在python上的生成树

Question

I have this hw:

1. Read edge list from a file
2. Turn it into an adjacency list
3. Output an unweighted, undirected spanning tree of the graph (we can assume starting point is at vertex 0)

I have problem getting 3. to output correctly. Namely, file 1 should output [[1],[0,2,3],[1],[1]] and I got [[1,2],[0,3],[0],[1]] which is sort of ok since they are both spanning trees for n=4 from file 1

but here's the major problem: I don't know what's wrong in my code, for file 2: I get: [[10], [], [10], [10], [], [], [], [], [], [], [0, 3, 2], [], []]

Data for the files at end of my code. (edit: starting from tree=[] is where the problems lie, the rest have no issues)

Here's my attempt at the problem:

import itertools

edge_i=[]
edge_j=[]
x = []
y = []
edgelist = []
n = int(input("Enter value for n:")) #input n for number of vertices
adjlist = [[] for i in range(n)] #create n sublists inside empty initial adjlist
data = [['0','1'],['2','1'],['0','2'],['1','3']]


for line in data: #for loop for appending into adjacency list the correct indices taken from out of the edgelist
    #(this line won't be needed when hardcoding input) line = line.replace("\n","").split(" ")
    for values in line:
        values_as_int = int(values)
        edgelist.append(values_as_int)



#set of vertices present in this file - pick out only n vertices
verticesset=set(edgelist)
listofusefulvertices=list(verticesset)[0:n]


P = list(itertools.permutations(listofusefulvertices,2))


x.append(edgelist[0::2])
y.append(edgelist[1::2])
x = sum(x,[])
y = sum(y,[])
dataint=zip(x,y)
datatuples=list(dataint)
outdata = set(datatuples)&set(P)
output=list(outdata)


for k in range(len(output)):
    edge_i.append(output[k][0])
    edge_i.append(output[k][1])
    edge_j.append(output[k][1])
    edge_j.append(output[k][0])

for i in range(len(edge_i)):
    u = edge_i[i]
    v = edge_j[i]
    adjlist[u].append(v)
print(adjlist)


tree = []
for vertexNum in range(len(listofusefulvertices)):
    tree.append([])
treeVertices = [0]*n
treeVertices[0]=1
for vertex in range(0,n): #(here the range in skeletal code from school used 1,n but it only worked for me when I used 0,n-1 or 0,n)
    if treeVertices[vertex] == 1:
        for adjVertex in adjlist[vertex]:
            if treeVertices[adjVertex] == 0:
                treeVertices[adjVertex]=1
                tree[adjVertex].append(vertex)
                tree[vertex].append(adjVertex)

print(tree)


#The data from files were: file 1: [['0','1'],['2','1'],['0','2'],['1','3']]
# file 2: [['10','2'],['7','4'],['11','3'],['1','12'],['6','8'],['10','3'],['4','9'],['5','7'],['8','12'],['2','11'],['1','6'],['0','10'],['7','2'],['12','5']]

Answer 1

I didn't wade through all your code, you really should look at the guidance Minimal, complete, verifiable example .

However, it is fairly simple to turn an edge-list into a graph, and then use a standard mst algorithm, eg Prim's:

def create_graph(edgelist):
    graph = {}
    for e1, e2 in edgelist:
        graph.setdefault(e1, []).append(e2)
        graph.setdefault(e2, []).append(e1)
    return graph

# Prim's
def mst(start, graph):
    closed = set()
    edges = []
    q = [(start, start)]
    while q:
        v1, v2 = q.pop()
        if v2 in closed:
            continue
        closed.add(v2)
        edges.append((v1, v2))
        for v in graph[v2]:
            if v in graph:
                q.append((v2, v))
    del edges[0]
    assert len(edges) == len(graph)-1
    return edges

