weight 10,
an edge between node 4 and node 14 with weight 9,
an edge between node 4 and node 6 with weight 3,
an edge between node 4 and node 13 with weight 2,
an edge between node 5 and node 14 with weight 9,
an edge between node 5 and node 12 with weight 10,
an edge between node 6 and node 8 with weight 8,
an edge between node 6 and node 15 with weight 8,
an edge between node 6 and node 14 with weight 7,
an edge between node 7 and node 15 with weight 7,
an edge between node 8 and node 10 with weight 10,
an edge between node 8 and node 12 with weight 10,
an edge between node 9 and node 14 with weight 3,
an edge between node 10 and node 11 with weight 9,
an edge between node 11 and node 13 with weight 8,
an edge between node 13 and node 14 with weight 9,
an edge between node 14 and node 15 with weight 1.
Q: Give the shortest path from node 2 to node 12.
A:

Answer: The shortest path from node 2 to node 12 is 2,15,3,5,12 with a total weight of 26


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 0 to node 4.
A: All the paths from node 0 to node 4 are:
0,1,4 with a total weight of 2 + 1 = 3,
0,2,3,4 with a total weight of 1 + 1 + 2 = 4.
The weight of path 0,1,4 is the smallest, so the shortest path from node 0 to node 4 is 0,1,4 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 4 and node 1 with weight 2,
an edge between node 2 and node 1 with weight 1,
an edge between node 3 and node 2 with weight 4,
an edge between node 2 and node 4 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 3 to node 1.
A: All the paths from node 3 to node 1 are:
3,2,1 with a total weight of 4 + 1 = 5,
3,2,4,1 with a total weight of 4 + 1 + 2 = 7,
3,4,1 with a total weight of 2 + 2 = 4,
3,4,2,1 with a total weight of 2 + 1 + 1 = 4,
3,0,4,1 with a total weight of 2 + 1 + 2 = 5,
3,0,2,1 with a total weight of 2 + 1 + 1 = 4,
3,4,2,4,1 with a total weight of 2 + 1 + 1 + 2 = 6.
The weight of path 3,4,1 is the smallest, so the shortest path from node 3 to node 1 is 3,4,1 with a total weight of 4.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 2 with weight 2,
an edge between node 1 and node 0 with weight 2,
an edge between node 5 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 3 and node 1 with weight 2,
an edge between node 5 and node 4 with weight 1.
Q: Give the shortest path from node 4 to node 2.
A: All the paths from node 4 to node 2 are:
4,5,1,0,2 with a total weight of 1 + 1 + 2 + 2 = 6,
4,5,1,2 with a total weight of 1 + 1 + 3 = 5.
The weight of path 4,5,1,2 is the smallest, so the shortest path from node 4 to node 2 is 4,5,1,2 with a total weight of 5.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 2 and node 1 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 3 and node 1 with weight 1,
an edge between node 5 and node 2 with weight 4,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 1.
Q: Give the shortest path from node 2 to node 0.
A: All the paths from node 2 to node 0 are:
2,1,0 with a total weight of 4 + 1 = 5,
2,5,1,0 with a total weight of 4 + 1 + 1 = 6,
2,3,1,0 with a total weight of 1 + 1 + 1 = 3.
The weight of path 2,3,1,0 is the smallest, so the shortest path from node 2 to node 0 is 2,3,1,0 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 4 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 4 and node 3 with weight 5,
an edge between node 6 and node 5 with weight 3,
an edge between node 3 and node 5 with weight 4.
Q: Give the shortest path from node 0 to node 5.
A: All the paths from node 0 to node 5 are:
0,2,6,5 with a total weight of 4 + 2 + 3 = 9,
0,1,2,6,5 with a total weight of 1 + 2 + 2 + 3 = 8,
0,4,6,5 with a total weight of 2 + 4 + 3 = 9,
0,4,3,5 with a total weight of 2 + 5 + 4 = 11.
The weight of path 0,1,2,6,5 is the smallest, so the shortest path from node 0 to node 5 is 0,1,2,6,5 with a total weight of 8.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 4,
an edge between node 0 and node 1 with weight 1,
an edge between node 0 and node 4 with weight 4,
an edge between node 0 and node 2 with weight 4,
an edge between node 1 and node 3 with weight 2,
an edge between node 2 and node 3 with weight 4,
an edge between node 3 and node 4 with weight 4.
Q: Give the shortest path from node 1 to node 4.
A:

