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

Answer: The shortest path from node 6 to node 1 is 6,9,5,3,2,1 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 7, and the edges are:
an edge between node 0 and node 6 with weight 3,
an edge between node 0 and node 4 with weight 2,
an edge between node 0 and node 5 with weight 4,
an edge between node 0 and node 2 with weight 2,
an edge between node 0 and node 1 with weight 3,
an edge between node 1 and node 3 with weight 3,
an edge between node 1 and node 6 with weight 4,
an edge between node 1 and node 7 with weight 1,
an edge between node 1 and node 4 with weight 3,
an edge between node 1 and node 5 with weight 3,
an edge between node 1 and node 2 with weight 1,
an edge between node 2 and node 3 with weight 3,
an edge between node 2 and node 6 with weight 4,
an edge between node 2 and node 7 with weight 3,
an edge between node 2 and node 4 with weight 4,
an edge between node 2 and node 5 with weight 3,
an edge between node 3 and node 6 with weight 1,
an edge between node 3 and node 7 with weight 1,
an edge between node 3 and node 5 with weight 3,
an edge between node 4 and node 6 with weight 2,
an edge between node 4 and node 5 with weight 1,
an edge between node 5 and node 6 with weight 4,
an edge between node 5 and node 7 with weight 2,
an edge between node 6 and node 7 with weight 2.
Q: Give the shortest path from node 3 to node 0.
A:

Answer: The shortest path from node 3 to node 0 is 3,6,0 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 4, and the edges are:
an edge between node 0 and node 3 with weight 3,
an edge between node 0 and node 4 with weight 1,
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 1 and node 2 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 0 to node 1.
A:

Answer: The shortest path from node 0 to node 1 is 0,3,1 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 7, and the edges are:
an edge between node 0 and node 5 with weight 2,
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 4 with weight 2,
an edge between node 0 and node 7 with weight 2,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 1 with weight 3,
an edge between node 0 and node 6 with weight 3,
an edge between node 1 and node 3 with weight 2,
an edge between node 1 and node 4 with weight 3,
an edge between node 1 and node 7 with weight 1,
an edge between node 1 and node 2 with weight 3,
an edge between node 2 and node 5 with weight 2,
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 3 and node 4 with weight 2,
an edge between node 3 and node 6 with weight 2,
an edge between node 4 and node 7 with weight 3,
an edge between node 5 and node 7 with weight 2,
an edge between node 6 and node 7 with weight 3.
Q: Give the shortest path from node 5 to node 4.
A:

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

Answer: The shortest path from node 5 to node 3 is 5,6,0,8,15,3 with a total weight of 36


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 7 with weight 2,
an edge between node 0 and node 2 with weight 3,
an edge between node 0 and node 4 with weight 1,
an edge between node 0 and node 3 with weight 3,
an edge between node 1 and node 2 with weight 1,
an edge between node 1 and node 4 with weight 4,
an edge between node 1 and node 3 with weight 2,
an edge between node 2 and node 5 with weight 3,
an edge between node 2 and node 7 with weight 4,
an edge between node 2 and node 4 with weight 4,
an edge between node 2 and node 6 with weight 4,
an edge between node 3 and node 4 with weight 2,
an edge between node 3 and node 6 with weight 3,
an edge between node 4 and node 6 with weight 3,
an edge between node 5 and node 7 with weight 3,
an edge between node 6 and node 7 with weight 4.
Q: Give the shortest path from node 5 to node 0.
A:

