def kruskal(V, E, W):
ds = DisjointSets()
min_weight_priority = MinEdgePriority(W)
heap = BinaryHeap(min_weight_priority)
A = []
for v in V:
ds.make_set(v)
for e in E:
heap.insert(e)
while not heap.is_empty():
(u, v) = heap.extract()
if ds.find_set(u) != ds.find_set(v):
A.append((u, v))
ds.union(u, v)
return A
def kruskal(V, E, W):
ds = DisjointSets()
min_weight_priority = MinEdgePriority(W)
heap = BinaryHeap(min_weight_priority)
A = []
for v in V:
ds.make_set(v)
for e in E:
heap.insert(e)
while not heap.is_empty():
(u,v) = heap.extract()
if ds.find_set(u) != ds.find_set(v):
A.append((u, v))
ds.union(u, v)
return A
def dijkstra(V, adj, W, s, infinity):
d,p = __initialise_sssp(V, s, infinity)
S = []
node = {}
Q = heap.make_heap()
for u in V:
node[u] = heap.make_node(VertexWeight(u, d[u]))
heap.insert(Q, node[u])
while not heap.is_empty(Q):
x = heap.extract(Q)
u = x.key.get_vertex()
if DEBUG: print "visit", u
S.append(u)
for v in adj[u]:
__relax(u, v, W, d, p)
heap.decrease_key(Q, node[v], VertexWeight(v, d[v]))
return (d, p)
def dijkstra(V, adj, W, s, infinity):
d, p = __initialise_sssp(V, s, infinity)
S = []
node = {}
Q = heap.make_heap()
for u in V:
node[u] = heap.make_node(VertexWeight(u, d[u]))
heap.insert(Q, node[u])
while not heap.is_empty(Q):
x = heap.extract(Q)
u = x.key.get_vertex()
if DEBUG: print "visit", u
S.append(u)
for v in adj[u]:
__relax(u, v, W, d, p)
heap.decrease_key(Q, node[v], VertexWeight(v, d[v]))
return (d, p)
def prim(V, E, W, r):
# initialise adj
adj = graph.make_adj(V, E)
# determine appropriate infinity
max_weight = None
for (u, v) in E:
if max_weight == None or max_weight < W[(u, v)]:
max_weight = W[(u, v)]
infinity = max_weight + 10
node = {}
parent = {}
inqueue = {}
for u in V:
if u == r:
uw = VertexWeight(u, 0)
else:
uw = VertexWeight(u, infinity)
node[u] = heap.make_node(uw)
parent[u] = None
Q = heap.make_heap()
for u in V:
heap.insert(Q, node[u])
inqueue[u] = True
while not heap.is_empty(Q):
if DEBUG:
print "--------------------------------------------------"
heap.show_heap(Q)
x = heap.extract(Q)
u, w = x.key.get_info()
assert (node[u].key.get_vertex() == u
and node[u].key.get_weight() == w)
inqueue[u] = False
for v in adj[u]:
if inqueue[v] and W[(u, v)] < node[v].key.weight:
parent[v] = u
heap.decrease_key(Q, node[v], VertexWeight(v, W[(u, v)]))
return parent
def prim(V, E, W, r):
# initialise adj
adj = graph.make_adj(V, E)
# determine appropriate infinity
max_weight = None
for (u,v) in E:
if max_weight == None or max_weight < W[(u,v)]:
max_weight = W[(u,v)]
infinity = max_weight + 10
node = {}
parent = {}
inqueue = {}
for u in V:
if u == r:
uw = VertexWeight(u, 0)
else:
uw = VertexWeight(u, infinity)
node[u] = heap.make_node(uw)
parent[u] = None
Q = heap.make_heap()
for u in V:
heap.insert(Q, node[u])
inqueue[u] = True
while not heap.is_empty(Q):
if DEBUG:
print "--------------------------------------------------"
heap.show_heap(Q)
x = heap.extract(Q)
u, w = x.key.get_info()
assert(node[u].key.get_vertex() == u and node[u].key.get_weight() == w)
inqueue[u] = False
for v in adj[u]:
if inqueue[v] and W[(u,v)] < node[v].key.weight:
parent[v] = u
heap.decrease_key(Q, node[v], VertexWeight(v, W[(u,v)]))
return parent
def max_aug_flow(n,s,t,Capacity,Flow,p): frozen=[-1 for x in range(n)] unfrozen=[-1 for x in range(n)] unfrozen_node_list=[-1 for x in range(n)] frozen_node_list=[] #freeze source frozen[0]=1; #initialize fib heap Uf_heap = make_heap() #first for source s. source_node= newNode(0,0,0) frozen_node_list.append(source_node) #unfrozen_node_list.append(source_node) new_s = s #initialize with source node while new_s!=t : for j in range(0,n): if Capacity[new_s][j]<0 : if p[j]!