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 breadth-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, 4, 5, 3, 2]

Algorithm

We generally use breadth-first search to determine the shortest path.

Add the current node to the queue and mark it as visited
While the queue is not empty
- Dequeue a node and visit it
- Iterate through each adjacent node
  - If the node has not been visited, add it to the queue and mark it as visited

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]:

    
from collections import deque


def bfs(root, visit_func):
    if root is None:
        return
    queue = deque()
    queue.append(root)
    root.visited = True
    while queue:
        node = queue.popleft()
        visit_func(node)
        for adjacent_node in node.adjacent:
            if not adjacent_node.visited:
                queue.append(adjacent_node)
                adjacent_node.visited = True

Unit Test



In [3]:

    
%run ../utils/results.py



In [4]:

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


class TestBfs(object):

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

    def test_bfs(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)
        bfs(nodes[0], self.results.add_result)
        assert_equal(str(self.results), "[0, 1, 4, 5, 3, 2]")

        print('Success: test_bfs')


def main():
    test = TestBfs()
    test.test_bfs()


if __name__ == '__main__':
    main()









    



Overwriting test_bfs.py



In [5]:

    
%run -i test_bfs.py









    



Success: test_bfs