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"""
https://en.wikipedia.org/wiki/Bidirectional_search
"""
import time
from math import sqrt
from typing import List, Tuple
# 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
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, pos_y, goal_x, goal_y, g_cost, parent):
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) -> 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, goal):
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 = []
self.reached = False
def search(self) -> List[Tuple[int]]:
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:
self.reached = True
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)
if not (self.reached):
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) -> List[Tuple[int]]:
"""
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, goal):
self.fwd_astar = AStar(start, goal)
self.bwd_astar = AStar(goal, start)
self.reached = False
def search(self) -> List[Tuple[int]]:
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:
self.reached = True
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)
if not self.reached:
return [self.fwd_astar.start.pos]
def retrace_bidirectional_path(
self, fwd_node: Node, bwd_node: Node
) -> List[Tuple[int]]:
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]
import doctest
doctest.testmod()
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)
path = bidir_astar.search()
bd_end_time = time.time() - bd_start_time
print(f"BidirectionalAStar execution time = {bd_end_time:f} seconds")
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