= -1 : if Capacity[new_s][j] < Capacity[p[j]][j] : p[j]=new_s #updates parent list unfrozen_node_list[j].key = Capacity[new_s][j] else: node = newNode(Capacity[new_s][j],j,new_s) unfrozen_node_list[j]=node unfrozen[j]= 1 #print "added new node j" insert(Uf_heap, node) p[j]=new_s ret_node= extract(Uf_heap) if ret_node == None: return 0 frozen[ret_node.vertex]= 1 frozen_node_list.append(ret_node) unfrozen[ret_node.vertex]= -1 new_s= ret_node.vertex #say no node left in unfrozen node list, hence see if everything is -1 p[0]=-1 flow=[] #Need to trace path from sink to source using parent p list trace_parent_index=n-1 while p[trace_parent_index] != -1 : curr_flow=Capacity[p[trace_parent_index]][trace_parent_index] if curr_flow <0 : flow.append(curr_flow) trace_parent_index = p[trace_parent_index] #Accordingly update a new flow list #Find the min. of flow list (or max. because negative capacities) #Min. is the maximum flow final_flow = max(flow) return -final_flow
def max_aug_flow(n,s,t,Capacity,Flow,p, No_Edge_Sat_Max_Flow): frozen=[-1 for x in range(n)] unfrozen=[-1 for x in range(n)] unfrozen_node_list=[-1 for x in range(n)] frozen_node_list=[] #p = [-1 for x in range(n)] print "Current source is: ", s print "Current sink is: ", t print "input parent list is: ", p print "input capacity graph is: ", Capacity #freeze source frozen[0]=1; #initialize fib heap Uf_heap = make_heap() #first for source s. source_node= newNode(0,s,0) frozen_node_list.append(source_node) #unfrozen_node_list.append(source_node) new_s = s #initialize with source node temp_var = 0 while new_s!=t : temp_var +=1 for j in range(0,n): print "edge capacity for", new_s," : ",j, "is" ,Capacity[new_s][j] if Capacity[new_s][j]<0 : #test call print "this j is ", j, "and parent is: ", p[j] if p[j]!= -1 : if Capacity[new_s][j] < Capacity[p[j]][j] : p[j]=new_s #updates parent list print "Current j is " , j unfrozen_node_list[j].key = Capacity[new_s][j] else: node = newNode(Capacity[new_s][j],j,new_s) print "new node ", j, "added" unfrozen_node_list[j]=node unfrozen[j]= 1 #print "added new node j" insert(Uf_heap, node) p[j]=new_s print "parent list is : ", p ret_node= extract(Uf_heap) if ret_node == None: print "temp_var is: ", temp_var return 0 print "returned node is ", ret_node.vertex frozen[ret_node.vertex]= 1 frozen_node_list.append(ret_node) unfrozen[ret_node.vertex]= -1 new_s= ret_node.vertex print "new_s is: ", new_s #say no node left in unfrozen node list, hence see if everything is -1 p[s]=-1 flow=[] #Need to trace path from sink to source using parent p list trace_parent_index=t print "n: ", n , " and current sink: ", t max_curr_flow = -1000 while p[trace_parent_index] != -1 : curr_flow=Capacity[p[trace_parent_index]][trace_parent_index] print "curr_flow: ", curr_flow if curr_flow <0 : flow.append(curr_flow) '''#store u and v for saturated edge(u,v) if curr_flow > max_curr_flow: sat_u = p[trace_parent_index] #store u and v for saturated edge(u,v) sat_v = trace_parent_index ''' trace_parent_index = p[trace_parent_index] #No_Edge_Sat_Max_Flow[sat_u][sat_v] += 1 #Separate loop and not using only the bottleneck capacity because multiple edges with same capacity might get saturated v = t while p[v] != -1 : if max(flow) == Capacity[p[v]][v]: No_Edge_Sat_Max_Flow[p[v]][v] += 1 v = p[v] print "flow ", flow print "parent here too: ", p #Accordingly update a new flow list #Find the min. of flow list (or max. because negative capacities) #Min. is the maximum flow final_flow = max(flow) return -final_flow #return -final_flow, sat_u, sat_v
def max_aug_flow(n, s, t, Capacity, Flow, p, No_Edge_Sat_Max_Flow):
frozen = [-1 for x in range(n)]
unfrozen = [-1 for x in range(n)]
unfrozen_node_list = [-1 for x in range(n)]
frozen_node_list = []
#p = [-1 for x in range(n)]
print "Current source is: ", s
print "Current sink is: ", t
print "input parent list is: ", p
print "input capacity graph is: ", Capacity
#freeze source
frozen[0] = 1
#initialize fib heap
Uf_heap = make_heap()
#first for source s.
