mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 05:21:09 +00:00
24d3cf8244
* The black formatter is no longer beta
* pre-commit autoupdate
* pre-commit autoupdate
* Remove project_euler/problem_145 which is killing our CI tests
* updating DIRECTORY.md
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
259 lines
8.0 KiB
Python
259 lines
8.0 KiB
Python
"""
|
|
https://en.wikipedia.org/wiki/Bidirectional_search
|
|
"""
|
|
from __future__ import annotations
|
|
|
|
import time
|
|
from math import sqrt
|
|
|
|
# 1 for manhattan, 0 for euclidean
|
|
HEURISTIC = 0
|
|
|
|
grid = [
|
|
[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 1, 0, 0, 0, 0, 0], # 0 are free path whereas 1's are obstacles
|
|
[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 1, 0, 0, 0, 0],
|
|
[1, 0, 1, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 0, 0, 0],
|
|
[0, 0, 0, 0, 1, 0, 0],
|
|
]
|
|
|
|
delta = [[-1, 0], [0, -1], [1, 0], [0, 1]] # up, left, down, right
|
|
|
|
TPosition = tuple[int, int]
|
|
|
|
|
|
class Node:
|
|
"""
|
|
>>> k = Node(0, 0, 4, 3, 0, None)
|
|
>>> k.calculate_heuristic()
|
|
5.0
|
|
>>> n = Node(1, 4, 3, 4, 2, None)
|
|
>>> n.calculate_heuristic()
|
|
2.0
|
|
>>> l = [k, n]
|
|
>>> n == l[0]
|
|
False
|
|
>>> l.sort()
|
|
>>> n == l[0]
|
|
True
|
|
"""
|
|
|
|
def __init__(
|
|
self,
|
|
pos_x: int,
|
|
pos_y: int,
|
|
goal_x: int,
|
|
goal_y: int,
|
|
g_cost: int,
|
|
parent: Node | None,
|
|
) -> None:
|
|
self.pos_x = pos_x
|
|
self.pos_y = pos_y
|
|
self.pos = (pos_y, pos_x)
|
|
self.goal_x = goal_x
|
|
self.goal_y = goal_y
|
|
self.g_cost = g_cost
|
|
self.parent = parent
|
|
self.h_cost = self.calculate_heuristic()
|
|
self.f_cost = self.g_cost + self.h_cost
|
|
|
|
def calculate_heuristic(self) -> float:
|
|
"""
|
|
Heuristic for the A*
|
|
"""
|
|
dy = self.pos_x - self.goal_x
|
|
dx = self.pos_y - self.goal_y
|
|
if HEURISTIC == 1:
|
|
return abs(dx) + abs(dy)
|
|
else:
|
|
return sqrt(dy**2 + dx**2)
|
|
|
|
def __lt__(self, other: Node) -> bool:
|
|
return self.f_cost < other.f_cost
|
|
|
|
|
|
class AStar:
|
|
"""
|
|
>>> astar = AStar((0, 0), (len(grid) - 1, len(grid[0]) - 1))
|
|
>>> (astar.start.pos_y + delta[3][0], astar.start.pos_x + delta[3][1])
|
|
(0, 1)
|
|
>>> [x.pos for x in astar.get_successors(astar.start)]
|
|
[(1, 0), (0, 1)]
|
|
>>> (astar.start.pos_y + delta[2][0], astar.start.pos_x + delta[2][1])
|
|
(1, 0)
|
|
>>> astar.retrace_path(astar.start)
|
|
[(0, 0)]
|
|
>>> astar.search() # doctest: +NORMALIZE_WHITESPACE
|
|
[(0, 0), (1, 0), (2, 0), (2, 1), (2, 2), (2, 3), (3, 3),
|
|
(4, 3), (4, 4), (5, 4), (5, 5), (6, 5), (6, 6)]
|
|
"""
|
|
|
|
def __init__(self, start: TPosition, goal: TPosition):
|
|
self.start = Node(start[1], start[0], goal[1], goal[0], 0, None)
|
|
self.target = Node(goal[1], goal[0], goal[1], goal[0], 99999, None)
|
|
|
|
self.open_nodes = [self.start]
|
|
self.closed_nodes: list[Node] = []
|
|
|
|
self.reached = False
|
|
|
|
def search(self) -> list[TPosition]:
|
|
while self.open_nodes:
|
|
# Open Nodes are sorted using __lt__
|
|
self.open_nodes.sort()
|
|
current_node = self.open_nodes.pop(0)
|
|
|
|
if current_node.pos == self.target.pos:
|
|
return self.retrace_path(current_node)
|
|
|
|
self.closed_nodes.append(current_node)
|
|
successors = self.get_successors(current_node)
|
|
|
|
for child_node in successors:
|
|
if child_node in self.closed_nodes:
|
|
continue
|
|
|
|
if child_node not in self.open_nodes:
|
|
self.open_nodes.append(child_node)
|
|
else:
|
|
# retrieve the best current path
|
|
better_node = self.open_nodes.pop(self.open_nodes.index(child_node))
|
|
|
|
if child_node.g_cost < better_node.g_cost:
|
|
self.open_nodes.append(child_node)
|
|
else:
|
|
self.open_nodes.append(better_node)
|
|
|
|
return [self.start.pos]
|
|
|
|
def get_successors(self, parent: Node) -> list[Node]:
