def test_week1_lecture_print():
"""Print."""
# -0
# -1
# -6
# --5
# -7
# -8
# -9
# --2
# --4
# ---3
print "\ntest_week1_lecture quick-union print 00:51"
alg = QuickUnionUF(10)
print alg
alg.ID = [0, 1, 9, 4, 9, 6, 6, 7, 8, 9]
print alg.ID
def test_week1_lecture_print(): """Print.""" # -0 # -1 # -6 # --5 # -7 # -8 # -9 # --2 # --4 # ---3 print "\ntest_week1_lecture quick-union print 00:51" alg = QuickUnionUF(10) print alg alg.ID = [0, 1, 9, 4, 9, 6, 6, 7, 8, 9] print alg.ID
def __init__(self, G): # t ~ O(E log E), s ~ V
self._weight = 0.0 # weight of MST. Edge weights can be +, 0, or -, need not be distinct.
self._mst = [] # new Queue<Edge>(); # edges in MST
# more efficient to build heap by passing array of edges
pq = [] # new MinPQ<Edge>()
for item in [(e.weight(), e) for e in G.edges()]:
heappush(pq, item) # insert(e)
# run greedy algorithm
uf = QuickUnionUF(G.V())
while not pq and len(self._mst) < (G.V() - 1):
edge_cur = heappop(pq) # .delMin()
v, w = edge_cur.get_vw()
if not uf.connected(v, w): # v-w does not create a cycle
uf.union(v, w) # merge v and w components
self._mst.append(edge_cur) # enqueue(e); # add edge e to mst
self._weight += edge_cur.weight()
def __init__(self, G): # t ~ O(E log E), s ~ V
self._weight = 0.0 # weight of MST. Edge weights can be +, 0, or -, need not be distinct.
self._mst = [] # new Queue<Edge>(); # edges in MST
# more efficient to build heap by passing array of edges
pq = [] # new MinPQ<Edge>()
for item in [(e.weight(), e) for e in G.edges()]:
heappush(pq, item) # insert(e)
# run greedy algorithm
uf = QuickUnionUF(G.V())
while not pq and len(self._mst) < (G.V() - 1):
edge_cur = heappop(pq) # .delMin()
v, w = edge_cur.get_vw()
if not uf.connected(v, w): # v-w does not create a cycle
uf.union(v, w) # merge v and w components
self._mst.append(edge_cur) # enqueue(e); # add edge e to mst
self._weight += edge_cur.weight()
def _check(MST, G):
"""check optimality conditions (takes time proportional to E V lg* V)"""
# check total weight
total = 0.0
for e in MST.edges():
total += e.weight()
if abs(total - MST.weight()) > MST.FLOATING_POINT_EPSILON:
sys.stderr.write("Weight of edges does not equal weight(): {} vs. {}\n".format(
total, MST.weight()))
return False
# check that it is acyclic
uf = QuickUnionUF(G.V())
for e in MST.edges():
v, w = e.get_vw()
if uf.connected(v, w):
sys.stderr.write("Not a forest\n")
return False
uf.union(v, w)
# check that it is a spanning forest
for e in G.edges():
print v, w
if not uf.connected(v, w):
sys.stderr.write("Not a spanning forest\n")
return False
# check that it is a minimal spanning forest (cut optimality conditions)
for e in edges():
# all edges in MST except e
uf = QuickUnionUF(G.V())
for f in MST._mst:
v, w = e.get_vw()
if f != e: uf.union(x, y)
# check that e is min weight edge in crossing cut
for f in G.edges():
x, y = f.get_vw()
if not uf.connected(x, y):
if f.weight() < e.weight():
sys.stderr.write("Edge {} violates cut optimality conditions\n".format(f))
return False
return True
def test_week1_exercise_Q2():
"""Test 2."""
alg = QuickUnionUF(10)
run_unions(alg, "1-2 7-9 0-4 8-0 4-6 1-9 3-4 7-0 0-5",
"\ntest_week1_exercise_Q2")
chk_arrays(alg.ID, [4, 2, 9, 6, 6, 5, 5, 9, 4, 6])
def test_week1_lecture():
"""From Quick Union (7:50) Lecture Example."""
alg = QuickUnionUF(10)
run_unions(alg, "4-3 3-8 6-5 9-4 2-1 8-9 5-0 7-2 6-1 7-3",
"\nwk1_lec quick-union", "QU_demo")
chk_arrays(alg.ID, [1, 8, 1, 8, 3, 0, 5, 1, 8, 8])
def _check(MST, G):
"""check optimality conditions (takes time proportional to E V lg* V)"""
# check total weight
total = 0.0
for e in MST.edges():
total += e.weight()
if abs(total - MST.weight()) > MST.FLOATING_POINT_EPSILON:
sys.stderr.write(
"Weight of edges does not equal weight(): {} vs. {}\n".format(
total, MST.weight()))
return False
# check that it is acyclic
uf = QuickUnionUF(G.V())
for e in MST.edges():
v, w = e.get_vw()
if uf.connected(v, w):
sys.stderr.write("Not a forest\n")
return False
uf.union(v, w)
# check that it is a spanning forest
for e in G.edges():
print v, w
if not uf.connected(v, w):
sys.stderr.write("Not a spanning forest\n")
return False
# check that it is a minimal spanning forest (cut optimality conditions)
for e in edges():
# all edges in MST except e
uf = QuickUnionUF(G.V())
for f in MST._mst:
v, w = e.get_vw()
if f != e: uf.union(x, y)
# check that e is min weight edge in crossing cut
for f in G.edges():
x, y = f.get_vw()
if not uf.connected(x, y):
if f.weight() < e.weight():
sys.stderr.write(
"Edge {} violates cut optimality conditions\n".format(
f))
return False
return True
