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

Answer: The shortest path from node 9 to node 2 is 9,7,2 with a total weight of 2


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

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

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

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

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

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

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

Answer: The shortest path from node 5 to node 1 is 5,4,1 with a total weight of 6


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

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

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

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

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

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

Answer: The shortest path from node 7 to node 0 is 7,15,4,11,0 with a total weight of 22


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

Answer: The shortest path from node 1 to node 12 is 1,14,11,3,12 with a total weight of 24


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

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

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

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

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

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

Answer: The shortest path from node 3 to node 1 is 3,4,1 with a total weight of 2


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

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

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

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

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

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

Answer: The shortest path from node 9 to node 3 is 9,1,10,3 with a total weight of 19


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

Answer: The shortest path from node 13 to node 0 is 13,9,14,0 with a total weight of 8


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

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

Answer: The shortest path from node 2 to node 6 is 2,7,4,6 with a total weight of 5


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

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

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

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

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

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

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

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


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

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

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

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

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

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

Answer: The shortest path from node 11 to node 9 is 11,4,7,15,9 with a total weight of 24


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

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

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

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

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

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

Answer: The shortest path from node 4 to node 10 is 4,8,10 with a total weight of 7


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

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

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

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

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

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

Answer: The shortest path from node 0 to node 6 is 0,9,1,12,4,7,3,11,6 with a total weight of 32


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

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

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

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

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

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

Answer: The shortest path from node 3 to node 7 is 3,2,12,9,8,10,7 with a total weight of 31


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

Answer: The shortest path from node 6 to node 4 is 6,9,4 with a total weight of 3