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Enumeratingspanningtrees -link.py
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Enumeratingspanningtrees -link.py
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#enumerating all spanning trees of a directed graph
#Constructed according to
#https://github.com/mmozolin/FindingAllSpanningTrees/blob/master/FindAllSpanningTrees/main.cpp
#reproduced by Rongjian Liu <rongjliu@foxmail.com>
#2018-06-11 17:11:50
#from C++ to python
#run with Python 3.6
#reference: Gabow, H. N., & Myers, E. W. (1978). Finding all spanning trees of directed and undirected graphs. SIAM Journal on Computing, 7(3), 280-287.
import copy
from enum import Enum
#define COLOR
class COLOR(Enum):
WHITE = 1,
GRAY = 2,
BLACK = 3
class edge:
def __init__(self,from_node=0,to_node=0):
self.from_node = from_node
self.to_node = to_node
class Vertex:
def __init__(self,d=0):
self.d=d
self.f=0
self.parent=-1
self.color=COLOR.WHITE
WHITE = COLOR.WHITE
GRAY = COLOR.GRAY
BLACK = COLOR.BLACK
#graph
class graph:
def __init__(self, V = 1):
self.V = V # the number of the nodes in graph
self.nverteces_originally_connected = 0
self.root_vertex = 0
self.edge = [[] for i in range(self.V)]
self.time = 0
self.vertex = [Vertex() for i in range(V)]
#debug
def print_vertex(self):
for i in range(len(self.vertex)):
print('vertex ',i,'is:',self.vertex[i].d,self.vertex[i].f,self.vertex[i].parent,self.vertex[i].color)
def ownsvertex(self,ind):
if len(self.edge[ind]) > 0:
return 1
for i in range(len(self.edge)):
for j in range(len(self.edge[i])):
if self.edge[i][j] == ind:
return 1
return 0
def nonownedge(self,*oneedge):
def nonownedge1(self,oneedge):
for i in range(len(self.edge[oneedge.from_node])):
if self.edge[oneedge.from_node][i] == oneedge.to_node:
return 0
return 1
def nonownedge2(self,from_node,to_node):
for i in range(len(self.edge[from_node])):
if self.edge[from_node][i] == to_node:
return 0
return 1
if len(oneedge) == 1:
return nonownedge1(self,*oneedge)
else:
return nonownedge2(self,*oneedge)
def removeedge(self,from_node,to_node):
if self.nonownedge(edge(from_node,to_node)):
return 1
else:
self.edge[from_node].remove(to_node)
def addedge(self,from_node,to_node):
if self.nonownedge(edge(from_node,to_node)) == 1:
self.edge[from_node].append(to_node)
else:
print('edge from ',from_node,'to ', to_node, 'has been added')
def graph_print(self):
print("the graph is:")
for i in range(len(self.edge)):
print('vertex ', i,': ' , self.edge[i])
def DFS_Visit(self,u):
self.vertex[u].color = GRAY
self.time=self.time+1
self.vertex[u].d = self.time
for i in range(len(self.edge[u])):
if self.vertex[ self.edge[u][i] ].color == WHITE:
self.vertex[ self.edge[u][i] ].parent = u
self.DFS_Visit(self.edge[u][i])
self.vertex[u].color = BLACK
self.time=self.time+1
self.vertex[u].f = self.time
def getNconnectedverteces(self):
Nconnected = 0
tally = [0 for i in range(self.V)]
for i in range(self.V):
if len(self.edge[i])>0:
tally[i]=tally[i]+1
for i in range(len(self.edge)):
for j in range(len(self.edge[i])):
tally[self.edge[i][j]] = tally[self.edge[i][j]]+1
for i in range(len(tally)):
if tally[i]>0:
Nconnected=Nconnected+1
return Nconnected
def GROW():
global V
global T
global L
global nspanningtrees
global G
global F
if T.getNconnectedverteces() == V:
L = copy.deepcopy(T)
nspanningtrees = nspanningtrees + 1
print("---------spanning tree ", nspanningtrees, "----------\n")
L.graph_print()
print( "----------------------------------\n")
L.DFS_Visit(L.root_vertex)
else:
FF = []
while True:
if len(F)>0:
e = F.pop(0)
else:
print('F is empty')
return 0
v = e.to_node
T.addedge(e.from_node,v)
Fcopy = []
Fcopy = copy.deepcopy(F)
#add edge to F
for i in range(len(G.edge[v])):
w = G.edge[v][i]
if T.ownsvertex(w) != 1:
F.insert(0,edge(v,w))
#delete edge from F
for iw in range(len(G.edge)):
atemp = T.ownsvertex(iw)
if T.ownsvertex(iw):
jtmp = []
for j in range(len(G.edge[iw])):
if G.edge[iw][j] == v:
jtmp.append(j)
if len(jtmp)>0:
# F.remove(edge(iw,v))
iFtemp = []
for iF in range(len(F)):
if F[iF].from_node == iw and F[iF].to_node == v:
iFtemp.append(iF)
if len(iFtemp)>0:
for df in range(len(iFtemp)-1,-1,-1):
F.pop(iFtemp[df])
GROW()
F = copy.deepcopy(Fcopy)
T.removeedge(e.from_node, e.to_node)
G.removeedge(e.from_node, e.to_node)
FF.insert(0,e)
#bridge test
b = 1
for w in range(len(G.edge)):
tempjj = -1
for jj in range(len(G.edge[w])):
if G.edge[w][jj] == v:
tempjj = jj
if tempjj != -1:
if ((L.vertex[v].d < L.vertex[w].d) and (L.vertex[w].d < L.vertex[w].f) and (L.vertex[w].f < L.vertex[v].f))==0:
b = 0
break
if b == 1:
break
while len(FF)> 0:
e1 = FF.pop(0)
F.insert(0,e1)
G.addedge(e1.from_node,e1.to_node)
V = 4
T = graph(V)
L = graph(V)
T.root_vertex = 0
L.root_vertex = 0
nspanningtrees = 0
F=[]
#initial graph G
G = graph(V)
G.root_vertex = 0;
G.addedge(0,2)
G.addedge(0,1)
G.addedge(1,3)
G.addedge(3,2)
G.addedge(1,2)
G.addedge(2,1)
G.graph_print()
for i in range(len(G.edge[G.root_vertex])):
F.insert(0,edge(G.root_vertex,G.edge[G.root_vertex][i]))
GROW()