Answer: The shortest path from node 1 to node 4 is 1,0,4 with a total weight of 5


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 0 to node 4.
A: All the paths from node 0 to node 4 are:
0,1,4 with a total weight of 2 + 1 = 3,
0,2,3,4 with a total weight of 1 + 1 + 2 = 4.
The weight of path 0,1,4 is the smallest, so the shortest path from node 0 to node 4 is 0,1,4 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 4 and node 1 with weight 2,
an edge between node 2 and node 1 with weight 1,
an edge between node 3 and node 2 with weight 4,
an edge between node 2 and node 4 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 3 to node 1.
A: All the paths from node 3 to node 1 are:
3,2,1 with a total weight of 4 + 1 = 5,
3,2,4,1 with a total weight of 4 + 1 + 2 = 7,
3,4,1 with a total weight of 2 + 2 = 4,
3,4,2,1 with a total weight of 2 + 1 + 1 = 4,
3,0,4,1 with a total weight of 2 + 1 + 2 = 5,
3,0,2,1 with a total weight of 2 + 1 + 1 = 4,
3,4,2,4,1 with a total weight of 2 + 1 + 1 + 2 = 6.
The weight of path 3,4,1 is the smallest, so the shortest path from node 3 to node 1 is 3,4,1 with a total weight of 4.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 2 with weight 2,
an edge between node 1 and node 0 with weight 2,
an edge between node 5 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 3 and node 1 with weight 2,
an edge between node 5 and node 4 with weight 1.
Q: Give the shortest path from node 4 to node 2.
A: All the paths from node 4 to node 2 are:
4,5,1,0,2 with a total weight of 1 + 1 + 2 + 2 = 6,
4,5,1,2 with a total weight of 1 + 1 + 3 = 5.
The weight of path 4,5,1,2 is the smallest, so the shortest path from node 4 to node 2 is 4,5,1,2 with a total weight of 5.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 2 and node 1 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 3 and node 1 with weight 1,
an edge between node 5 and node 2 with weight 4,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 1.
Q: Give the shortest path from node 2 to node 0.
A: All the paths from node 2 to node 0 are:
2,1,0 with a total weight of 4 + 1 = 5,
2,5,1,0 with a total weight of 4 + 1 + 1 = 6,
2,3,1,0 with a total weight of 1 + 1 + 1 = 3.
The weight of path 2,3,1,0 is the smallest, so the shortest path from node 2 to node 0 is 2,3,1,0 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 4 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 4 and node 3 with weight 5,
an edge between node 6 and node 5 with weight 3,
an edge between node 3 and node 5 with weight 4.
Q: Give the shortest path from node 0 to node 5.
A: All the paths from node 0 to node 5 are:
0,2,6,5 with a total weight of 4 + 2 + 3 = 9,
0,1,2,6,5 with a total weight of 1 + 2 + 2 + 3 = 8,
0,4,6,5 with a total weight of 2 + 4 + 3 = 9,
0,4,3,5 with a total weight of 2 + 5 + 4 = 11.
The weight of path 0,1,2,6,5 is the smallest, so the shortest path from node 0 to node 5 is 0,1,2,6,5 with a total weight of 8.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 5 with weight 1,
an edge between node 0 and node 6 with weight 3,
an edge between node 0 and node 4 with weight 1,
an edge between node 1 and node 5 with weight 4,
an edge between node 1 and node 3 with weight 1,
an edge between node 2 and node 5 with weight 3,
an edge between node 2 and node 6 with weight 1,
an edge between node 2 and node 3 with weight 3,
an edge between node 3 and node 5 with weight 3,
an edge between node 3 and node 6 with weight 1,
an edge between node 3 and node 4 with weight 4,
an edge between node 4 and node 5 with weight 1,
an edge between node 4 and node 6 with weight 4.
Q: Give the shortest path from node 1 to node 2.
A:

