Dynamic Maze Solver using BFS

PathPlanning/BreadthFirstSearch/dynamic_maze_solver.py

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+import matplotlib.pyplot as plt
+import matplotlib.colors as mcolors
+import numpy as np
+from collections import deque
+import random
+import matplotlib.animation as animation
+
+
+class MazeVisualizer:
+    """
+    Dynamic BFS maze-solving visualizer with moving target and evolving obstacles.
+    """
+
+    def __init__(self, maze, start, target):
+        self.maze = np.array(maze, dtype=int)
+        self.start_pos = start
+        self.target_pos = target
+        self.solver_pos = start
+
+        self.rows, self.cols = self.maze.shape
+        self.step_delay_ms = 200          # Animation frame delay
+        self.target_move_interval = 5     # Target moves every N frames
+        self.obstacle_change_prob = 0.01  # Random obstacle toggle probability
+
+        # --- State Tracking ---
+        self.path = []
+        self.visited_nodes = set()
+        self.breadcrumb_trail = [self.solver_pos]
+        self.frame_count = 0
+
+        # --- Plot Setup ---
+        self.fig, self.ax = plt.subplots(figsize=(8, 6))
+        plt.style.use('seaborn-v0_8-darkgrid')
+        self.fig.patch.set_facecolor('#2c2c2c')
+        self.ax.set_facecolor('#1e1e1e')
+
+        self.ax.set_xticks([])
+        self.ax.set_yticks([])
+
+        # Base maze
+        self.maze_plot = self.ax.imshow(self.maze, cmap='magma', interpolation='nearest')
+
+        # Visited overlay
+        self.visited_overlay = np.zeros((*self.maze.shape, 4))
+        self.visited_plot = self.ax.imshow(self.visited_overlay, interpolation='nearest')
+
+        # Path, breadcrumbs, solver, target
+        self.path_line, = self.ax.plot([], [], 'g-', linewidth=3, alpha=0.7, label='Path')
+        self.breadcrumbs_plot = self.ax.scatter([], [], c=[], cmap='viridis_r', s=50, alpha=0.6, label='Trail')
+        self.solver_plot, = self.ax.plot(
+            [self.solver_pos[1]], [self.solver_pos[0]],
+            'o', markersize=15, color='#00ffdd', label='Solver'
+        )
+        self.target_plot, = self.ax.plot(
+            [self.target_pos[1]], [self.target_pos[0]],
+            '*', markersize=20, color='#ff006a', label='Target'
+        )
+
+        self.ax.legend(facecolor='gray', framealpha=0.5, loc='upper right')
+        self.title = self.ax.set_title("Initializing Maze...", color='white', fontsize=14)
+
+    def _bfs(self):
+        """Performs BFS to find shortest path."""
+        queue = deque([(self.solver_pos, [self.solver_pos])])
+        visited = {self.solver_pos}
+
+        while queue:
+            (r, c), path = queue.popleft()
+
+            if (r, c) == self.target_pos:
+                return path, visited
+
+            for dr, dc in [(-1, 0), (1, 0), (0, -1), (0, 1)]:
+                nr, nc = r + dr, c + dc
+                if 0 <= nr < self.rows and 0 <= nc < self.cols and \
+                        self.maze[nr][nc] == 0 and (nr, nc) not in visited:
+                    visited.add((nr, nc))
+                    queue.append(((nr, nc), path + [(nr, nc)]))
+
+        return None, visited
+
+    def _update_target(self):
+        """Moves the target randomly to an adjacent open cell."""
+        tr, tc = self.target_pos
+        moves = [(-1, 0), (1, 0), (0, -1), (0, 1)]
+        random.shuffle(moves)
+        for dr, dc in moves:
+            nr, nc = tr + dr, tc + dc
+            if 0 <= nr < self.rows and 0 <= nc < self.cols and self.maze[nr][nc] == 0:
+                self.target_pos = (nr, nc)
+                break
+
+    def _update_obstacles(self):
+        """Randomly toggle a few obstacles."""