source_node = newNode(0, s, 0)
frozen_node_list.append(source_node)
#unfrozen_node_list.append(source_node)
new_s = s #initialize with source node
temp_var = 0
while new_s != t:
temp_var += 1
for j in range(0, n):
print "edge capacity for", new_s, " : ", j, "is", Capacity[new_s][
j]
if Capacity[new_s][j] < 0:
#test call
print "this j is ", j, "and parent is: ", p[j]
if p[j] != -1:
if Capacity[new_s][j] < Capacity[p[j]][j]:
p[j] = new_s #updates parent list
print "Current j is ", j
unfrozen_node_list[j].key = Capacity[new_s][j]
else:
if j != s:
node = newNode(Capacity[new_s][j], j, new_s)
print "new node ", j, "added"
unfrozen_node_list[j] = node
unfrozen[j] = 1
#print "added new node j"
insert(Uf_heap, node)
p[j] = new_s
print "parent list is : ", p
ret_node = extract(Uf_heap)
if ret_node == None:
print "temp_var is: ", temp_var
return 0
print "returned node is ", ret_node.vertex
frozen[ret_node.vertex] = 1
frozen_node_list.append(ret_node)
unfrozen[ret_node.vertex] = -1
new_s = ret_node.vertex
print "new_s is: ", new_s
#say no node left in unfrozen node list, hence see if everything is -1
p[s] = -1
flow = []
#Need to trace path from sink to source using parent p list
trace_parent_index = t
print "Current source is :", s, " and current sink: ", t
max_curr_flow = -1000
while p[trace_parent_index] != -1:
curr_flow = Capacity[p[trace_parent_index]][trace_parent_index]
print "curr_flow: ", curr_flow
if curr_flow < 0:
flow.append(curr_flow)
'''#store u and v for saturated edge(u,v)
if curr_flow > max_curr_flow:
sat_u = p[trace_parent_index] #store u and v for saturated edge(u,v)
sat_v = trace_parent_index '''
trace_parent_index = p[trace_parent_index]
#No_Edge_Sat_Max_Flow[sat_u][sat_v] += 1
#Separate loop and not using only the bottleneck capacity because multiple edges with same capacity might get saturated
v = t
while p[v] != -1:
if max(flow) == Capacity[p[v]][v]:
No_Edge_Sat_Max_Flow[p[v]][v] += 1
v = p[v]
print "flow ", flow
print "parent here too: ", p
#Accordingly update a new flow list
#Find the min. of flow list (or max. because negative capacities)
#Min. is the maximum flow
final_flow = max(flow)
return -final_flow
def max_aug_flow(n, s, t, Capacity, Flow, p):
frozen = [-1 for x in range(n)]
unfrozen = [-1 for x in range(n)]
unfrozen_node_list = [-1 for x in range(n)]
frozen_node_list = []
#p = [-1 for x in range(n)]
print "input parent list is: ", p
print "input capacity graph is: ", Capacity
#freeze source
frozen[0] = 1
#initialize fib heap
Uf_heap = make_heap()
#first for source s.
