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: Determine whether there is a path between two nodes in 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:

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

Algorithm

To determine if there is a path, we can use either breadth-first or depth-first search.

Breadth-first search can also be used to determine the shortest path. Depth-first search is easier to implement with just straight recursion, but often results in a longer path.

We'll use a breadth-first search approach:

Add the start node to the queue and mark it as visited
If the start node is the end node, return True
While the queue is not empty
- Dequeue a node and visit it
- If the node is the end node, return True
- Iterate through each adjacent node
  - If the node has not been visited, add it to the queue and mark it as visited
Return False

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 path_exists(start, end):
    if start is None or end is None:
        return False
    if start is end:
        return True
    queue = deque()
    queue.append(start)
    start.visited = True
    while queue:
        node = queue.popleft()
        if node is None:
            continue
        if node is end:
            return True
        for adj_node in node.adjacent:
            if not adj_node.visited:
                queue.append(adj_node)
                adj_node.visited = True
    return False

Unit Test



In [3]:

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


class TestPathExists(object):

    def test_path_exists(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)

        assert_equal(path_exists(nodes[0], nodes[2]), True)
        assert_equal(path_exists(nodes[0], nodes[0]), True)
        assert_equal(path_exists(nodes[4], nodes[5]), False)

        print('Success: test_path_exists')


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


if __name__ == '__main__':
    main()









    



Overwriting test_path_exists.py



In [4]:

    
%run -i test_path_exists.py









    



Success: test_path_exists