7_expspace_enchanted_maze.py

# The Enchanted Maze

'''Deep within a mystical forest, there lies an enchanted maze guarded by magical creatures. The maze is filled with twisting pathways and hidden traps. The only way to navigate through the maze safely is by following a specific sequence of moves.

Your task is to determine if it is possible to find a sequence of moves that leads you through the maze without encountering any traps. We can encode this problem as an EXP-Space problem.

Let's assume that the maze consists of a grid of cells, and each cell can be represented by its coordinates (x, y). The moves can be represented as a sequence of directions, such as 'up', 'down', 'left', and 'right'.

To solve this EXP-Space problem, we can use a backtracking algorithm combined with pruning techniques. We will systematically generate and explore all possible sequences of moves and check if any of them lead to the maze's exit without encountering any traps. Pruning techniques can be applied to eliminate certain branches of the search tree based on early failures or constraints.'''


def navigate_maze(maze, start, exit):
    n = len(maze)
    
    def backtrack(position, path):
        if position == exit:
            return path
        
        x, y = position
        for move in ['up', 'down', 'left', 'right']:
            new_x, new_y = get_new_position(position, move)
            if is_valid_move(new_x, new_y) and not is_trap(new_x, new_y):
                new_position = (new_x, new_y)
                result = backtrack(new_position, path + [move])
                if result:
                    return result
        
        return None
    
    def get_new_position(position, move):
        x, y = position
        if move == 'up':
            return x - 1, y
        elif move == 'down':
            return x + 1, y
        elif move == 'left':
            return x, y - 1
        elif move == 'right':
            return x, y + 1
    
    def is_valid_move(x, y):
        return 0 <= x < n and 0 <= y < n
    
    def is_trap(x, y):
        # Additional logic to check if the cell at (x, y) is a trap
        return False
    
    return backtrack(start, [])

# Example usage
maze = [
    [0, 0, 0, 0],
    [0, 1, 1, 0],
    [0, 0, 0, 0],
    [0, 1, 1, 0]
]
start = (0, 0)
exit = (3, 3)

path = navigate_maze(maze, start, exit)
if path:
    print("A valid path through the maze is:", path)
else:
    print("No valid path through the maze exists.")


'''In this code, we define a function navigate_maze() that takes a maze, a starting position, and an exit position as input. The main algorithm is implemented in the backtrack() function using a backtracking approach.

The backtrack() function systematically generates and explores all possible sequences of moves by recursively trying out each direction. At each step, it checks if the current move leads to a valid cell and if the cell is a trap by applying the is_valid_move() and is_trap() functions, respectively. If a valid path to the exit is found, it is returned; otherwise, the search continues.

The `get_new_position(), is_valid_move(), and is_trap()` functions provide the necessary logic to determine the new position after a move, check if the move is within the maze boundaries, and identify if the cell at the current position is a trap, respectively.'''