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

Challenge Notebook

Problem: Determine whether there is a path between two nodes in a graph.

Constraints

  • Is the graph directed?
    • Yes
  • Can we assume we already have Graph and Node classes?
    • 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, 5)
graph.add_edge(0, 4, 3)
graph.add_edge(0, 5, 2)
graph.add_edge(1, 3, 5)
graph.add_edge(1, 4, 4)
graph.add_edge(2, 1, 6)
graph.add_edge(3, 2, 7)
graph.add_edge(3, 4, 8)

Result:

  • search_path(start=0, end=2) -> True
  • search_path(start=0, end=0) -> True
  • search_path(start=4, end=5) -> False

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 GraphPathExists(Graph):

    def path_exists(self, start, end):
        # TODO: Implement me
        pass

Unit Test

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

In [ ]:
# %load test_path_exists.py
import unittest


class TestPathExists(unittest.TestCase):

    def test_path_exists(self):
        nodes = []
        graph = GraphPathExists()
        for id in range(0, 6):
            nodes.append(graph.add_node(id))
        graph.add_edge(0, 1, 5)
        graph.add_edge(0, 4, 3)
        graph.add_edge(0, 5, 2)
        graph.add_edge(1, 3, 5)
        graph.add_edge(1, 4, 4)
        graph.add_edge(2, 1, 6)
        graph.add_edge(3, 2, 7)
        graph.add_edge(3, 4, 8)

        self.assertEqual(graph.path_exists(nodes[0], nodes[2]), True)
        self.assertEqual(graph.path_exists(nodes[0], nodes[0]), True)
        self.assertEqual(graph.path_exists(nodes[4], nodes[5]), False)

        print('Success: test_path_exists')


def main():
    test = TestPathExists()
    test.test_path_exists()


if __name__ == '__main__':
    main()

Solution Notebook

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