<p>You are given a <strong>0-indexed</strong> 2D integer matrix <code>grid</code> of size <code>3 * 3</code>, representing the number of stones in each cell. The grid contains exactly <code>9</code> stones, and there can be <strong>multiple</strong> stones in a single cell.</p>

<p>In one move, you can move a single stone from its current cell to any other cell if the two cells share a side.</p>

<p>Return <em>the <strong>minimum number of moves</strong> required to place one stone in each cell</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2023/08/23/example1-3.svg" style="width: 401px; height: 281px;" />
<pre>
<strong>Input:</strong> grid = [[1,1,0],[1,1,1],[1,2,1]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> One possible sequence of moves to place one stone in each cell is: 
1- Move one stone from cell (2,1) to cell (2,2).
2- Move one stone from cell (2,2) to cell (1,2).
3- Move one stone from cell (1,2) to cell (0,2).
In total, it takes 3 moves to place one stone in each cell of the grid.
It can be shown that 3 is the minimum number of moves required to place one stone in each cell.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2023/08/23/example2-2.svg" style="width: 401px; height: 281px;" />
<pre>
<strong>Input:</strong> grid = [[1,3,0],[1,0,0],[1,0,3]]
<strong>Output:</strong> 4
<strong>Explanation:</strong> One possible sequence of moves to place one stone in each cell is:
1- Move one stone from cell (0,1) to cell (0,2).
2- Move one stone from cell (0,1) to cell (1,1).
3- Move one stone from cell (2,2) to cell (1,2).
4- Move one stone from cell (2,2) to cell (2,1).
In total, it takes 4 moves to place one stone in each cell of the grid.
It can be shown that 4 is the minimum number of moves required to place one stone in each cell.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>grid.length == grid[i].length == 3</code></li>
	<li><code>0 &lt;= grid[i][j] &lt;= 9</code></li>
	<li>Sum of <code>grid</code> is equal to <code>9</code>.</li>
</ul>

from collections import deque

class Solution:
    def minimumMoves(self, grid: List[List[int]]) -> int:
        def neighbors(r, c):
            for nr, nc in ((r-1, c), (r+1, c), (r, c-1), (r, c+1)):
                if 0 <= nr < 3 and 0 <= nc < 3:
                    yield nr, nc

        initial = tuple(tuple(row) for row in grid)
        target = ((1, 1, 1), (1, 1, 1), (1, 1, 1))
        if initial == target:
            return 0
        
        queue = deque([(initial, 0)])  # (current configuration, move count)
        seen = {initial}

        while queue:
            current, moves = queue.popleft()
            # Convert to list of lists for mutability
            grid = [list(row) for row in current]
            
            # Try moving each stone
            for r in range(3):
                for c in range(3):
                    if grid[r][c] > 1:  # More than one stone, can move one out
                        for nr, nc in neighbors(r, c):
                            new_grid = [row[:] for row in grid]
                            new_grid[r][c] -= 1
                            new_grid[nr][nc] += 1
                            new_config = tuple(tuple(row) for row in new_grid)
                            if new_config == target:
                                return moves + 1
                            if new_config not in seen:
                                seen.add(new_config)
                                queue.append((new_config, moves + 1))

        return -1  # Should never be reached if input is guaranteed to be solvable
     
18900