Answer: The shortest path from node 1 to node 2 is 1,3,6,2 with a total weight of 3


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 0 to node 4.
A: All the paths from node 0 to node 4 are:
0,1,4 with a total weight of 2 + 1 = 3,
0,2,3,4 with a total weight of 1 + 1 + 2 = 4.
The weight of path 0,1,4 is the smallest, so the shortest path from node 0 to node 4 is 0,1,4 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 4 and node 1 with weight 2,
an edge between node 2 and node 1 with weight 1,
an edge between node 3 and node 2 with weight 4,
an edge between node 2 and node 4 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 3 to node 1.
A: All the paths from node 3 to node 1 are:
3,2,1 with a total weight of 4 + 1 = 5,
3,2,4,1 with a total weight of 4 + 1 + 2 = 7,
3,4,1 with a total weight of 2 + 2 = 4,
3,4,2,1 with a total weight of 2 + 1 + 1 = 4,
3,0,4,1 with a total weight of 2 + 1 + 2 = 5,
3,0,2,1 with a total weight of 2 + 1 + 1 = 4,
3,4,2,4,1 with a total weight of 2 + 1 + 1 + 2 = 6.
The weight of path 3,4,1 is the smallest, so the shortest path from node 3 to node 1 is 3,4,1 with a total weight of 4.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 2 with weight 2,
an edge between node 1 and node 0 with weight 2,
an edge between node 5 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 3 and node 1 with weight 2,
an edge between node 5 and node 4 with weight 1.
Q: Give the shortest path from node 4 to node 2.
A: All the paths from node 4 to node 2 are:
4,5,1,0,2 with a total weight of 1 + 1 + 2 + 2 = 6,
4,5,1,2 with a total weight of 1 + 1 + 3 = 5.
The weight of path 4,5,1,2 is the smallest, so the shortest path from node 4 to node 2 is 4,5,1,2 with a total weight of 5.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 2 and node 1 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 3 and node 1 with weight 1,
an edge between node 5 and node 2 with weight 4,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 1.
Q: Give the shortest path from node 2 to node 0.
A: All the paths from node 2 to node 0 are:
2,1,0 with a total weight of 4 + 1 = 5,
2,5,1,0 with a total weight of 4 + 1 + 1 = 6,
2,3,1,0 with a total weight of 1 + 1 + 1 = 3.
The weight of path 2,3,1,0 is the smallest, so the shortest path from node 2 to node 0 is 2,3,1,0 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 4 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 4 and node 3 with weight 5,
an edge between node 6 and node 5 with weight 3,
an edge between node 3 and node 5 with weight 4.
Q: Give the shortest path from node 0 to node 5.
A: All the paths from node 0 to node 5 are:
0,2,6,5 with a total weight of 4 + 2 + 3 = 9,
0,1,2,6,5 with a total weight of 1 + 2 + 2 + 3 = 8,
0,4,6,5 with a total weight of 2 + 4 + 3 = 9,
0,4,3,5 with a total weight of 2 + 5 + 4 = 11.
The weight of path 0,1,2,6,5 is the smallest, so the shortest path from node 0 to node 5 is 0,1,2,6,5 with a total weight of 8.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 2 with weight 3,
an edge between node 0 and node 4 with weight 3,
an edge between node 1 and node 3 with weight 4,
an edge between node 1 and node 4 with weight 3,
an edge between node 2 and node 3 with weight 4,
an edge between node 2 and node 4 with weight 3,
an edge between node 3 and node 4 with weight 3.
Q: Give the shortest path from node 2 to node 1.
A:

Answer: The shortest path from node 2 to node 1 is 2,4,1 with a total weight of 6


