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

# Solution Notebook¶

## 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(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

class GraphPathExists(Graph):

def path_exists(self, start, end):
if start is None or end is None:
return False
if start is end:
return True
queue = deque()
queue.append(start)
start.visit_state = State.visited
while queue:
node = queue.popleft()
if node is end:
return True
return False


## Unit Test¶

In [3]:
%%writefile test_path_exists.py
import unittest

class TestPathExists(unittest.TestCase):

def test_path_exists(self):
nodes = []
graph = GraphPathExists()
for id in range(0, 6):

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()

Overwriting test_path_exists.py

In [4]:
%run -i test_path_exists.py

Success: test_path_exists