All paths of length L from node n using python

Question

Given a graph G, a node n and a length L, I\'d like to collect all (non-cyclic) paths of length L that depart from n.

Do you have any idea on how to approach this?

Answer 1

Here is another (rather naive) implementation I came up with after reading the answers here:

def findAllPaths(node, childrenFn, depth, _depth=0, _parents={}):
    if _depth == depth - 1:
        # path found with desired length, create path and stop traversing
        path = []
        parent = node
        for i in xrange(depth):
            path.insert(0, parent)
            if not parent in _parents:
                continue
            parent = _parents[parent]
            if parent in path:
                return # this path is cyclic, forget
        yield path
        return

    for nb in childrenFn(node):
        _parents[nb] = node # keep track of where we came from
        for p in findAllPaths(nb, childrenFn, depth, _depth + 1, _parents):
            yield p


graph = {
    0: [1, 2],
    1: [4, 5],
    2: [3, 10],
    3: [8, 9],
    4: [6],
    5: [6],
    6: [7],
    7: [],
    8: [],
    9: [],
    10: [2] # cycle
}

for p in findAllPaths(0, lambda n: graph[n], depth=4):
    print(p)

# [0, 1, 4, 6]
# [0, 1, 5, 6]
# [0, 2, 3, 8]
# [0, 2, 3, 9]