Python/graphs/bidirectional_breadth_first_search.py

"""
https://en.wikipedia.org/wiki/Bidirectional_search
"""

import time
from typing import List, Tuple

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:
    def __init__(self, pos_x, pos_y, goal_x, goal_y, 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.parent = parent


class BreadthFirstSearch:
    """
    >>> bfs = BreadthFirstSearch((0, 0), (len(grid) - 1, len(grid[0]) - 1))
    >>> (bfs.start.pos_y + delta[3][0], bfs.start.pos_x + delta[3][1])
    (0, 1)
    >>> [x.pos for x in bfs.get_successors(bfs.start)]
    [(1, 0), (0, 1)]
    >>> (bfs.start.pos_y + delta[2][0], bfs.start.pos_x + delta[2][1])
    (1, 0)
    >>> bfs.retrace_path(bfs.start)
    [(0, 0)]
    >>> bfs.search()  # doctest: +NORMALIZE_WHITESPACE
    [(0, 0), (1, 0), (2, 0), (3, 0), (3, 1), (4, 1),
     (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (6, 5), (6, 6)]
    """

    def __init__(self, start, goal):
        self.start = Node(start[1], start[0], goal[1], goal[0], None)
        self.target = Node(goal[1], goal[0], goal[1], goal[0], None)

        self.node_queue = [self.start]
        self.reached = False

    def search(self) -> List[Tuple[int]]:
        while self.node_queue:
            current_node = self.node_queue.pop(0)

            if current_node.pos == self.target.pos:
                self.reached = True
                return self.retrace_path(current_node)

            successors = self.get_successors(current_node)

            for node in successors:
                self.node_queue.append(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)
            )
        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 BidirectionalBreadthFirstSearch:
    """
    >>> bd_bfs = BidirectionalBreadthFirstSearch((0, 0), (len(grid) - 1,
    ...                                                   len(grid[0]) - 1))
    >>> bd_bfs.fwd_bfs.start.pos == bd_bfs.bwd_bfs.target.pos
    True
    >>> bd_bfs.retrace_bidirectional_path(bd_bfs.fwd_bfs.start,
    ...                                     bd_bfs.bwd_bfs.start)
    [(0, 0)]
    >>> bd_bfs.search()  # doctest: +NORMALIZE_WHITESPACE
    [(0, 0), (0, 1), (0, 2), (1, 2), (2, 2), (2, 3),
     (2, 4), (3, 4), (3, 5), (3, 6), (4, 6), (5, 6), (6, 6)]
    """

    def __init__(self, start, goal):
        self.fwd_bfs = BreadthFirstSearch(start, goal)
        self.bwd_bfs = BreadthFirstSearch(goal, start)
        self.reached = False

    def search(self) -> List[Tuple[int]]:
        while self.fwd_bfs.node_queue or self.bwd_bfs.node_queue:
            current_fwd_node = self.fwd_bfs.node_queue.pop(0)
            current_bwd_node = self.bwd_bfs.node_queue.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_bfs.target = current_bwd_node
            self.bwd_bfs.target = current_fwd_node

            successors = {
                self.fwd_bfs: self.fwd_bfs.get_successors(current_fwd_node),
                self.bwd_bfs: self.bwd_bfs.get_successors(current_bwd_node),
            }

            for bfs in [self.fwd_bfs, self.bwd_bfs]:
                for node in successors[bfs]:
                    bfs.node_queue.append(node)

        if not self.reached:
            return [self.fwd_bfs.start.pos]

    def retrace_bidirectional_path(
        self, fwd_node: Node, bwd_node: Node
    ) -> List[Tuple[int]]:
        fwd_path = self.fwd_bfs.retrace_path(fwd_node)
        bwd_path = self.bwd_bfs.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_bfs_time = time.time()
    bfs = BreadthFirstSearch(init, goal)
    path = bfs.search()
    bfs_time = time.time() - start_bfs_time

    print("Unidirectional BFS computation time : ", bfs_time)

    start_bd_bfs_time = time.time()
    bd_bfs = BidirectionalBreadthFirstSearch(init, goal)
    bd_path = bd_bfs.search()
    bd_bfs_time = time.time() - start_bd_bfs_time

    print("Bidirectional BFS computation time : ", bd_bfs_time)