Answer: The shortest path from node 5 to node 0 is 5,7,0 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 13 with weight 10,
an edge between node 0 and node 14 with weight 4,
an edge between node 0 and node 4 with weight 8,
an edge between node 0 and node 7 with weight 2,
an edge between node 1 and node 9 with weight 2,
an edge between node 1 and node 2 with weight 10,
an edge between node 1 and node 5 with weight 2,
an edge between node 2 and node 13 with weight 2,
an edge between node 2 and node 3 with weight 2,
an edge between node 2 and node 6 with weight 3,
an edge between node 2 and node 7 with weight 7,
an edge between node 3 and node 12 with weight 5,
an edge between node 4 and node 9 with weight 2,
an edge between node 4 and node 10 with weight 5,
an edge between node 4 and node 6 with weight 10,
an edge between node 5 and node 11 with weight 7,
an edge between node 5 and node 8 with weight 10,
an edge between node 5 and node 6 with weight 1,
an edge between node 7 and node 13 with weight 4,
an edge between node 7 and node 10 with weight 9,
an edge between node 7 and node 12 with weight 9,
an edge between node 8 and node 13 with weight 2,
an edge between node 8 and node 9 with weight 8,
an edge between node 9 and node 12 with weight 3,
an edge between node 10 and node 14 with weight 10,
an edge between node 12 and node 13 with weight 5.
Q: Give the shortest path from node 14 to node 11.
A:

Answer: The shortest path from node 14 to node 11 is 14,0,7,13,2,6,5,11 with a total weight of 23


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

Answer: The shortest path from node 7 to node 2 is 7,11,5,8,2 with a total weight of 14


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 4 with weight 4,
an edge between node 0 and node 6 with weight 3,
an edge between node 0 and node 3 with weight 1,
an edge between node 0 and node 5 with weight 4,
an edge between node 0 and node 2 with weight 4,
an edge between node 0 and node 1 with weight 2,
an edge between node 1 and node 4 with weight 2,
an edge between node 1 and node 3 with weight 1,
an edge between node 1 and node 5 with weight 3,
an edge between node 1 and node 2 with weight 1,
an edge between node 2 and node 6 with weight 3,
an edge between node 2 and node 3 with weight 2,
an edge between node 2 and node 5 with weight 1,
an edge between node 2 and node 7 with weight 2,
an edge between node 3 and node 4 with weight 3,
an edge between node 3 and node 6 with weight 1,
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 4 and node 6 with weight 1,
an edge between node 4 and node 7 with weight 1,
an edge between node 5 and node 6 with weight 1,
an edge between node 5 and node 7 with weight 1,
an edge between node 6 and node 7 with weight 2.
Q: Give the shortest path from node 0 to node 7.
A:

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

Answer: The shortest path from node 16 to node 6 is 16,3,1,6 with a total weight of 15


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

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

Answer: The shortest path from node 0 to node 9 is 0,10,13,1,4,9 with a total weight of 14


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 1 with weight 2,
an edge between node 0 and node 4 with weight 2,
an edge between node 0 and node 3 with weight 1,
an edge between node 1 and node 2 with weight 1,
an edge between node 2 and node 4 with weight 2,
an edge between node 2 and node 3 with weight 3.
Q: Give the shortest path from node 2 to node 0.
A:

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

Answer: The shortest path from node 11 to node 7 is 11,5,1,8,2,7 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 6, and the edges are:
an edge between node 0 and node 3 with weight 2,
an edge between node 0 and node 1 with weight 4,
an edge between node 0 and node 6 with weight 1,
an edge between node 0 and node 2 with weight 3,
an edge between node 1 and node 3 with weight 2,
an edge between node 1 and node 4 with weight 4,
an edge between node 1 and node 2 with weight 2,
an edge between node 2 and node 5 with weight 2,
an edge between node 2 and node 6 with weight 3,
an edge between node 2 and node 4 with weight 2,
an edge between node 3 and node 5 with weight 1,
an edge between node 3 and node 4 with weight 3,
an edge between node 4 and node 5 with weight 2,
an edge between node 5 and node 6 with weight 4.
Q: Give the shortest path from node 3 to node 6.
A:

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

Answer: The shortest path from node 16 to node 8 is 16,3,0,11,12,18,6,8 with a total weight of 38


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

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

Answer: The shortest path from node 0 to node 6 is 0,5,10,3,9,12,6 with a total weight of 22