问题
I'm having a problem with finding fastest path that do not exceed specified cost. There's similar question to this one, however there's a big difference between them. Here, the only records that can appear in the data are the ones, that lead from a lower point to a higher point (eg. 1 -> 3 might appear but 3 -> 1 might not) (see below). Without knowing that, I'd use Dijkstra. That additional information, might let it do in a time faster than Dijkstras algorithm. What do you think about it?
Let's say I've got specified maximum cost, and 4 records.
// specified cost
10
// end point
5
//(start point) (finish point) (time) (cost)
2 5 50 5
3 5 20 9
1 2 30 5
1 3 30 7
// all the records lead from a lower to a higher point no.
I have to decide, whether It's possible to get from point (1) to (5) (its impossible when theres no path that costs <= than we've got or when theres no connection between 1-5) and if so, what would be the fastest way to get in there.
The output for such data would be:
80 // fastest time
3 1 // number of points that (1 -> 2) -> (2 -> 5)
Keep in mind, that if there's a record saying you can move 1->2
1 2 30 5
It doesnt allow you to move 2<-1.
回答1:
For each node at depth n, the minimum cost of path to it is n/2 * (minimal first edge at the path + minimal edge connecting to the node) - sum of arithmetic series. If this computation exceeds the required maximum, no need to check the nodes that follow. Cut these nodes off and apply Dijkstra on the rest.
来源：https://stackoverflow.com/questions/13414769/is-there-better-way-than-a-dijkstra-algorithm-for-finding-fastest-path-that-do-n