## Python, graph, bidirectional_a_star.py

``````"""
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")
``````