This notebook was prepared by Donne Martin. Source and license info is on GitHub.

Challenge Notebook

Problem: Find the shortest path between two nodes in a graph.

Constraints

  • Is the graph directed?
    • Yes
  • Is the graph weighted?
    • No
  • Can we assume we already have Graph and Node classes?
    • Yes
  • Are the inputs two Nodes?
    • Yes
  • Is the output a list of Node keys that make up the shortest path?
    • Yes
  • If there is no path, should we return None?
    • Yes
  • Can we assume this is a connected graph?
    • Yes
  • Can we assume the inputs are valid?
    • Yes
  • Can we assume this fits memory?
    • Yes

Test Cases

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:

  • search_path(start=0, end=2) -> [0, 1, 3, 2]
  • search_path(start=0, end=0) -> [0]
  • search_path(start=4, end=5) -> None

Algorithm

Refer to the Solution Notebook. If you are stuck and need a hint, the solution notebook's algorithm discussion might be a good place to start.

Code

In [ ]:
%run ../graph/graph.py
%load ../graph/graph.py
In [ ]:
class GraphShortestPath(Graph):

    def shortest_path(self, source_key, dest_key):
        # TODO: Implement me
        pass

Unit Test

The following unit test is expected to fail until you solve the challenge.

In [ ]:
# %load 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()

Solution Notebook

Review the Solution Notebook for a discussion on algorithms and code solutions.