+        for r in range(self.rows):
+            for c in range(self.cols):
+                if (r, c) in [self.solver_pos, self.target_pos]:
+                    continue
+                if random.random() < self.obstacle_change_prob:
+                    self.maze[r, c] = 1 - self.maze[r, c]
+
+    def _update_frame(self, frame):
+        """Main animation loop."""
+        self.frame_count += 1
+
+        # --- State ---
+        if self.frame_count % self.target_move_interval == 0:
+            self._update_target()
+        self._update_obstacles()
+
+        self.path, self.visited_nodes = self._bfs()
+
+        # Move solver one step
+        if self.path and len(self.path) > 1:
+            self.solver_pos = self.path[1]
+            self.breadcrumb_trail.append(self.solver_pos)
+
+        # --- Visuals ---
+        self.maze_plot.set_data(self.maze)
+
+        # Visited overlay
+        self.visited_overlay.fill(0)
+        visited_color = mcolors.to_rgba('#0077b6', alpha=0.3)
+        for r, c in self.visited_nodes:
+            self.visited_overlay[r, c] = visited_color
+        self.visited_plot.set_data(self.visited_overlay)
+
+        # Path line
+        if self.path:
+            y, x = zip(*self.path)
+            self.path_line.set_data(x, y)
+        else:
+            self.path_line.set_data([], [])
+
+        # set_data() now receives sequences
+        self.solver_plot.set_data([self.solver_pos[1]], [self.solver_pos[0]])
+        self.target_plot.set_data([self.target_pos[1]], [self.target_pos[0]])
+
+        # Breadcrumbs
+        if self.breadcrumb_trail:
+            y, x = zip(*self.breadcrumb_trail)
+            colors = np.linspace(0.1, 1.0, len(y))
+            self.breadcrumbs_plot.set_offsets(np.c_[x, y])
+            self.breadcrumbs_plot.set_array(colors)
+
+        # Title update
+        if self.solver_pos == self.target_pos:
+            self.title.set_text("Dynamic Maze Solver")
+            self.title.set_color('lightgreen')
+            self.anim.event_source.stop()
+        else:
+            path_len = len(self.path) if self.path else "N/A"
+            self.title.set_text(f"Frame: {self.frame_count} | Path Length: {path_len}")
+            self.title.set_color('white' if self.path else 'coral')
+
+        return [
+            self.maze_plot, self.visited_plot, self.path_line,
+            self.solver_plot, self.target_plot, self.breadcrumbs_plot, self.title
+        ]
+
+    def run(self):
+        """Starts the animation."""
+        self.anim = animation.FuncAnimation(
+            self.fig,
+            self._update_frame,
+            frames=500,
+            interval=self.step_delay_ms,
+            blit=False,  
+            repeat=False
+        )
+        plt.show()
+
+
+if __name__ == "__main__":
+    initial_maze = [
+        [0, 1, 0, 0, 0, 0, 0, 0, 1, 0],
+        [0, 1, 0, 1, 1, 0, 1, 0, 1, 0],
+        [0, 0, 0, 1, 0, 0, 1, 0, 0, 0],
+        [0, 1, 0, 1, 0, 1, 1, 1, 1, 0],
+        [0, 1, 0, 0, 0, 0, 0, 0, 1, 0],
+        [0, 1, 1, 1, 1, 1, 1, 0, 1, 0],
+        [0, 0, 0, 0, 0, 0, 1, 0, 0, 0],
+        [1, 1, 1, 1, 0, 1, 1, 1, 1, 0],
+        [0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
+    ]
+
+    start_point = (0, 0)
+    end_point = (8, 9)
+
+    visualizer = MazeVisualizer(initial_maze, start_point, end_point)
+    visualizer.run()

docs/modules/5_path_planning/dynamic_bfs_maze_Solver/Dynamic_maze_Slover.rst

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+Dynamic Maze Solver using Breadth-First Search (BFS)
+====================================================
+
+.. contents:: Table of Contents
+   :local:
+   :depth: 2
+
+Overview
+--------
+
+This example demonstrates a **dynamic maze-solving algorithm** based on the
+**Breadth-First Search (BFS)** strategy. The visualizer dynamically updates a maze
+in real-time while the solver attempts to reach a moving target. 
