def MST_Kruskal(g):
"""Compute a minimum spanning tree of a simple connected weighted graph g
using Kruskal's algorithm.
Return a list of edges that comprise the MST.
"""
tree = [] # list of edges in spanning tree
pq = HeapPriorityQueue() # entries are edges in g, with weights as key
forest = Partition() # keeps track of forest clusters
position = {} # map each node to its Partition entry
for v in g.vertices():
position[v] = forest.make_group(v)
for e in g.edges():
pq.add(e.element(), e) # edge's element is assumed to be its weight
size = g.vertex_count()
while len(tree) != size - 1 and not pq.is_empty():
# tree not spanning and unprocessed remain
weight, edge = pq.remove_min()
u, v = edge.endpoints()
a = forest.find(position[u])
b = forest.find(position[v])
if a != b:
tree.append(edge)
forest.union(a, b)
return tree
def MST_Kruskal(g):
"""Compute a minimum spanning tree of a simple connected weighted graph g
using Kruskal's algorithm.
Return a list of edges that comprise the MST.
"""
tree = [] # list of edges in spanning tree
pq = HeapPriorityQueue() # entries are edges in g, with weights as key
forest = Partition() # keeps track of forest clusters
position = {} # map each node to its Partition entry
for v in g.vertices():
position[v] = forest.make_group(v)
for e in g.edges():
pq.add(e.element(), e) # edge's element is assumed to be its weight
size = g.vertex_count()
while len(tree) != size - 1 and not pq.is_empty():
# tree not spanning and unprocessed remain
weight, edge = pq.remove_min()
u, v = edge.endpoints()
a = forest.find(position[u])
b = forest.find(position[v])
if a != b:
tree.append(edge)
forest.union(a, b)
return tree
def _compose_ht_tree(self, text):
"""Huffman tree construction for text."""
freq_table = self._compute_chr_freq(text)
ht_queue = HeapPriorityQueue()
for freq, lett in freq_table:
ht_tree = LinkedBinaryTree()
ht_tree._add_root((freq, lett))
ht_queue.add(freq, ht_tree)
while len(ht_queue) > 1:
(freq1, subtree1) = ht_queue.remove_min()
(freq2, subtree2) = ht_queue.remove_min()
freq = freq1 + freq2
ht_tree = LinkedBinaryTree()
ht_tree._add_root((freq, None))
ht_tree._attach(ht_tree.root(), subtree1, subtree2)
ht_queue.add(freq, ht_tree)
_, ht_tree = ht_queue.remove_min()
return ht_tree
