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leetcode-problemset/leetcode-cn/originData/maximum-sum-of-an-hourglass.json
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"question": {
"questionId": "2508",
"questionFrontendId": "2428",
"categoryTitle": "Algorithms",
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"title": "Maximum Sum of an Hourglass",
"titleSlug": "maximum-sum-of-an-hourglass",
"content": "<p>You are given an <code>m x n</code> integer matrix <code>grid</code>.</p>\n\n<p>We define an <strong>hourglass</strong> as a part of the matrix with the following form:</p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/08/21/img.jpg\" style=\"width: 243px; height: 243px;\" />\n<p>Return <em>the <strong>maximum</strong> sum of the elements of an hourglass</em>.</p>\n\n<p><strong>Note</strong> that an hourglass cannot be rotated and must be entirely contained within the matrix.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/08/21/1.jpg\" style=\"width: 323px; height: 323px;\" />\n<pre>\n<strong>Input:</strong> grid = [[6,2,1,3],[4,2,1,5],[9,2,8,7],[4,1,2,9]]\n<strong>Output:</strong> 30\n<strong>Explanation:</strong> The cells shown above represent the hourglass with the maximum sum: 6 + 2 + 1 + 2 + 9 + 2 + 8 = 30.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/08/21/2.jpg\" style=\"width: 243px; height: 243px;\" />\n<pre>\n<strong>Input:</strong> grid = [[1,2,3],[4,5,6],[7,8,9]]\n<strong>Output:</strong> 35\n<strong>Explanation:</strong> There is only one hourglass in the matrix, with the sum: 1 + 2 + 3 + 5 + 7 + 8 + 9 = 35.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>m == grid.length</code></li>\n\t<li><code>n == grid[i].length</code></li>\n\t<li><code>3 &lt;= m, n &lt;= 150</code></li>\n\t<li><code>0 &lt;= grid[i][j] &lt;= 10<sup>6</sup></code></li>\n</ul>\n",
"translatedTitle": "沙漏的最大总和",
"translatedContent": "<p>给你一个大小为 <code>m x n</code> 的整数矩阵 <code>grid</code> 。</p>\n\n<p>按以下形式将矩阵的一部分定义为一个 <strong>沙漏</strong> </p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/08/21/img.jpg\" style=\"width: 243px; height: 243px;\">\n<p>返回沙漏中元素的 <strong>最大</strong> 总和。</p>\n\n<p><strong>注意:</strong>沙漏无法旋转且必须整个包含在矩阵中。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/08/21/1.jpg\" style=\"width: 323px; height: 323px;\">\n<pre><strong>输入:</strong>grid = [[6,2,1,3],[4,2,1,5],[9,2,8,7],[4,1,2,9]]\n<strong>输出:</strong>30\n<strong>解释:</strong>上图中的单元格表示元素总和最大的沙漏6 + 2 + 1 + 2 + 9 + 2 + 8 = 30 。\n</pre>\n\n<p><strong>示例 2</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/08/21/2.jpg\" style=\"width: 243px; height: 243px;\">\n<pre><strong>输入:</strong>grid = [[1,2,3],[4,5,6],[7,8,9]]\n<strong>输出:</strong>35\n<strong>解释:</strong>上图中的单元格表示元素总和最大的沙漏1 + 2 + 3 + 5 + 7 + 8 + 9 = 35 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>m == grid.length</code></li>\n\t<li><code>n == grid[i].length</code></li>\n\t<li><code>3 &lt;= m, n &lt;= 150</code></li>\n\t<li><code>0 &lt;= grid[i][j] &lt;= 10<sup>6</sup></code></li>\n</ul>\n",
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"Each 3x3 submatrix has exactly one hourglass.",
"Find the sum of each hourglass in the matrix and return the largest of these values."
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