def Prim(self, w, r):
'''G.Prim(weight, root) -- Given weight function
and an arbitrary vertex root of the graph G,
compute minimum spanning tree using Prim's algorithm'''
for v in self.vertices:
v.weight = float("Inf")
v.p = None
r.weight = 0
q = min_priority_queue(self.vertices, 'weight')
while q.heap_size > 0:
u = q.heap_extract_min()
for v in self.adj[u]:
if v in q and w(u, v) < v.weight:
v.p = u
q.heap_decrease_key(v.index, w(u, v))
def Dijkstra(self, w, s):
'''
Dijkstra's algorithm solves the single-source shortest-paths problem
on a weighted, directed graph G = (V, E) for the case in which all edge
weights are nonnegative.
'''
self.initialize_signle_source(s)
S = set()
Q = min_priority_queue(self.vertices, 'd')
while Q.heap_size > 1:
u = Q.heap_extract_min()
S = S.union({u})
for v in self.adj[u]:
if v.d > u.d + w(u, v):
v.d = u.d + w(u, v)
v.p = u
Q.heap_decrease_key(v.index, u.d + w(u, v))
def cut(self, x, y, w):
'''For a given edge (x, y) contained in some minimum spanning tree,
form a minimum spanning tree that contains (x, y) using a method like Prim's algorithm,
and construct a cut (S, V - S) such that (x, y) is the light edge crossing
the cut, S = {u: u.root = x}'''
for v in self.vertices:
v.weight = float("Inf")
v.p = None
v.root = None
x.weight = 0
y.weight = 0
x.root = x
y.root = y
q = min_priority_queue(self.vertices, 'weight')
while q.heap_size > 0:
u = q.heap_extract_min()
for v in self.adj[u]:
if v in q and w(u, v) < v.weight:
v.root = u.root
q.heap_decrease_key(v.index, w(u, v))
v.p = u
def test_heap_insert(self):
a = [1, 10, 3, 2, 7, 8, 9, 4, 14, 16]
q = min_priority_queue(a)
q.heap_extract_min()
q.min_heap_insert(0)
self.assertEquals(q, [0, 2, 3, 10, 4, 8, 9, 16, 14, 7])
def test_heap_decrease_key(self):
a = [1, 10, 3, 2, 7, 8, 9, 4, 14, 16]
q = min_priority_queue(a)
q.heap_decrease_key(8, 1)
self.assertEquals(q, [1, 1, 3, 2, 7, 8, 9, 10, 4, 16])
def test_heap_extract_min(self):
a = [1, 10, 3, 2, 7, 8, 9, 4, 14, 16]
q = min_priority_queue(a)
self.assertEquals(q.heap_extract_min(), 1)
self.assertEquals(q, [2, 4, 3, 10, 7, 8, 9, 16, 14, 16])
def test_heap_minimum(self):
a = [1, 10, 3, 2, 7, 8, 9, 4, 14, 16]
self.assertEquals(min_priority_queue(a).heap_minimum(), 1)
def test_init(self):
a = [1, 10, 3, 2, 7, 8, 9, 4, 14, 16]
q = min_priority_queue(a)
self.assertEquals(q, [1, 2, 3, 4, 7, 8, 9, 10, 14, 16])
def test_heap_insert(self):
a = [1, 10, 3, 2, 7, 8, 9, 4, 14, 16]
q = min_priority_queue(a)
q.heap_extract_min()
q.min_heap_insert(0)
self.assertEquals(q, [0, 2, 3, 10, 4, 8, 9, 16, 14, 7])
def test_heap_decrease_key(self):
a = [1, 10, 3, 2, 7, 8, 9, 4, 14, 16]
q = min_priority_queue(a)
q.heap_decrease_key(8, 1)
self.assertEquals(q, [1, 1, 3, 2, 7, 8, 9, 10, 4, 16])
def test_heap_extract_min(self):
a = [1, 10, 3, 2, 7, 8, 9, 4, 14, 16]
q = min_priority_queue(a)
self.assertEquals(q.heap_extract_min(), 1)
self.assertEquals(q, [2, 4, 3, 10, 7, 8, 9, 16, 14, 16])
def test_heap_minimum(self):
a = [1, 10, 3, 2, 7, 8, 9, 4, 14, 16]
self.assertEquals(min_priority_queue(a).heap_minimum(), 1)
def test_init(self):
a = [1, 10, 3, 2, 7, 8, 9, 4, 14, 16]
q = min_priority_queue(a)
self.assertEquals(q, [1, 2, 3, 4, 7, 8, 9, 10, 14, 16])
