Minimum Moves to Move a Box to Their Target Location

Description

In a Sokoban-inspired puzzle, a player pushes a box through a grid to reach a target.

The m x n grid uses these characters:

- 'S' — the player's starting position (moves freely through empty cells).

- '.' — a free floor tile.

- '#' — an impassable wall.

- 'B' — the box (exactly one).

- 'T' — the target (exactly one).

A push occurs when the player moves into the box from one side, shoving it one step in the same direction — but only if the box's destination is empty. The player cannot walk through the box.

Return the minimum number of pushes to move the box onto the target, or -1 if impossible.

Code

class Solution:
    def minPushBox(self, grid: List[List[str]]) -> int: