R

```
"""Breadth-first search shortest path implementations.
doctest:
python -m doctest -v bfs_shortest_path.py
Manual test:
python bfs_shortest_path.py
"""
demo_graph = {
"A": ["B", "C", "E"],
"B": ["A", "D", "E"],
"C": ["A", "F", "G"],
"D": ["B"],
"E": ["A", "B", "D"],
"F": ["C"],
"G": ["C"],
}
def bfs_shortest_path(graph: dict, start, goal) -> list[str]:
"""Find shortest path between `start` and `goal` nodes.
Args:
graph (dict): node/list of neighboring nodes key/value pairs.
start: start node.
goal: target node.
Returns:
Shortest path between `start` and `goal` nodes as a string of nodes.
'Not found' string if no path found.
Example:
>>> bfs_shortest_path(demo_graph, "G", "D")
['G', 'C', 'A', 'B', 'D']
>>> bfs_shortest_path(demo_graph, "G", "G")
['G']
>>> bfs_shortest_path(demo_graph, "G", "Unknown")
[]
"""
# keep track of explored nodes
explored = set()
# keep track of all the paths to be checked
queue = [[start]]
# return path if start is goal
if start == goal:
return [start]
# keeps looping until all possible paths have been checked
while queue:
# pop the first path from the queue
path = queue.pop(0)
# get the last node from the path
node = path[-1]
if node not in explored:
neighbours = graph[node]
# go through all neighbour nodes, construct a new path and
# push it into the queue
for neighbour in neighbours:
new_path = list(path)
new_path.append(neighbour)
queue.append(new_path)
# return path if neighbour is goal
if neighbour == goal:
return new_path
# mark node as explored
explored.add(node)
# in case there's no path between the 2 nodes
return []
def bfs_shortest_path_distance(graph: dict, start, target) -> int:
"""Find shortest path distance between `start` and `target` nodes.
Args:
graph: node/list of neighboring nodes key/value pairs.
start: node to start search from.
target: node to search for.
Returns:
Number of edges in shortest path between `start` and `target` nodes.
-1 if no path exists.
Example:
>>> bfs_shortest_path_distance(demo_graph, "G", "D")
4
>>> bfs_shortest_path_distance(demo_graph, "A", "A")
0
>>> bfs_shortest_path_distance(demo_graph, "A", "Unknown")
-1
"""
if not graph or start not in graph or target not in graph:
return -1
if start == target:
return 0
queue = [start]
visited = set(start)
# Keep tab on distances from `start` node.
dist = {start: 0, target: -1}
while queue:
node = queue.pop(0)
if node == target:
dist[target] = (
dist[node] if dist[target] == -1 else min(dist[target], dist[node])
)
for adjacent in graph[node]:
if adjacent not in visited:
visited.add(adjacent)
queue.append(adjacent)
dist[adjacent] = dist[node] + 1
return dist[target]
if __name__ == "__main__":
print(bfs_shortest_path(demo_graph, "G", "D")) # returns ['G', 'C', 'A', 'B', 'D']
print(bfs_shortest_path_distance(demo_graph, "G", "D")) # returns 4
```