This notebook was prepared by Donne Martin. Source and license info is on GitHub.
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:
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:
Complexity:
%run ../graph/graph.py
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
for adj_node in node.adj_nodes.values():
if adj_node.visit_state == State.unvisited:
queue.append(adj_node)
adj_node.visit_state = State.visited
return False
%%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):
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)
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
%run -i test_path_exists.py
Success: test_path_exists