如何在 Python 递归图 function 中返回多条路径？

Question

1) Suppose A1, B1, and C1 are nodes in this graph. C1 is upstream to B1, and B1 is upstream to A1. See this picture: https://imgur.com/fHxuCpH

If I call get_path_to_most_upstream(A1,[]) then I get [[A1, B1, C1]] .

2) However, this doesn't work when a node has more than one parent upstream to it. See this picture: https://imgur.com/YQ5Q1zx

When I call get_path_to_most_upstream(A1,[]) , I am getting an empty list [] but I want to get [[A1, B1, C1],[A1,B1,C2],[A1,B2,C3],[A1,B2,C4]] . How can I adjust this function to return that?

def get_path_to_most_upstream(start_key, path):
    current_top = start_key
    path = path + [current_top] #add top node to path

    parents = get_nodes_upstream_one_hop(current_top) #returns list of nodes directly above
    #parents = [B1] in first case
    #parents = [B1, B2] in second

    if not parents: #base case
        return [path]

    paths = [] 
    for parent in parents:
        if parent not in path:
            extended_paths = get_path_to_most_upstream(parent, path)
            for p in extended_paths:
                paths.append(p)
    return paths

Answer 1

Your code works with small mod.

Mods

1. In function get_path_to_most_upstream give path default value of None

   get_path_to_most_upstream(start_key, path = None):

2. Set path to list, if path is None

   if path is None: path = []

Refactored Code

def get_nodes_upstream_one_hop(node):
  return [neighbor for neighbor in graph[node]]

 def get_path_to_most_upstream(start_key, path = None):
    if path is None:
      path = []
    current_top = start_key

    path = path + [current_top] #add top node to path

    parents = get_nodes_upstream_one_hop(current_top) #returns list of nodes directly above
    #parents = [B1] in first case
    #parents = [B1, B2] in second

    if not parents: #base case
        return [path]

    paths = [] 
    for parent in parents:
        if parent not in path:
            extended_paths = get_path_to_most_upstream(parent, path)
            for p in extended_paths:
                paths.append(p)
    return paths

Graph Code

Reference

from collections import defaultdict 

# function for adding edge to graph 
graph = defaultdict(list) 
def addEdge(graph,u,v): 
    graph[u].append(v) 

# definition of function 
def generate_edges(graph): 
    edges = [] 

    # for each node in graph 
    for node in graph: 

        # for each neighbour node of a single node 
        for neighbour in graph[node]: 

            # if edge exists then append 
            edges.append((node, neighbour)) 
    return edges 

Testing

Test 1

graph = defaultdict(list)
addEdge(graph, 'A1', 'B1')
addEdge(graph, 'B1', 'C1')
print(get_path_to_most_upstream('A1')) # [['A1', 'B1', 'C1']]

Test 2

graph = defaultdict(list)
addEdge(graph, 'A1', 'B1')
addEdge(graph, 'A1', 'B2')
addEdge(graph, 'B1', 'C1')
addEdge(graph, 'B1', 'C2')
addEdge(graph, 'B2', 'C3')
addEdge(graph, 'B2', 'C4')
print(get_path_to_most_upstream('A1')) 
# [['A1', 'B1', 'C1'], 
#  ['A1', 'B1', 'C2'], 
#  ['A1', 'B2', 'C3'], 
#  ['A1', 'B2', 'C4']]