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A*算法在迷宫中的应用

问题描述

在一个迷宫游戏中，小怪物需要自动绕过障碍物并寻找主角。迷宫通常由小方格组成，红色格子是终点，绿色格子是起点，蓝色格子是墙壁。AI角色从起点开始，每一步只能向上、下、左、右移动一格，且不能穿越墙壁。目标是让AI角色用最少的步数到达终点。

解题思路

为了实现这一目标，我们引入了两个集合和一个公式：

每个格子都有三个属性：

• G：从起点走到当前格子的步数成本。
• H：在不考虑障碍的情况下，从当前格子走到终点的距离。
• F：综合评估，等于G和H之和，即从起点到当前格子再到终点的总步数。

算法步骤如下：

代码实现

def a_star_search(start, end):    open_list = []    close_list = []    open_list.append(start)        while len(open_list) > 0:        current_grid = find_min_grid(open_list)        open_list.remove(current_grid)        close_list.append(current_grid)                neighbors = get_neighbors(current_grid, open_list, close_list)        for grid in neighbors:            if grid not in open_list:                grid.init_grid(current_grid, end)                open_list.append(grid)                if any((grid.x == end.x and grid.y == end.y) for grid in open_list):            result_grid = next((grid for grid in open_list if grid.x == end.x and grid.y == end.y), None)            break            return result_griddef find_min_grid(open_list):    if not open_list:        return None    min_grid = open_list[0]    for grid in open_list:        if grid.f < min_grid.f:            min_grid = grid    return min_griddef get_neighbors(grid, open_list, close_list):    neighbors = []    if is_valid(grid.x, grid.y - 1, open_list, close_list):        neighbors.append(Grid(grid.x, grid.y - 1))    if is_valid(grid.x, grid.y + 1, open_list, close_list):        neighbors.append(Grid(grid.x, grid.y + 1))    if is_valid(grid.x - 1, grid.y, open_list, close_list):        neighbors.append(Grid(grid.x - 1, grid.y))    if is_valid(grid.x + 1, grid.y, open_list, close_list):        neighbors.append(Grid(grid.x + 1, grid.y))    return neighborsdef is_valid(x, y, open_list, close_list):    if x < 0 or x >= len(MAZE) or y < 0 or y >= len(MAZE[0]):        return False    if MAZE[x][y] == 1:        return False    if any(grid.x == x and grid.y == y for grid in open_list):        return False    if any(grid.x == x and grid.y == y for grid in close_list):        return False    return Trueclass Grid:    def __init__(self, x, y):        self.x = x        self.y = y        self.f = 0        self.g = 0        self.h = 0        self.parent = None        def init_grid(self, parent, end):        self.parent = parent        if parent is not None:            self.g = parent.g + 1        else:            self.g = 1        self.h = abs(self.x - end.x) + abs(self.y - end.y)        self.f = self.g + self.h

代码解释

迷宫设置与路径回溯

MAZE = [    [0, 0, 0, 0, 0, 0, 0],    [0, 0, 0, 1, 0, 0, 0],    [0, 0, 0, 1, 0, 0, 0],    [0, 0, 0, 1, 0, 0, 0],    [0, 0, 0, 0, 0, 0, 0]]start_grid = Grid(2, 1)end_grid = Grid(2, 5)result_grid = a_star_search(start_grid, end_grid)path = []while result_grid is not None:    path.append(Grid(result_grid.x, result_grid.y))    result_grid = result_grid.parentfor i in range(len(MAZE)):    for j in range(len(MAZE[0])):        if (i, j) in path:            print("*", end="")        else:            print(str(MAZE[i][j]), end="")    print()

结果展示

运行上述代码后，您可以看到迷宫地图和路径。路径用星号表示，迷宫中的0表示空地，1表示墙壁。

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