+
+Unlike static pathfinding examples, this version introduces:
+
+- **A moving target** that relocates periodically.
+- **Randomly evolving obstacles** that can appear or disappear.
+- **Animated BFS exploration**, showing visited cells, computed paths, and breadcrumbs.
+
+This simulation provides intuition for dynamic pathfinding problems such as
+robot navigation in unpredictable environments.
+
+
+Algorithmic Background
+----------------------
+
+### Breadth-First Search (BFS)
+
+The BFS algorithm is a graph traversal method that explores nodes in layers, 
+guaranteeing the shortest path in an unweighted grid.
+
+Let the maze be represented as a grid:
+
+.. math::
+
+   M = \{ (i, j) \mid 0 \leq i < R, 0 \leq j < C \}
+
+where each cell is either *free (0)* or *obstacle (1)*.
+
+The BFS frontier expands as:
+
+.. math::
+
+   Q = [(s, [s])]
+
+where *s* is the start position, and the second term is the path history.
+
+At each iteration:
+
+.. math::
+
+   (r, c), path = Q.pop(0)
+
+   \text{for each neighbor } (r', c') \text{ in } N(r, c):
+       \text{if } (r', c') \text{ is free and unvisited:}
+           Q.append((r', c'), path + [(r', c')])
+
+The algorithm halts when the target node *t* is reached.
+
+Because BFS explores all nodes in increasing distance order, the path returned
+is the shortest (in terms of number of moves).
+
+
+Dynamic Components
+------------------
+
+### Moving Target
+
+Every few frames, the target moves randomly to an adjacent open cell:
+
+.. math::
+
+   T_{new} = T_{old} + \Delta
+
+where :math:`\Delta \in \{ (-1,0), (1,0), (0,-1), (0,1) \}`.
+
+This simulates dynamic goals or moving entities in robotic navigation.
+
+### Evolving Obstacles
+
+With a small probability :math:`p`, each cell toggles between *free* and *blocked*:
+
+.. math::
+
+   M_{i,j}^{t+1} =
+   \begin{cases}
+       1 - M_{i,j}^{t} & \text{with probability } p \\
+       M_{i,j}^{t} & \text{otherwise}
+   \end{cases}
+
+This reflects real-world conditions like temporary obstructions or environment changes.
+
+
+Visualization
+-------------
+
+The maze, solver, target, and BFS layers are visualized using **Matplotlib**.
+
+Elements include:
+
+- **Maze cells** – magma colormap (black = wall, bright = open)
+- **Visited nodes** – blue overlay with transparency
+- **Path line** – green connecting line
+- **Solver (robot)** – cyan circle
+- **Target** – magenta star
+- **Breadcrumbs** – trail of previously visited solver positions
+
+A sample animation frame:
+
+.. image:: ezgif.com-crop.jpg
+   :alt: Maze BFS dynamic visualizer frame
+   :align: center
+   :scale: 80 %
+
+
+Mathematical Insights
+---------------------
+
+- **BFS guarantees optimality** in unweighted grids.
+- The evolving maze introduces **non-stationarity**, requiring recomputation per frame.
+- The path length :math:`L_t` fluctuates as the environment changes.
+
+If :math:`E_t` is the set of explored nodes at frame :math:`t`, then:
+
+.. math::
+
+   L_t = |P_t|, \quad E_t = |V_t|
+
+where :math:`P_t` is the discovered path and :math:`V_t` is the visited node set.
+
+The solver continually re-estimates the path to accommodate new maze configurations.
+
+
+References
+----------
+
+- **Algorithm:** Breadth-First Search (BFS) :-`<https://en.wikipedia.org/wiki/Breadth-first_search>`_
+- **Visualization:** Matplotlib animation
+- **Maze Solver:**:-`<https://medium.com/@luthfisauqi17_68455/artificial-intelligence-search-problem-solve-maze-using-breadth-first-search-bfs-algorithm-255139c6e1a3>`__
+
+
+