def __init__(self, Verts = Set(), Edges = Set()):
self.Matrix = BooleanMatrix(0)
self.VM = {}
self.IVM = {}
self.n = 0
self.m = 0
for v in Verts:
self.add_vertex(v)
for (u,v) in Edges:
self.add_edge(u,v)
class AdjacencyMatrix(Graph):
#O(|V| + |E|) = O(n + m)
def __init__(self, Verts = Set(), Edges = Set()):
self.Matrix = BooleanMatrix(0)
self.VM = {}
self.IVM = {}
self.n = 0
self.m = 0
for v in Verts:
self.add_vertex(v)
for (u,v) in Edges:
self.add_edge(u,v)
#O(n)
def V(self):
return Set({v for v in self.VM})
#O(n^2)
def E(self):
S = { Edge(self.IVM[i], self.IVM[j])
for i in range(self.n)
for j in range(self.n)
if self.Matrix[i,j] }
return Set(S)
#TODO: Abstract the iteration for matrix numpy?
def M(self):
return self.Matrix
#O(1)
def add_vertex(self, v):
if v in self.VM:
return
self.VM[v] = self.n
self.IVM[self.n] = v
self.Matrix.inc()
self.n += 1
#TODO: fix this so that VM and IVM point to the right places
def remove_vertex(self, v):
if v not in self.VM:
return
i = self.VM[v]
for u in self.N(v):
self.remove_edge(u,v)
P = [ (j,self.IVM[j]) for j in range(i + 1, self.n) ]
for (j,k) in P:
self.VM[k] = j - 1
self.IVM[j-1] = k
del self.VM[v]
del self.IVM[self.n - 1]
self.Matrix = self.Matrix.minor(i)
self.n -= 1
#O(1) if e is an edge
#crashes if e is not an edge
def add_edge(self, u, v):
if self.adjacent(u,v):
return False
i = self.VM[u]
j = self.VM[v]
self.Matrix[i,j] = 1
self.Matrix[j,i] = 1
self.m += 1
return True
#O(1) if e is in E
def remove_edge(self, u, v):
if not self.adjacent(u,v):
return
i = self.VM[u]
j = self.VM[v]
self.Matrix[i,j] = 0
self.Matrix[j,i] = 0
self.m -= 1
#O(1) if (u,v) is in E
def adjacent(self, u, v):
i = self.VM[u]
j = self.VM[v]
return self.Matrix[i,j]
#O(n)
#Open Neighbourhood of v
def N(self, v):
S = Set()
i = self.VM[v]
v_i = self.Matrix[i]
for k,v in enumerate(v_i):
if v:
S.add( self.IVM[k] )
return S