|
|
"""
|
|
Returns a list of successors (both in the grid and free spaces)
|
|
"""
|
|
successors = []
|
|
for action in delta:
|
|
pos_x = parent.pos_x + action[1]
|
|
pos_y = parent.pos_y + action[0]
|
|
if not (0 <= pos_x <= len(grid[0]) - 1 and 0 <= pos_y <= len(grid) - 1):
|
|
continue
|
|
|
|
if grid[pos_y][pos_x] != 0:
|
|
continue
|
|
|
|
successors.append(
|
|
Node(
|
|
pos_x,
|
|
pos_y,
|
|
self.target.pos_y,
|
|
self.target.pos_x,
|
|
parent.g_cost + 1,
|
|
parent,
|
|
)
|
|
)
|
|
return successors
|
|
|
|
def retrace_path(self, node: Node | None) -> list[TPosition]:
|
|
"""
|
|
Retrace the path from parents to parents until start node
|
|
"""
|
|
current_node = node
|
|
path = []
|
|
while current_node is not None:
|
|
path.append((current_node.pos_y, current_node.pos_x))
|
|
current_node = current_node.parent
|
|
path.reverse()
|
|
return path
|
|
|
|
|
|
class BidirectionalAStar:
|
|
"""
|
|
>>> bd_astar = BidirectionalAStar((0, 0), (len(grid) - 1, len(grid[0]) - 1))
|
|
>>> bd_astar.fwd_astar.start.pos == bd_astar.bwd_astar.target.pos
|
|
True
|
|
>>> bd_astar.retrace_bidirectional_path(bd_astar.fwd_astar.start,
|
|
... bd_astar.bwd_astar.start)
|
|
[(0, 0)]
|
|
>>> bd_astar.search() # doctest: +NORMALIZE_WHITESPACE
|
|
[(0, 0), (0, 1), (0, 2), (1, 2), (1, 3), (2, 3), (2, 4),
|
|
(2, 5), (3, 5), (4, 5), (5, 5), (5, 6), (6, 6)]
|
|
"""
|
|
|
|
def __init__(self, start: TPosition, goal: TPosition) -> None:
|
|
self.fwd_astar = AStar(start, goal)
|
|
self.bwd_astar = AStar(goal, start)
|
|
self.reached = False
|
|
|
|
def search(self) -> list[TPosition]:
|
|
while self.fwd_astar.open_nodes or self.bwd_astar.open_nodes:
|
|
self.fwd_astar.open_nodes.sort()
|
|
self.bwd_astar.open_nodes.sort()
|
|
current_fwd_node = self.fwd_astar.open_nodes.pop(0)
|
|
current_bwd_node = self.bwd_astar.open_nodes.pop(0)
|
|
|
|
if current_bwd_node.pos == current_fwd_node.pos:
|
|
return self.retrace_bidirectional_path(
|
|
current_fwd_node, current_bwd_node
|
|
)
|
|
|
|
self.fwd_astar.closed_nodes.append(current_fwd_node)
|
|
self.bwd_astar.closed_nodes.append(current_bwd_node)
|
|
|
|
self.fwd_astar.target = current_bwd_node
|
|
self.bwd_astar.target = current_fwd_node
|
|
|
|
successors = {
|
|
self.fwd_astar: self.fwd_astar.get_successors(current_fwd_node),
|
|
self.bwd_astar: self.bwd_astar.get_successors(current_bwd_node),
|
|
}
|
|
|
|
for astar in [self.fwd_astar, self.bwd_astar]:
|
|
for child_node in successors[astar]:
|
|
if child_node in astar.closed_nodes:
|
|
continue
|
|
|
|
if child_node not in astar.open_nodes:
|
|
astar.open_nodes.append(child_node)
|
|
else:
|
|
# retrieve the best current path
|
|
better_node = astar.open_nodes.pop(
|
|
astar.open_nodes.index(child_node)
|
|
)
|
|
|
|
if child_node.g_cost < better_node.g_cost:
|
|
astar.open_nodes.append(child_node)
|
|
else:
|
|
astar.open_nodes.append(better_node)
|
|
|
|
return [self.fwd_astar.start.pos]
|
|
|
|
def retrace_bidirectional_path(
|
|
self, fwd_node: Node, bwd_node: Node
|
|
) -> list[TPosition]:
|
|
fwd_path = self.fwd_astar.retrace_path(fwd_node)
|
|
bwd_path = self.bwd_astar.retrace_path(bwd_node)
|
|
bwd_path.pop()
|
|
bwd_path.reverse()
|
|
path = fwd_path + bwd_path
|
|
return path
|
|
|
|
|
|
if __name__ == "__main__":
|
|
# all coordinates are given in format [y,x]
|
|
init = (0, 0)
|
|
goal = (len(grid) - 1, len(grid[0]) - 1)
|
|
for elem in grid:
|
|
print(elem)
|
|
|
|
start_time = time.time()
|
|
a_star = AStar(init, goal)
|
|
path = a_star.search()
|
|
end_time = time.time() - start_time
|
|
print(f"AStar execution time = {end_time:f} seconds")
|
|
|
|
bd_start_time = time.time()
|
|
bidir_astar = BidirectionalAStar(init, goal)
|
|
bd_end_time = time.time() - bd_start_time
|
|
print(f"BidirectionalAStar execution time = {bd_end_time:f} seconds")
|