2850 - Minimum Moves to Spread Stones Over Grid.

Medium

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

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

Return the minimum number of moves required to place one stone in each cell.

Example 1:

Input: grid = [1,1,0,1,1,1,1,2,1]

Output: 3

Explanation: 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.

Example 2:

Input: grid = [1,3,0,1,0,0,1,0,3]

Output: 4

Explanation: 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.

Constraints:

• grid.length == grid[i].length == 3

• 0 <= grid[i][j] <= 9

• Sum of grid is equal to 9.