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 0 to node 4.
A: All the paths from node 0 to node 4 are:
0,1,4 with a total weight of 2 + 1 = 3,
0,2,3,4 with a total weight of 1 + 1 + 2 = 4.
The weight of path 0,1,4 is the smallest, so the shortest path from node 0 to node 4 is 0,1,4 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 4 and node 1 with weight 2,
an edge between node 2 and node 1 with weight 1,
an edge between node 3 and node 2 with weight 4,
an edge between node 2 and node 4 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 3 to node 1.
A: All the paths from node 3 to node 1 are:
3,2,1 with a total weight of 4 + 1 = 5,
3,2,4,1 with a total weight of 4 + 1 + 2 = 7,
3,4,1 with a total weight of 2 + 2 = 4,
3,4,2,1 with a total weight of 2 + 1 + 1 = 4,
3,0,4,1 with a total weight of 2 + 1 + 2 = 5,
3,0,2,1 with a total weight of 2 + 1 + 1 = 4,
3,4,2,4,1 with a total weight of 2 + 1 + 1 + 2 = 6.
The weight of path 3,4,1 is the smallest, so the shortest path from node 3 to node 1 is 3,4,1 with a total weight of 4.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 2 with weight 2,
an edge between node 1 and node 0 with weight 2,
an edge between node 5 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 3 and node 1 with weight 2,
an edge between node 5 and node 4 with weight 1.
Q: Give the shortest path from node 4 to node 2.
A: All the paths from node 4 to node 2 are:
4,5,1,0,2 with a total weight of 1 + 1 + 2 + 2 = 6,
4,5,1,2 with a total weight of 1 + 1 + 3 = 5.
The weight of path 4,5,1,2 is the smallest, so the shortest path from node 4 to node 2 is 4,5,1,2 with a total weight of 5.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 2 and node 1 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 3 and node 1 with weight 1,
an edge between node 5 and node 2 with weight 4,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 1.
Q: Give the shortest path from node 2 to node 0.
A: All the paths from node 2 to node 0 are:
2,1,0 with a total weight of 4 + 1 = 5,
2,5,1,0 with a total weight of 4 + 1 + 1 = 6,
2,3,1,0 with a total weight of 1 + 1 + 1 = 3.
The weight of path 2,3,1,0 is the smallest, so the shortest path from node 2 to node 0 is 2,3,1,0 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 4 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 4 and node 3 with weight 5,
an edge between node 6 and node 5 with weight 3,
an edge between node 3 and node 5 with weight 4.
Q: Give the shortest path from node 0 to node 5.
A: All the paths from node 0 to node 5 are:
0,2,6,5 with a total weight of 4 + 2 + 3 = 9,
0,1,2,6,5 with a total weight of 1 + 2 + 2 + 3 = 8,
0,4,6,5 with a total weight of 2 + 4 + 3 = 9,
0,4,3,5 with a total weight of 2 + 5 + 4 = 11.
The weight of path 0,1,2,6,5 is the smallest, so the shortest path from node 0 to node 5 is 0,1,2,6,5 with a total weight of 8.

In an undirected graph, the nodes are numbered from 0 to 11, and the edges are:
an edge between node 0 and node 5 with weight 8,
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 10 with weight 2,
an edge between node 1 and node 8 with weight 8,
an edge between node 2 and node 4 with weight 2,
an edge between node 2 and node 7 with weight 4,
an edge between node 2 and node 8 with weight 9,
an edge between node 3 and node 4 with weight 3,
an edge between node 3 and node 10 with weight 8,
an edge between node 3 and node 8 with weight 4,
an edge between node 5 and node 9 with weight 1,
an edge between node 6 and node 8 with weight 9,
an edge between node 7 and node 11 with weight 1,
an edge between node 7 and node 8 with weight 9.
Q: Give the shortest path from node 11 to node 9.
A:

Answer: The shortest path from node 11 to node 9 is 11,7,8,1,0,5,9 with a total weight of 29


