This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges).

Solution Notebook

Problem: Implement depth-first search on a graph.

Constraints
Test Cases
Algorithm
Code
Unit Test

Constraints

Is the graph directed?
- Yes
Can we assume we already have Graph and Node classes?
- 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 + E)

Code



In [1]:

    
%run ../graph/graph.py



In [2]:

    
def dfs(root, visit_func):
    if root is None:
        return
    visit_func(root)
    root.visited = True
    for node in root.adjacent:
        if not node.visited:
            dfs(node, visit_func)

Unit Test



In [3]:

    
%run ../utils/results.py



In [4]:

    
%%writefile test_dfs.py
from nose.tools import assert_equal


class TestDfs(object):

    def __init__(self):
        self.results = Results()

    def test_dfs(self):
        nodes = []
        graph = Graph()
        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)
        dfs(nodes[0], self.results.add_result)
        assert_equal(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