source_node = newNode(0, s, 0)
frozen_node_list.append(source_node)
#unfrozen_node_list.append(source_node)
new_s = s #initialize with source node
temp_var = 0
while new_s != t:
temp_var += 1
for j in range(0, n):
print "edge capacity for", new_s, " : ", j, "is", Capacity[new_s][
j]
if Capacity[new_s][j] < 0:
#test call
print "this j is ", j, "and parent is: ", p[j]
if p[j] != -1:
if Capacity[new_s][j] < Capacity[p[j]][j]:
p[j] = new_s #updates parent list
print "Current j is ", j
unfrozen_node_list[j].key = Capacity[new_s][j]
else:
node = newNode(Capacity[new_s][j], j, new_s)
print "new node ", j, "added"
unfrozen_node_list[j] = node
unfrozen[j] = 1
#print "added new node j"
insert(Uf_heap, node)
p[j] = new_s
print "parent list is : ", p
ret_node = extract(Uf_heap)
if ret_node == None:
print "temp_var is: ", temp_var
return 0
print "returned node is ", ret_node.vertex
frozen[ret_node.vertex] = 1
frozen_node_list.append(ret_node)
unfrozen[ret_node.vertex] = -1
new_s = ret_node.vertex
print "new_s is: ", new_s
#say no node left in unfrozen node list, hence see if everything is -1
p[0] = -1
flow = []
#Need to trace path from sink to source using parent p list
trace_parent_index = n - 1
while p[trace_parent_index] != -1:
curr_flow = Capacity[p[trace_parent_index]][trace_parent_index]
if curr_flow < 0:
flow.append(curr_flow)
trace_parent_index = p[trace_parent_index]
print "parent here too: ", p
#Accordingly update a new flow list
#Find the min. of flow list (or max. because negative capacities)
#Min. is the maximum flow
final_flow = max(flow)
return -final_flow
def max_aug_flow(n,s,t,Capacity,Flow,p): frozen=[-1 for x in range(n)] unfrozen=[-1 for x in range(n)] unfrozen_node_list=[-1 for x in range(n)] frozen_node_list=[] #p = [-1 for x in range(n)] print "input parent list is: ", p print "input capacity graph is: ", Capacity #freeze source frozen[0]=1; #initialize fib heap Uf_heap = make_heap() #first for source s. source_node= newNode(0,s,0) frozen_node_list.append(source_node) #unfrozen_node_list.append(source_node) new_s = s #initialize with source node temp_var = 0 while new_s!=t : temp_var +=1 for j in range(0,n): print "edge capacity for", new_s," : ",j, "is" ,Capacity[new_s][j] if Capacity[new_s][j]<0 : #test call print "this j is ", j, "and parent is: ", p[j] if p[j]!= -1 : if Capacity[new_s][j] < Capacity[p[j]][j] : p[j]=new_s #updates parent list print "Current j is " , j unfrozen_node_list[j].key = Capacity[new_s][j] else: node = newNode(Capacity[new_s][j],j,new_s) print "new node ", j, "added" unfrozen_node_list[j]=node unfrozen[j]= 1 #print "added new node j" insert(Uf_heap, node) p[j]=new_s print "parent list is : ", p ret_node= extract(Uf_heap) if ret_node == None: print "temp_var is: ", temp_var return 0 print "returned node is ", ret_node.vertex frozen[ret_node.vertex]= 1 frozen_node_list.append(ret_node) unfrozen[ret_node.vertex]= -1 new_s= ret_node.vertex print "new_s is: ", new_s #say no node left in unfrozen node list, hence see if everything is -1 p[0]=-1 flow=[] #Need to trace path from sink to source using parent p list trace_parent_index=n-1 while p[trace_parent_index] != -1 : curr_flow=Capacity[p[trace_parent_index]][trace_parent_index] if curr_flow <0 : flow.append(curr_flow) trace_parent_index = p[trace_parent_index] print "parent here too: ", p #Accordingly update a new flow list #Find the min. of flow list (or max. because negative capacities) #Min. is the maximum flow final_flow = max(flow) return -final_flow
#initialize fib heap Uf_heap = make_heap() # Define source s and sink t s=0 t=n-1 #first for source s. source_node= newNode(0,0,0) #need to think about parent vertex of s, keep -1 but that might mess up later frozen_node_list.append(source_node) for j in range(0,n): if Capacity[0][j]<0: #add corres. j nodes to unfrozen heap, i.e. make nodes for them in heap node = newNode(Capacity[0][j],j,0) unfrozen_node_list[j]=node #Does this thing pass a reference to node into the list or does it pass a copy? insert(Uf_heap, node) p[j]=0 ret_node= extract(Uf_heap) #returned node frozen[ret_node.vertex]= 1 #freeze that node frozen_node_list.append(ret_node) #append it to frozen node list new_s= ret_node.vertex while new_s!=t : for j in range(0,n): if Capacity[new_s][j]<0 : if p[j]!= -1 : if Capacity[new_s][j] < Capacity[p[j]][j] : p[j]=new_s #updates parent list
