leetcode-problemset/leetcode-cn/originData/minimum-moves-to-spread-stones-over-grid.json

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            "title": "Minimum Moves to Spread Stones Over Grid",
            "titleSlug": "minimum-moves-to-spread-stones-over-grid",
            "content": "<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>\n\n<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>\n\n<p>Return <em>the <strong>minimum number of moves</strong> required to place one stone in each cell</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/08/23/example1-3.svg\" style=\"width: 401px; height: 281px;\" />\n<pre>\n<strong>Input:</strong> grid = [[1,1,0],[1,1,1],[1,2,1]]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> One possible sequence of moves to place one stone in each cell is: \n1- Move one stone from cell (2,1) to cell (2,2).\n2- Move one stone from cell (2,2) to cell (1,2).\n3- Move one stone from cell (1,2) to cell (0,2).\nIn total, it takes 3 moves to place one stone in each cell of the grid.\nIt can be shown that 3 is the minimum number of moves required to place one stone in each cell.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/08/23/example2-2.svg\" style=\"width: 401px; height: 281px;\" />\n<pre>\n<strong>Input:</strong> grid = [[1,3,0],[1,0,0],[1,0,3]]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> One possible sequence of moves to place one stone in each cell is:\n1- Move one stone from cell (0,1) to cell (0,2).\n2- Move one stone from cell (0,1) to cell (1,1).\n3- Move one stone from cell (2,2) to cell (1,2).\n4- Move one stone from cell (2,2) to cell (2,1).\nIn total, it takes 4 moves to place one stone in each cell of the grid.\nIt can be shown that 4 is the minimum number of moves required to place one stone in each cell.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>grid.length == grid[i].length == 3</code></li>\n\t<li><code>0 &lt;= grid[i][j] &lt;= 9</code></li>\n\t<li>Sum of <code>grid</code> is equal to <code>9</code>.</li>\n</ul>\n",
            "translatedTitle": "将石头分散到网格图的最少移动次数",
            "translatedContent": "<p>给你一个大小为 <code>3 * 3</code>&nbsp;，下标从 <strong>0</strong>&nbsp;开始的二维整数矩阵&nbsp;<code>grid</code>&nbsp;，分别表示每一个格子里石头的数目。网格图中总共恰好有&nbsp;<code>9</code>&nbsp;个石头，一个格子里可能会有 <strong>多个</strong>&nbsp;石头。</p>\n\n<p>每一次操作中，你可以将一个石头从它当前所在格子移动到一个至少有一条公共边的相邻格子。</p>\n\n<p>请你返回每个格子恰好有一个石头的 <strong>最少移动次数</strong>&nbsp;。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/08/23/example1-3.svg\" style=\"width: 401px; height: 281px;\" /></p>\n\n<pre>\n<b>输入：</b>grid = [[1,1,0],[1,1,1],[1,2,1]]\n<b>输出：</b>3\n<b>解释：</b>让每个格子都有一个石头的一个操作序列为：\n1 - 将一个石头从格子 (2,1) 移动到 (2,2) 。\n2 - 将一个石头从格子 (2,2) 移动到 (1,2) 。\n3 - 将一个石头从格子 (1,2) 移动到 (0,2) 。\n总共需要 3 次操作让每个格子都有一个石头。\n让每个格子都有一个石头的最少操作次数为 3 。\n</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/08/23/example2-2.svg\" style=\"width: 401px; height: 281px;\" /></p>\n\n<pre>\n<b>输入：</b>grid = [[1,3,0],[1,0,0],[1,0,3]]\n<b>输出：</b>4\n<b>解释：</b>让每个格子都有一个石头的一个操作序列为：\n1 - 将一个石头从格子 (0,1) 移动到 (0,2) 。\n2 - 将一个石头从格子 (0,1) 移动到 (1,1) 。\n3 - 将一个石头从格子 (2,2) 移动到 (1,2) 。\n4 - 将一个石头从格子 (2,2) 移动到 (2,1) 。\n总共需要 4 次操作让每个格子都有一个石头。\n让每个格子都有一个石头的最少操作次数为 4 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>grid.length == grid[i].length == 3</code></li>\n\t<li><code>0 &lt;= grid[i][j] &lt;= 9</code></li>\n\t<li><code>grid</code>&nbsp;中元素之和为&nbsp;<code>9</code> 。</li>\n</ul>\n",
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                "There are at most <code>4</code> cells with more than one stone.",
                "Let <code>a</code> be the number of cells containing more than one stone, and <code>b</code> be the number of cells containing no stones. <code></code>. <code>b^a ≤ 6561</code>. Use this fact to come up with a bruteforce.",
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