This notebook was prepared by Donne Martin. Source and license info is on GitHub.
Input:
add_edge(source, destination, weight)
graph.add_edge(0, 1)
graph.add_edge(0, 4)
graph.add_edge(0, 5)
graph.add_edge(1, 3)
graph.add_edge(1, 4)
graph.add_edge(2, 1)
graph.add_edge(3, 2)
graph.add_edge(3, 4)
Result:
To determine the shorted path in an unweighted graph, we can use breadth-first search keeping track of the previous nodes ids for each node. Previous nodes ids can be a dictionary of key: current node id and value: previous node id.
Walk the previous node ids backwards to get the path.
Complexity:
%run ../graph/graph.py
from collections import deque
class GraphShortestPath(Graph):
def shortest_path(self, source_key, dest_key):
if source_key is None or dest_key is None:
return None
if source_key is dest_key:
return [source_key]
prev_node_keys = self._shortest_path(source_key, dest_key)
if prev_node_keys is None:
return None
else:
path_ids = [dest_key]
prev_node_key = prev_node_keys[dest_key]
while prev_node_key is not None:
path_ids.append(prev_node_key)
prev_node_key = prev_node_keys[prev_node_key]
return path_ids[::-1]
def _shortest_path(self, source_key, dest_key):
queue = deque()
queue.append(self.nodes[source_key])
prev_node_keys = {source_key: None}
self.nodes[source_key].visit_state = State.visited
while queue:
node = queue.popleft()
if node.key is dest_key:
return prev_node_keys
prev_node = node
for adj_node in node.adj_nodes.values():
if adj_node.visit_state == State.unvisited:
queue.append(adj_node)
prev_node_keys[adj_node.key] = prev_node.key
adj_node.visit_state = State.visited
return None
%%writefile test_shortest_path.py
import unittest
class TestShortestPath(unittest.TestCase):
def test_shortest_path(self):
nodes = []
graph = GraphShortestPath()
for id in range(0, 6):
nodes.append(graph.add_node(id))
graph.add_edge(0, 1)
graph.add_edge(0, 4)
graph.add_edge(0, 5)
graph.add_edge(1, 3)
graph.add_edge(1, 4)
graph.add_edge(2, 1)
graph.add_edge(3, 2)
graph.add_edge(3, 4)
self.assertEqual(graph.shortest_path(nodes[0].key, nodes[2].key), [0, 1, 3, 2])
self.assertEqual(graph.shortest_path(nodes[0].key, nodes[0].key), [0])
self.assertEqual(graph.shortest_path(nodes[4].key, nodes[5].key), None)
print('Success: test_shortest_path')
def main():
test = TestShortestPath()
test.test_shortest_path()
if __name__ == '__main__':
main()
Overwriting test_shortest_path.py
%run -i test_shortest_path.py
Success: test_shortest_path