>>> graph = create_graph([[10, 2], [7, 4], [11, 3], [1, 12], [6, 8], [10, 3], [4, 9], [5, 7], [8, 12], [2, 11], [1, 6], [0, 10], [7, 2], [12, 5]])
>>> min_gragh = create_graph(mst(0, graph))
>>> min_graph
{0: [10],
 1: [6],
 2: [11, 7],
 3: [10, 11],
 4: [7, 9],
 5: [7, 12],
 6: [8, 1],
 7: [2, 5, 4],
 8: [12, 6],
 9: [4],
 10: [0, 3],
 11: [3, 2],
 12: [5, 8]}
>>> [sorted(min_graph[k]) for k in sorted(min_graph)]
[[10], [6], [7, 11], [10, 11], [7, 9], [7, 12], [1, 8], [2, 4, 5], [6, 12], [4], [0, 3], [2, 3], [5, 8]]

There are potentially multiple valid MST for a graph, eg your smaller edgelist produces [[2], [2, 3], [0, 1], [1]] , which is also a valid MST but different from your expected output.

Answer 2

The problem is in your main processing loop at the end. You use node 0 as the starting node, but then assume that your connectivity runs in numerical order. You flag all the nodes adjacent to node 0 (only node 10), and then take up node 1 next. That's not yet connected, so you skip it ... but you never come back.

Here's the code and trace from my low-tech debugging run:

for vertex in range(0,n): #(here the range in skeletal code from school used 1,n but it only worked for me when I used 0,n-1 or 0,n)
    print ("Working on vertex", vertex, treeVertices[vertex] == 1)
    if treeVertices[vertex] == 1:
        for adjVertex in adjlist[vertex]:
            print ("  Adjacent vertex", adjVertex, treeVertices[adjVertex] == 0)
            if treeVertices[adjVertex] == 0:
                treeVertices[adjVertex]=1
                tree[adjVertex].append(vertex)
                tree[vertex].append(adjVertex)

print("Spanning tree", tree)

Output:

Adjacency list [[10], [12, 6], [11, 7, 10], [11, 10], [9, 7], [7, 12], [8, 1], [5, 4, 2], [6, 12], [4], [0, 3, 2], [2, 3], [1, 8, 5]]

Working on vertex 0 True
  Adjacent vertex 10 True
Working on vertex 1 False
Working on vertex 2 False
Working on vertex 3 False
Working on vertex 4 False
Working on vertex 5 False
Working on vertex 6 False
Working on vertex 7 False
Working on vertex 8 False
Working on vertex 9 False
Working on vertex 10 True
  Adjacent vertex 0 False
  Adjacent vertex 3 True
  Adjacent vertex 2 True
Working on vertex 11 False
Working on vertex 12 False
Spanning tree [[10], [], [10], [10], [], [], [], [], [], [], [0, 3, 2], [], []]

See the problem? The algorithm assumes that the flow of finding the spanning tree will always succeed if you move from available nodes to higher-numbered nodes. Since this tree requires several "down" moves, you don't get them all. You start at 0, mark 10, and then skip nodes 1-9. When you get to 10, you add nodes 2 and 3 ... but you never go back to expand on them, and that's all you get.

To get them all, do one of two things:

1. Put the "unexpanded" nodes on a "to do" list, starting with [0]. Your top for loop changes to a while that continues until that list is empty.
2. Keep your current structure, but add an outer loop that continues until either all nodes are tagged, or no edges get added (no spanning tree found).

Does that get you moving to a solution?

Answer 3

I think I may have fixed it, by adding the outer loop while all(treeVertices) == 0: above the for loops for vertex. Now for n= 13 in the file2 long list, I get this output: [[10], [12, 6], [10, 11, 7], [10], [7, 9], [7, 12], [1], [2, 5, 4], [12], [4], [0, 3, 2], [2], [5, 1, 8]] What I don't understand is, why didn't while any(treeVertices) == 0: work and it had to be all()? I thought when the treeVertices list gets partially filled by 1s, it won't contain "all" zeros, but "any" zeroes in it, should send the iterator back into its loop again. I've encountered multiple instances of coding in python now where the useage of any() and all() have had the opposite effect for me where any() acted like all(), and all() acted like any(). Any idea why?