In some cases, we want to find a path which is not only the shortest one,
but also satisfies certain condition. For example, in the following graph each
edge is associated with a distance (the first number) and a bandwidth (the
second number) . We need to find the shortest path with at least B
bandwidth. This means every edge in the path must have a bandwidth of B or more.
Implement Dijkstra's algorithm and find the shortest path.
Modify the algorithm to add the bandwidth condition.
The first number is total number of nodes. The second number is total number of edges. Starting from the third line, each line represents a edge. The first two numbers are the pair of nodes that this edge connects. The third number is the distance between the two nodes. The last number is the bandwidth of the edge.
9 // total number of nodes
15 // total number of edges
1 2 2 3 //node node distance bandwidth
2 3 4 9
3 4 2 6
........
........
........
1 to 3 1-2-3
1 to
4 1-2-3-4
1 to
5 1-2-3-4-5
Print out the
shortest path from node 1 to node 3 with bandwidth at least 5.
1-7-9-5-4-3
Print out the shortest path from node 1 to node 4 with bandwidth at least 6. 1-7-8-4
Print out the shortest path from node 1 to node 5 with bandwidth at least 8. 1- 6-5
