{leetcode}/problems/minimum-moves-to-spread-stones-over-grid/[LeetCode - 2850. Minimum Moves to Spread Stones Over Grid ^]
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: <img alt="" src="https://assets.leetcode.com/uploads/2023/08/23/example1-3.svg" style="width: 401px; height: 281px;" />
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: <img alt="" src="https://assets.leetcode.com/uploads/2023/08/23/example2-2.svg" style="width: 401px; height: 281px;" />
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
gridis equal to9.