mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-30 16:31:08 +00:00
ac111ee463
* Reduce the complexity of graphs/bi_directional_dijkstra.py
* Try to lower the --max-complexity threshold in the file .flake8
* Lower the --max-complexity threshold in the file .flake8
* updating DIRECTORY.md
* updating DIRECTORY.md
* Try to lower max-complexity
* Try to lower max-complexity
* Try to lower max-complexity
---------
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
140 lines
3.3 KiB
Python
140 lines
3.3 KiB
Python
"""
|
|
Bi-directional Dijkstra's algorithm.
|
|
|
|
A bi-directional approach is an efficient and
|
|
less time consuming optimization for Dijkstra's
|
|
searching algorithm
|
|
|
|
Reference: shorturl.at/exHM7
|
|
"""
|
|
|
|
# Author: Swayam Singh (https://github.com/practice404)
|
|
|
|
|
|
from queue import PriorityQueue
|
|
from typing import Any
|
|
|
|
import numpy as np
|
|
|
|
|
|
def pass_and_relaxation(
|
|
graph: dict,
|
|
v: str,
|
|
visited_forward: set,
|
|
visited_backward: set,
|
|
cst_fwd: dict,
|
|
cst_bwd: dict,
|
|
queue: PriorityQueue,
|
|
parent: dict,
|
|
shortest_distance: float | int,
|
|
) -> float | int:
|
|
for nxt, d in graph[v]:
|
|
if nxt in visited_forward:
|
|
continue
|
|
old_cost_f = cst_fwd.get(nxt, np.inf)
|
|
new_cost_f = cst_fwd[v] + d
|
|
if new_cost_f < old_cost_f:
|
|
queue.put((new_cost_f, nxt))
|
|
cst_fwd[nxt] = new_cost_f
|
|
parent[nxt] = v
|
|
if nxt in visited_backward:
|
|
if cst_fwd[v] + d + cst_bwd[nxt] < shortest_distance:
|
|
shortest_distance = cst_fwd[v] + d + cst_bwd[nxt]
|
|
return shortest_distance
|
|
|
|
|
|
def bidirectional_dij(
|
|
source: str, destination: str, graph_forward: dict, graph_backward: dict
|
|
) -> int:
|
|
"""
|
|
Bi-directional Dijkstra's algorithm.
|
|
|
|
Returns:
|
|
shortest_path_distance (int): length of the shortest path.
|
|
|
|
Warnings:
|
|
If the destination is not reachable, function returns -1
|
|
|
|
>>> bidirectional_dij("E", "F", graph_fwd, graph_bwd)
|
|
3
|
|
"""
|
|
shortest_path_distance = -1
|
|
|
|
visited_forward = set()
|
|
visited_backward = set()
|
|
cst_fwd = {source: 0}
|
|
cst_bwd = {destination: 0}
|
|
parent_forward = {source: None}
|
|
parent_backward = {destination: None}
|
|
queue_forward: PriorityQueue[Any] = PriorityQueue()
|
|
queue_backward: PriorityQueue[Any] = PriorityQueue()
|
|
|
|
shortest_distance = np.inf
|
|
|
|
queue_forward.put((0, source))
|
|
queue_backward.put((0, destination))
|
|
|
|
if source == destination:
|
|
return 0
|
|
|
|
while not queue_forward.empty() and not queue_backward.empty():
|
|
_, v_fwd = queue_forward.get()
|
|
visited_forward.add(v_fwd)
|
|
|
|
_, v_bwd = queue_backward.get()
|
|
visited_backward.add(v_bwd)
|
|
|
|
shortest_distance = pass_and_relaxation(
|
|
graph_forward,
|
|
v_fwd,
|
|
visited_forward,
|
|
visited_backward,
|
|
cst_fwd,
|
|
cst_bwd,
|
|
queue_forward,
|
|
parent_forward,
|
|
shortest_distance,
|
|
)
|
|
|
|
shortest_distance = pass_and_relaxation(
|
|
graph_backward,
|
|
v_bwd,
|
|
visited_backward,
|
|
visited_forward,
|
|
cst_bwd,
|
|
cst_fwd,
|
|
queue_backward,
|
|
parent_backward,
|
|
shortest_distance,
|
|
)
|
|
|
|
if cst_fwd[v_fwd] + cst_bwd[v_bwd] >= shortest_distance:
|
|
break
|
|
|
|
if shortest_distance != np.inf:
|
|
shortest_path_distance = shortest_distance
|
|
return shortest_path_distance
|
|
|
|
|
|
graph_fwd = {
|
|
"B": [["C", 1]],
|
|
"C": [["D", 1]],
|
|
"D": [["F", 1]],
|
|
"E": [["B", 1], ["G", 2]],
|
|
"F": [],
|
|
"G": [["F", 1]],
|
|
}
|
|
graph_bwd = {
|
|
"B": [["E", 1]],
|
|
"C": [["B", 1]],
|
|
"D": [["C", 1]],
|
|
"F": [["D", 1], ["G", 1]],
|
|
"E": [[None, np.inf]],
|
|
"G": [["E", 2]],
|
|
}
|
|
|
|
if __name__ == "__main__":
|
|
import doctest
|
|
|
|
doctest.testmod()
|