Question

Suppose we have the directed, weighted graph. Our task is to find all paths beetween two vertices (source and destination) which cost is less or equal =< N. We visit every vertex only once. In later version I’d like to add a condition that the source can be the destination (we just make a loop).

I think it can be done with modified Dijkstra’s algorithm, but I have no idea how implement such thing. Thanks for any help.

Answer 1

You could use recursive backtracking to solve this problem. Terminate your recursion when:

• You get to the destination
• You visit a node that was already visited
• Your path length exceeds N.

Pseudocode:

list curpath := {}
int dest, maxlen
def findPaths (curNode, dist):
    if curNode = dest:
        print curpath
        return
    if curNode is marked:
        return
    if dist > maxlen:
        return
    add curNode to curpath
    mark curNode
    for nextNode, edgeDist adjacent to curNode:
        findPaths(nextNode, dist + edgeDist)
    remove last element of curpath