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 0 to node 4.
A: All the paths from node 0 to node 4 are:
0,1,4 with a total weight of 2 + 1 = 3,
0,2,3,4 with a total weight of 1 + 1 + 2 = 4.
The weight of path 0,1,4 is the smallest, so the shortest path from node 0 to node 4 is 0,1,4 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 4 and node 1 with weight 2,
an edge between node 2 and node 1 with weight 1,
an edge between node 3 and node 2 with weight 4,
an edge between node 2 and node 4 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 3 to node 1.
A: All the paths from node 3 to node 1 are:
3,2,1 with a total weight of 4 + 1 = 5,
3,2,4,1 with a total weight of 4 + 1 + 2 = 7,
3,4,1 with a total weight of 2 + 2 = 4,
3,4,2,1 with a total weight of 2 + 1 + 1 = 4,
3,0,4,1 with a total weight of 2 + 1 + 2 = 5,
3,0,2,1 with a total weight of 2 + 1 + 1 = 4,
3,4,2,4,1 with a total weight of 2 + 1 + 1 + 2 = 6.
The weight of path 3,4,1 is the smallest, so the shortest path from node 3 to node 1 is 3,4,1 with a total weight of 4.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 2 with weight 2,
an edge between node 1 and node 0 with weight 2,
an edge between node 5 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 3 and node 1 with weight 2,
an edge between node 5 and node 4 with weight 1.
Q: Give the shortest path from node 4 to node 2.
A: All the paths from node 4 to node 2 are:
4,5,1,0,2 with a total weight of 1 + 1 + 2 + 2 = 6,
4,5,1,2 with a total weight of 1 + 1 + 3 = 5.
The weight of path 4,5,1,2 is the smallest, so the shortest path from node 4 to node 2 is 4,5,1,2 with a total weight of 5.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 2 and node 1 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 3 and node 1 with weight 1,
an edge between node 5 and node 2 with weight 4,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 1.
Q: Give the shortest path from node 2 to node 0.
A: All the paths from node 2 to node 0 are:
2,1,0 with a total weight of 4 + 1 = 5,
2,5,1,0 with a total weight of 4 + 1 + 1 = 6,
2,3,1,0 with a total weight of 1 + 1 + 1 = 3.
The weight of path 2,3,1,0 is the smallest, so the shortest path from node 2 to node 0 is 2,3,1,0 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 4 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 4 and node 3 with weight 5,
an edge between node 6 and node 5 with weight 3,
an edge between node 3 and node 5 with weight 4.
Q: Give the shortest path from node 0 to node 5.
A: All the paths from node 0 to node 5 are:
0,2,6,5 with a total weight of 4 + 2 + 3 = 9,
0,1,2,6,5 with a total weight of 1 + 2 + 2 + 3 = 8,
0,4,6,5 with a total weight of 2 + 4 + 3 = 9,
0,4,3,5 with a total weight of 2 + 5 + 4 = 11.
The weight of path 0,1,2,6,5 is the smallest, so the shortest path from node 0 to node 5 is 0,1,2,6,5 with a total weight of 8.

In an undirected graph, the nodes are numbered from 0 to 8, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 0 and node 2 with weight 2,
an edge between node 0 and node 7 with weight 2,
an edge between node 1 and node 8 with weight 4,
an edge between node 1 and node 3 with weight 4,
an edge between node 1 and node 6 with weight 1,
an edge between node 2 and node 8 with weight 2,
an edge between node 2 and node 7 with weight 4,
an edge between node 3 and node 6 with weight 4,
an edge between node 3 and node 7 with weight 1,
an edge between node 4 and node 5 with weight 1,
an edge between node 4 and node 6 with weight 4,
an edge between node 5 and node 6 with weight 3,
an edge between node 5 and node 7 with weight 3,
an edge between node 7 and node 8 with weight 2.
Q: Give the shortest path from node 5 to node 8.
A:

Answer: The shortest path from node 5 to node 8 is 5,7,8 with a total weight of 5


