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

Solution Notebook¶

Problem: Implement depth-first search on 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:

Order of nodes visited: [0, 1, 3, 2, 4, 5]

Algorithm¶

If we want to visit every node in a graph, we generally prefer depth-first search since it is simpler (no need to use a queue). For shortest path, we generally use breadth-first search.

Visit the current node and mark it visited
Iterate through each adjacent node
- If the node has not been visited, call dfs on it

Complexity:

Time: O(V + E), where V = number of vertices and E = number of edges
Space: O(V), for the recursion depth

Code¶

In [1]:

%run ../graph/graph.py

In [2]:

class GraphDfs(Graph):

    def dfs(self, root, visit_func):
        if root is None:
            return
        visit_func(root)
        root.visit_state = State.visited
        for node in root.adj_nodes.values():
            if node.visit_state == State.unvisited:
                self.dfs(node, visit_func)

Unit Test¶

In [3]:

%run ../utils/results.py

In [4]:

%%writefile test_dfs.py
import unittest


class TestDfs(unittest.TestCase):

    def __init__(self, *args, **kwargs):
        super(TestDfs, self).__init__()
        self.results = Results()

    def test_dfs(self):
        nodes = []
        graph = GraphDfs()
        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)
        graph.dfs(nodes[0], self.results.add_result)
        self.assertEqual(str(self.results), "[0, 1, 3, 2, 4, 5]")

        print('Success: test_dfs')


def main():
    test = TestDfs()
    test.test_dfs()


if __name__ == '__main__':
    main()

Overwriting test_dfs.py

In [5]:

%run -i test_dfs.py

Success: test_dfs