1263 - Minimum Moves to Move a Box to Their Target Location\.

Hard

A storekeeper is a game in which the player pushes boxes around in a warehouse trying to get them to target locations.

The game is represented by an m x n grid of characters grid where each element is a wall, floor, or box.

Your task is to move the box 'B' to the target position 'T' under the following rules:

• The character 'S' represents the player. The player can move up, down, left, right in grid if it is a floor (empty cell).

• The character '.' represents the floor which means a free cell to walk.

• The character '#' represents the wall which means an obstacle (impossible to walk there).

• There is only one box 'B' and one target cell 'T' in the grid.

• The box can be moved to an adjacent free cell by standing next to the box and then moving in the direction of the box. This is a push.

• The player cannot walk through the box.

Return the minimum number of pushes to move the box to the target. If there is no way to reach the target, return -1.

Example 1:

Input:

grid = [ ["#","#","#","#","#","#"],
        ["#","T","#","#","#","#"],
        ["#",".",".","B",".","#"],
        ["#",".","#","#",".","#"],
        ["#",".",".",".","S","#"],
        ["#","#","#","#","#","#"]]

Output: 3

Explanation: We return only the number of times the box is pushed.

Example 2:

Input:

grid = [ ["#","#","#","#","#","#"],
        ["#","T","#","#","#","#"],
        ["#",".",".","B",".","#"],
        ["#","#","#","#",".","#"],
        ["#",".",".",".","S","#"],
        ["#","#","#","#","#","#"]]

Output: -1

Example 3:

Input:

grid = [ ["#","#","#","#","#","#"],
        ["#","T",".",".","#","#"],
        ["#",".","#","B",".","#"],
        ["#",".",".",".",".","#"],
        ["#",".",".",".","S","#"],
        ["#","#","#","#","#","#"]]

Output: 5

Explanation: push the box down, left, left, up and up.

Constraints:

• m == grid.length

• n == grid[i].length

• 1 <= m, n <= 20

• grid contains only characters '.', '#', 'S', 'T', or 'B'.

• There is only one character 'S', 'B', and 'T' in the grid.