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 0 to node 4.
A: All the paths from node 0 to node 4 are:
0,1,4 with a total weight of 2 + 1 = 3,
0,2,3,4 with a total weight of 1 + 1 + 2 = 4.
The weight of path 0,1,4 is the smallest, so the shortest path from node 0 to node 4 is 0,1,4 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 4 and node 1 with weight 2,
an edge between node 2 and node 1 with weight 1,
an edge between node 3 and node 2 with weight 4,
an edge between node 2 and node 4 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 3 to node 1.
A: All the paths from node 3 to node 1 are:
3,2,1 with a total weight of 4 + 1 = 5,
3,2,4,1 with a total weight of 4 + 1 + 2 = 7,
3,4,1 with a total weight of 2 + 2 = 4,
3,4,2,1 with a total weight of 2 + 1 + 1 = 4,
3,0,4,1 with a total weight of 2 + 1 + 2 = 5,
3,0,2,1 with a total weight of 2 + 1 + 1 = 4,
3,4,2,4,1 with a total weight of 2 + 1 + 1 + 2 = 6.
The weight of path 3,4,1 is the smallest, so the shortest path from node 3 to node 1 is 3,4,1 with a total weight of 4.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 2 with weight 2,
an edge between node 1 and node 0 with weight 2,
an edge between node 5 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 3 and node 1 with weight 2,
an edge between node 5 and node 4 with weight 1.
Q: Give the shortest path from node 4 to node 2.
A: All the paths from node 4 to node 2 are:
4,5,1,0,2 with a total weight of 1 + 1 + 2 + 2 = 6,
4,5,1,2 with a total weight of 1 + 1 + 3 = 5.
The weight of path 4,5,1,2 is the smallest, so the shortest path from node 4 to node 2 is 4,5,1,2 with a total weight of 5.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 2 and node 1 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 3 and node 1 with weight 1,
an edge between node 5 and node 2 with weight 4,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 1.
Q: Give the shortest path from node 2 to node 0.
A: All the paths from node 2 to node 0 are:
2,1,0 with a total weight of 4 + 1 = 5,
2,5,1,0 with a total weight of 4 + 1 + 1 = 6,
2,3,1,0 with a total weight of 1 + 1 + 1 = 3.
The weight of path 2,3,1,0 is the smallest, so the shortest path from node 2 to node 0 is 2,3,1,0 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 4 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 4 and node 3 with weight 5,
an edge between node 6 and node 5 with weight 3,
an edge between node 3 and node 5 with weight 4.
Q: Give the shortest path from node 0 to node 5.
A: All the paths from node 0 to node 5 are:
0,2,6,5 with a total weight of 4 + 2 + 3 = 9,
0,1,2,6,5 with a total weight of 1 + 2 + 2 + 3 = 8,
0,4,6,5 with a total weight of 2 + 4 + 3 = 9,
0,4,3,5 with a total weight of 2 + 5 + 4 = 11.
The weight of path 0,1,2,6,5 is the smallest, so the shortest path from node 0 to node 5 is 0,1,2,6,5 with a total weight of 8.

In an undirected graph, the nodes are numbered from 0 to 14, and the edges are:
an edge between node 0 and node 7 with weight 4,
an edge between node 0 and node 13 with weight 2,
an edge between node 0 and node 2 with weight 10,
an edge between node 1 and node 10 with weight 10,
an edge between node 1 and node 12 with weight 8,
an edge between node 1 and node 3 with weight 6,
an edge between node 1 and node 6 with weight 10,
an edge between node 2 and node 9 with weight 4,
an edge between node 2 and node 11 with weight 6,
an edge between node 2 and node 13 with weight 8,
an edge between node 3 and node 14 with weight 3,
an edge between node 3 and node 10 with weight 8,
an edge between node 4 and node 5 with weight 6,
an edge between node 4 and node 6 with weight 9,
an edge between node 5 and node 9 with weight 10,
an edge between node 5 and node 11 with weight 1,
an edge between node 5 and node 13 with weight 3,
an edge between node 8 and node 10 with weight 8,
an edge between node 10 and node 11 with weight 9,
an edge between node 11 and node 12 with weight 6,
an edge between node 11 and node 13 with weight 3,
an edge between node 12 and node 13 with weight 3.
Q: Give the shortest path from node 6 to node 7.
A:

Answer: The shortest path from node 6 to node 7 is 6,4,5,13,0,7 with a total weight of 24


