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# mst.py
# From Classic Computer Science Problems in Python Chapter 4
# Copyright 2018 David Kopec
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import TypeVar, List, Optional
from weighted_graph import WeightedGraph
from weighted_edge import WeightedEdge
from priority_queue import PriorityQueue
V = TypeVar('V') # type of the vertices in the graph
WeightedPath = List[WeightedEdge] # type alias for paths
def total_weight(wp: WeightedPath) -> float:
return sum([e.weight for e in wp])
def mst(wg: WeightedGraph[V], start: int = 0) -> Optional[WeightedPath]:
if start > (wg.vertex_count - 1) or start < 0:
return None
result: WeightedPath = [] # holds the final MST
pq: PriorityQueue[WeightedEdge] = PriorityQueue()
visited: [bool] = [False] * wg.vertex_count # where we've been
def visit(index: int):
visited[index] = True # mark as visited
for edge in wg.edges_for_index(index):
# add all edges coming from here to pq
if not visited[edge.v]:
pq.push(edge)
visit(start) # the first vertex is where everything begins
while not pq.empty: # keep going while there are edges to process
edge = pq.pop()
if visited[edge.v]:
continue # don't ever revisit
# this is the current smallest, so add it to solution
result.append(edge)
visit(edge.v) # visit where this connects
return result
def print_weighted_path(wg: WeightedGraph, wp: WeightedPath) -> None:
for edge in wp:
print(f"{wg.vertex_at(edge.u)} {edge.weight}> {wg.vertex_at(edge.v)}")
print(f"Total Weight: {total_weight(wp)}")
if __name__ == "__main__":
city_graph2: WeightedGraph[str] = WeightedGraph(["Seattle", "San Francisco", "Los Angeles", "Riverside", "Phoenix", "Chicago", "Boston", "New York", "Atlanta", "Miami", "Dallas", "Houston", "Detroit", "Philadelphia", "Washington"])
city_graph2.add_edge_by_vertices("Seattle", "Chicago", 1737)
city_graph2.add_edge_by_vertices("Seattle", "San Francisco", 678)
city_graph2.add_edge_by_vertices("San Francisco", "Riverside", 386)
city_graph2.add_edge_by_vertices("San Francisco", "Los Angeles", 348)
city_graph2.add_edge_by_vertices("Los Angeles", "Riverside", 50)
city_graph2.add_edge_by_vertices("Los Angeles", "Phoenix", 357)
city_graph2.add_edge_by_vertices("Riverside", "Phoenix", 307)
city_graph2.add_edge_by_vertices("Riverside", "Chicago", 1704)
city_graph2.add_edge_by_vertices("Phoenix", "Dallas", 887)
city_graph2.add_edge_by_vertices("Phoenix", "Houston", 1015)
city_graph2.add_edge_by_vertices("Dallas", "Chicago", 805)
city_graph2.add_edge_by_vertices("Dallas", "Atlanta", 721)
city_graph2.add_edge_by_vertices("Dallas", "Houston", 225)
city_graph2.add_edge_by_vertices("Houston", "Atlanta", 702)
city_graph2.add_edge_by_vertices("Houston", "Miami", 968)
city_graph2.add_edge_by_vertices("Atlanta", "Chicago", 588)
city_graph2.add_edge_by_vertices("Atlanta", "Washington", 543)
city_graph2.add_edge_by_vertices("Atlanta", "Miami", 604)
city_graph2.add_edge_by_vertices("Miami", "Washington", 923)
city_graph2.add_edge_by_vertices("Chicago", "Detroit", 238)
city_graph2.add_edge_by_vertices("Detroit", "Boston", 613)
city_graph2.add_edge_by_vertices("Detroit", "Washington", 396)
city_graph2.add_edge_by_vertices("Detroit", "New York", 482)
city_graph2.add_edge_by_vertices("Boston", "New York", 190)
city_graph2.add_edge_by_vertices("New York", "Philadelphia", 81)
city_graph2.add_edge_by_vertices("Philadelphia", "Washington", 123)
result: Optional[WeightedPath] = mst(city_graph2)
if result is None:
print("No solution found!")
else:
print_weighted_path(city_graph2, result)