Graphs : Bidirectional A* (#2015)

* implement bidirectional astar

* add type hints

* add wikipedia url

* format with black

* changes from review

graphs/bidirectional_a_star.py

@@ -0,0 +1,218 @@
+"""
+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:
+    """
+    >>> k = Node(0, 0, 4, 5, 0, None)
+    >>> k.calculate_heuristic()
+    9
+    >>> n = Node(1, 4, 3, 4, 2, None)
+    >>> n.calculate_heuristic()
+    2
+    >>> 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:
+        """
+        The heuristic here is the Manhattan Distance
+        Could elaborate to offer more than one choice
+        """
+        dy = abs(self.pos_x - self.goal_x)
+        dx = abs(self.pos_y - self.goal_y)
+        return dx + dy
+
+    def __lt__(self, other):
+        return self.f_cost < other.f_cost
+
+
+class AStar:
+    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
+
+        self.path = [(self.start.pos_y, self.start.pos_x)]
+        self.costs = [0]
+
+    def search(self):
+        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
+                self.path = self.retrace_path(current_node)
+                break
+
+            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):
+            print("No path found")
+
+    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
+
+            node_ = Node(
+                pos_x,
+                pos_y,
+                self.target.pos_y,
+                self.target.pos_x,
+                parent.g_cost + 1,
+                parent,
+            )
+            successors.append(node_)
+        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:
+    def __init__(self, start, goal):
+        self.fwd_astar = AStar(start, goal)
+        self.bwd_astar = AStar(goal, start)
+        self.reached = False
+        self.path = self.fwd_astar.path
+
+    def search(self):
+        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
+                self.retrace_bidirectional_path(current_fwd_node, current_bwd_node)
+                break
+
+            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)
+
+    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)
+        fwd_path.reverse()
+        path = fwd_path + bwd_path
+        return path
+
+
+# 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)
+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)
+bidir_astar.search()
+bd_end_time = time.time() - bd_start_time
+print(f"BidirectionalAStar execution time = {bd_end_time:f} seconds")