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 0 to node 4.
A: All the paths from node 0 to node 4 are:
0,1,4 with a total weight of 2 + 1 = 3,
0,2,3,4 with a total weight of 1 + 1 + 2 = 4.
The weight of path 0,1,4 is the smallest, so the shortest path from node 0 to node 4 is 0,1,4 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 4 and node 1 with weight 2,
an edge between node 2 and node 1 with weight 1,
an edge between node 3 and node 2 with weight 4,
an edge between node 2 and node 4 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 3 to node 1.
A: All the paths from node 3 to node 1 are:
3,2,1 with a total weight of 4 + 1 = 5,
3,2,4,1 with a total weight of 4 + 1 + 2 = 7,
3,4,1 with a total weight of 2 + 2 = 4,
3,4,2,1 with a total weight of 2 + 1 + 1 = 4,
3,0,4,1 with a total weight of 2 + 1 + 2 = 5,
3,0,2,1 with a total weight of 2 + 1 + 1 = 4,
3,4,2,4,1 with a total weight of 2 + 1 + 1 + 2 = 6.
The weight of path 3,4,1 is the smallest, so the shortest path from node 3 to node 1 is 3,4,1 with a total weight of 4.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 2 with weight 2,
an edge between node 1 and node 0 with weight 2,
an edge between node 5 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 3 and node 1 with weight 2,
an edge between node 5 and node 4 with weight 1.
Q: Give the shortest path from node 4 to node 2.
A: All the paths from node 4 to node 2 are:
4,5,1,0,2 with a total weight of 1 + 1 + 2 + 2 = 6,
4,5,1,2 with a total weight of 1 + 1 + 3 = 5.
The weight of path 4,5,1,2 is the smallest, so the shortest path from node 4 to node 2 is 4,5,1,2 with a total weight of 5.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 2 and node 1 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 3 and node 1 with weight 1,
an edge between node 5 and node 2 with weight 4,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 1.
Q: Give the shortest path from node 2 to node 0.
A: All the paths from node 2 to node 0 are:
2,1,0 with a total weight of 4 + 1 = 5,
2,5,1,0 with a total weight of 4 + 1 + 1 = 6,
2,3,1,0 with a total weight of 1 + 1 + 1 = 3.
The weight of path 2,3,1,0 is the smallest, so the shortest path from node 2 to node 0 is 2,3,1,0 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 4 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 4 and node 3 with weight 5,
an edge between node 6 and node 5 with weight 3,
an edge between node 3 and node 5 with weight 4.
Q: Give the shortest path from node 0 to node 5.
A: All the paths from node 0 to node 5 are:
0,2,6,5 with a total weight of 4 + 2 + 3 = 9,
0,1,2,6,5 with a total weight of 1 + 2 + 2 + 3 = 8,
0,4,6,5 with a total weight of 2 + 4 + 3 = 9,
0,4,3,5 with a total weight of 2 + 5 + 4 = 11.
The weight of path 0,1,2,6,5 is the smallest, so the shortest path from node 0 to node 5 is 0,1,2,6,5 with a total weight of 8.

In an undirected graph, the nodes are numbered from 0 to 11, and the edges are:
an edge between node 0 and node 3 with weight 10,
an edge between node 0 and node 8 with weight 5,
an edge between node 0 and node 4 with weight 2,
an edge between node 1 and node 10 with weight 1,
an edge between node 1 and node 3 with weight 8,
an edge between node 1 and node 8 with weight 4,
an edge between node 2 and node 6 with weight 7,
an edge between node 2 and node 11 with weight 2,
an edge between node 3 and node 9 with weight 8,
an edge between node 4 and node 7 with weight 9,
an edge between node 5 and node 10 with weight 8,
an edge between node 6 and node 8 with weight 5,
an edge between node 6 and node 7 with weight 7,
an edge between node 7 and node 9 with weight 10.
Q: Give the shortest path from node 6 to node 10.
A:

Answer: The shortest path from node 6 to node 10 is 6,8,1,10 with a total weight of 10


