def connected_components(g):
vertices = g.vertices
components = vertices
s = dsf.DSF(vertices)
for edge in g.el:
components -= s.union(edge.source,edge.dest)
return components
def kruskal(G,trace=False):
weight_heap = min_heap.MinHeap()
S = dsf.DSF(len(G.al))
for v in range(len(G.al)):
for edge in G.al[v]:
if v<edge.dest:
weight_heap.insert(min_heap.HeapRecord(edge.weight,[v,edge.dest,edge.weight]))
mst = graph.Graph(len(G.al),weighted=True)
count = 0
while count<len(G.al)-1 and len(weight_heap.heap)>0:
next_edge = weight_heap.extractMin().data
if S.union(next_edge[0],next_edge[1])==1:
mst.insert_edge(next_edge[0],next_edge[1],next_edge[2])
count+=1
if trace:
draw_over(G,mst,'Kruskal '+str(count))
print(next_edge,'added to mst')
else:
if trace:
print(next_edge,'rejected')
if count == len(G.al)-1:
return mst
print('Graph has no minimum spanning tree')
return None
def connected_components(g):
vertices = len(g.al)
components = vertices
s = dsf.DSF(vertices)
for v in range(vertices):
for edge in g.al[v]:
components -= s.union(v, edge.dest)
return components
def connected_components(G, trace=False):
# Returns the disjoint set forest representing the connected components of G
S = dsf.DSF(len(G.al))
for v in range(len(G.al)):
for edge in G.al[v]:
if v < edge.dest:
S.union(v, edge.dest)
if trace:
print('last edge: ({},{})'.format(v, edge.dest))
print('dsf:', S.parent)
return S
def connected_components(g):
vertices = len(g.al)
components = vertices
s = dsf.DSF(vertices)
for v in range(vertices):
for edge in g.al[v]:
components -= s.union(v, edge.dest)
s.draw()
if components > 1:
return True
return False
for i in s.set_list():
if v in i and len(i) == 1:
return True
return False
def is_compressed(s):
for i in s.parent:
if i != -1 and s.parent[i] != -1:
return False
return True
if __name__ == "__main__":
plt.close("all")
s = dsf.DSF(8)
s.union(0, 1)
print(s.parent)
print(is_compressed(s)) # True
s.draw()
s.union(7, 2)
print(s.parent)
print(is_compressed(s)) # True
s.draw()
s.union(3, 5)
print(s.parent)
print(is_compressed(s)) # True
s.draw()
g.insert_edge(0,1)
g.insert_edge(0,2)
g.insert_edge(1,2)
g.insert_edge(1,3)
g.insert_edge(2,3)
g.insert_edge(3,4)
g.insert_edge(4,1)
g.display()
g.draw('Question 6')
p = bfs(g)
for i in range(5):
print('vertex',i,'distance from source',dist_from_prev(p,i))
print('\n *********** Question 7 **************')
s = dsf.DSF(6)
s.union(0,1)
s.union(4,2)
s.union(3,1)
print(s.parent)
s.draw('Question 7')
for i in range(6):
print('element',i,' elements in same set:',in_same_set(s,i))
print('\n *********** Question 8 **************')
s = [2,5,7,11,14,-6,-10]
for i in range(-10,10):
print('goal:',i,'subset:',subsetsum(s,i,sum(s)))