推箱子

「推箱子」是一款风靡全球的益智小游戏，玩家需要将箱子推到仓库中的目标位置。

游戏地图用大小为 m x n 的网格 grid 表示，其中每个元素可以是墙、地板或者是箱子。

现在你将作为玩家参与游戏，按规则将箱子 'B' 移动到目标位置 'T' ：

• 玩家用字符 'S' 表示，只要他在地板上，就可以在网格中向上、下、左、右四个方向移动。
• 地板用字符 '.' 表示，意味着可以自由行走。
• 墙用字符 '#' 表示，意味着障碍物，不能通行。 
• 箱子仅有一个，用字符 'B' 表示。相应地，网格上有一个目标位置 'T'。
• 玩家需要站在箱子旁边，然后沿着箱子的方向进行移动，此时箱子会被移动到相邻的地板单元格。记作一次「推动」。
• 玩家无法越过箱子。

返回将箱子推到目标位置的最小 推动 次数，如果无法做到，请返回 -1。

 

示例 1：

输入：grid = [["#","#","#","#","#","#"],
             ["#","T","#","#","#","#"],
             ["#",".",".","B",".","#"],
             ["#",".","#","#",".","#"],
             ["#",".",".",".","S","#"],
             ["#","#","#","#","#","#"]]
输出：3
解释：我们只需要返回推箱子的次数。

示例 2：

输入：grid = [["#","#","#","#","#","#"],
             ["#","T","#","#","#","#"],
             ["#",".",".","B",".","#"],
             ["#","#","#","#",".","#"],
             ["#",".",".",".","S","#"],
             ["#","#","#","#","#","#"]]
输出：-1

示例 3：

输入：grid = [["#","#","#","#","#","#"],
             ["#","T",".",".","#","#"],
             ["#",".","#","B",".","#"],
             ["#",".",".",".",".","#"],
             ["#",".",".",".","S","#"],
             ["#","#","#","#","#","#"]]
输出：5
解释：向下、向左、向左、向上再向上。

 

提示：

• m == grid.length
• n == grid[i].length
• 1 <= m, n <= 20
• grid 仅包含字符 '.', '#',  'S' , 'T', 以及 'B'。
• grid 中 'S', 'B' 和 'T' 各只能出现一个。

This solution uses a Breadth-First Search (BFS) approach to simulate the movement of both the player and the box in a grid-based puzzle game. The algorithm involves checking every possible movement of the box and corresponding positioning of the player necessary to push the box. For every box move, the player's ability to reach the position needed to make that push is verified through another BFS that takes into account the current box's position as an obstacle.

O((m*n)^3)

O((m*n)^2)