Question:
In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 0 to node 4.
A: All the paths from node 0 to node 4 are:
0,1,4 with a total weight of 2 + 1 = 3,
0,2,3,4 with a total weight of 1 + 1 + 2 = 4.
The weight of path 0,1,4 is the smallest, so the shortest path from node 0 to node 4 is 0,1,4 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 4, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 2 with weight 1,
an edge between node 4 and node 1 with weight 2,
an edge between node 2 and node 1 with weight 1,
an edge between node 3 and node 2 with weight 4,
an edge between node 2 and node 4 with weight 1,
an edge between node 3 and node 4 with weight 2.
Q: Give the shortest path from node 3 to node 1.
A: All the paths from node 3 to node 1 are:
3,2,1 with a total weight of 4 + 1 = 5,
3,2,4,1 with a total weight of 4 + 1 + 2 = 7,
3,4,1 with a total weight of 2 + 2 = 4,
3,4,2,1 with a total weight of 2 + 1 + 1 = 4,
3,0,4,1 with a total weight of 2 + 1 + 2 = 5,
3,0,2,1 with a total weight of 2 + 1 + 1 = 4,
3,4,2,4,1 with a total weight of 2 + 1 + 1 + 2 = 6.
The weight of path 3,4,1 is the smallest, so the shortest path from node 3 to node 1 is 3,4,1 with a total weight of 4.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 2 with weight 2,
an edge between node 1 and node 0 with weight 2,
an edge between node 5 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 3 and node 1 with weight 2,
an edge between node 5 and node 4 with weight 1.
Q: Give the shortest path from node 4 to node 2.
A: All the paths from node 4 to node 2 are:
4,5,1,0,2 with a total weight of 1 + 1 + 2 + 2 = 6,
4,5,1,2 with a total weight of 1 + 1 + 3 = 5.
The weight of path 4,5,1,2 is the smallest, so the shortest path from node 4 to node 2 is 4,5,1,2 with a total weight of 5.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 2 and node 1 with weight 4,
an edge between node 1 and node 5 with weight 1,
an edge between node 3 and node 1 with weight 1,
an edge between node 5 and node 2 with weight 4,
an edge between node 2 and node 3 with weight 1,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 1.
Q: Give the shortest path from node 2 to node 0.
A: All the paths from node 2 to node 0 are:
2,1,0 with a total weight of 4 + 1 = 5,
2,5,1,0 with a total weight of 4 + 1 + 1 = 6,
2,3,1,0 with a total weight of 1 + 1 + 1 = 3.
The weight of path 2,3,1,0 is the smallest, so the shortest path from node 2 to node 0 is 2,3,1,0 with a total weight of 3.

In an undirected graph, the nodes are numbered from 0 to 6, and the edges are:
an edge between node 0 and node 1 with weight 1,
an edge between node 1 and node 2 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 4 with weight 2,
an edge between node 2 and node 6 with weight 2,
an edge between node 4 and node 6 with weight 4,
an edge between node 4 and node 3 with weight 5,
an edge between node 6 and node 5 with weight 3,
an edge between node 3 and node 5 with weight 4.
Q: Give the shortest path from node 0 to node 5.
A: All the paths from node 0 to node 5 are:
0,2,6,5 with a total weight of 4 + 2 + 3 = 9,
0,1,2,6,5 with a total weight of 1 + 2 + 2 + 3 = 8,
0,4,6,5 with a total weight of 2 + 4 + 3 = 9,
0,4,3,5 with a total weight of 2 + 5 + 4 = 11.
The weight of path 0,1,2,6,5 is the smallest, so the shortest path from node 0 to node 5 is 0,1,2,6,5 with a total weight of 8.

In an undirected graph, the nodes are numbered from 0 to 5, and the edges are:
an edge between node 0 and node 3 with weight 1,
an edge between node 0 and node 4 with weight 2,
an edge between node 1 and node 3 with weight 2,
an edge between node 1 and node 4 with weight 2,
an edge between node 2 and node 3 with weight 1,
an edge between node 2 and node 4 with weight 4,
an edge between node 3 and node 5 with weight 4,
an edge between node 4 and node 5 with weight 2.
Q: Give the shortest path from node 0 to node 2.
A:

Answer: The shortest path from node 0 to node 2 is 0,3,2 with a total weight of 2