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"""Breadth-first search shortest path implementations.

doctest:

python -m doctest -v bfs_shortest_path.py

Manual test:

python bfs_shortest_path.py

"""

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) -> 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(graph, "G", "D")

['G', 'C', 'A', 'B', 'D']

"""

# keep track of explored nodes

explored = []

# keep track of all the paths to be checked

queue = [[start]]

# return path if start is goal

if start == goal:

return "That was easy! Start = goal"

# 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.append(node)

# in case there's no path between the 2 nodes

return "So sorry, but a connecting path doesn't exist :("

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(graph, "G", "D")

>>> bfs_shortest_path_distance(graph, "A", "A")

>>> bfs_shortest_path_distance(graph, "A", "H")

-1

"""

if not graph or start not in graph or target not in graph:

return -1

if start == target:

return 0

queue = [start]

visited = [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.append(adjacent)

queue.append(adjacent)

dist[adjacent] = dist[node] + 1

return dist[target]

if __name__ == "__main__":

print(bfs_shortest_path(graph, "G", "D")) # returns ['G', 'C', 'A', 'B', 'D']

print(bfs_shortest_path_distance(graph, "G", "D")) # returns 4

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