leetcode-problemset/leetcode-cn/originData/get-biggest-three-rhombus-sums-in-a-grid.json

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            "categoryTitle": "Algorithms",
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            "title": "Get Biggest Three Rhombus Sums in a Grid",
            "titleSlug": "get-biggest-three-rhombus-sums-in-a-grid",
            "content": "<p>You are given an <code>m x n</code> integer matrix <code>grid</code>​​​.</p>\n\n<p>A <strong>rhombus sum</strong> is the sum of the elements that form <strong>the</strong> <strong>border</strong> of a regular rhombus shape in <code>grid</code>​​​. The rhombus must have the shape of a square rotated 45 degrees with each of the corners centered in a grid cell. Below is an image of four valid rhombus shapes with the corresponding colored cells that should be included in each <strong>rhombus sum</strong>:</p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/04/23/pc73-q4-desc-2.png\" style=\"width: 385px; height: 385px;\" />\n<p>Note that the rhombus can have an area of 0, which is depicted by the purple rhombus in the bottom right corner.</p>\n\n<p>Return <em>the biggest three <strong>distinct rhombus sums</strong> in the </em><code>grid</code><em> in <strong>descending order</strong></em><em>. If there are less than three distinct values, return all of them</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/2021/04/23/pc73-q4-ex1.png\" style=\"width: 360px; height: 361px;\" />\n<pre>\n<strong>Input:</strong> grid = [[3,4,5,1,3],[3,3,4,2,3],[20,30,200,40,10],[1,5,5,4,1],[4,3,2,2,5]]\n<strong>Output:</strong> [228,216,211]\n<strong>Explanation:</strong> The rhombus shapes for the three biggest distinct rhombus sums are depicted above.\n- Blue: 20 + 3 + 200 + 5 = 228\n- Red: 200 + 2 + 10 + 4 = 216\n- Green: 5 + 200 + 4 + 2 = 211\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/04/23/pc73-q4-ex2.png\" style=\"width: 217px; height: 217px;\" />\n<pre>\n<strong>Input:</strong> grid = [[1,2,3],[4,5,6],[7,8,9]]\n<strong>Output:</strong> [20,9,8]\n<strong>Explanation:</strong> The rhombus shapes for the three biggest distinct rhombus sums are depicted above.\n- Blue: 4 + 2 + 6 + 8 = 20\n- Red: 9 (area 0 rhombus in the bottom right corner)\n- Green: 8 (area 0 rhombus in the bottom middle)\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> grid = [[7,7,7]]\n<strong>Output:</strong> [7]\n<strong>Explanation:</strong> All three possible rhombus sums are the same, so return [7].\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>1 &lt;= m, n &lt;= 50</code></li>\n\t<li><code>1 &lt;= grid[i][j] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
            "translatedTitle": "矩阵中最大的三个菱形和",
            "translatedContent": "<p>给你一个 <code>m x n</code> 的整数矩阵 <code>grid</code> 。</p>\n\n<p><strong>菱形和</strong> 指的是 <code>grid</code> 中一个正菱形 <strong>边界</strong> 上的元素之和。本题中的菱形必须为正方形旋转45度，且四个角都在一个格子当中。下图是四个可行的菱形，每个菱形和应该包含的格子都用了相应颜色标注在图中。</p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/04/23/pc73-q4-desc-2.png\" style=\"width: 385px; height: 385px;\" />\n<p> </p>\n\n<p>注意，菱形可以是一个面积为 0 的区域，如上图中右下角的紫色菱形所示。</p>\n\n<p>请你按照 <strong>降序</strong> 返回 <code>grid</code> 中三个最大的 <strong>互不相同的菱形和</strong> 。如果不同的和少于三个，则将它们全部返回。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/04/23/pc73-q4-ex1.png\" style=\"width: 360px; height: 361px;\" />\n<pre>\n<b>输入：</b>grid = [[3,4,5,1,3],[3,3,4,2,3],[20,30,200,40,10],[1,5,5,4,1],[4,3,2,2,5]]\n<b>输出：</b>[228,216,211]\n<b>解释：</b>最大的三个菱形和如上图所示。\n- 蓝色：20 + 3 + 200 + 5 = 228\n- 红色：200 + 2 + 10 + 4 = 216\n- 绿色：5 + 200 + 4 + 2 = 211\n</pre>\n\n<p><strong>示例 2：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/04/23/pc73-q4-ex2.png\" style=\"width: 217px; height: 217px;\" />\n<pre>\n<b>输入：</b>grid = [[1,2,3],[4,5,6],[7,8,9]]\n<b>输出：</b>[20,9,8]\n<b>解释：</b>最大的三个菱形和如上图所示。\n- 蓝色：4 + 2 + 6 + 8 = 20\n- 红色：9 （右下角红色的面积为 0 的菱形）\n- 绿色：8 （下方中央面积为 0 的菱形）\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<b>输入：</b>grid = [[7,7,7]]\n<b>输出：</b>[7]\n<b>解释：</b>所有三个可能的菱形和都相同，所以返回 [7] 。\n</pre>\n\n<p> </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>1 <= m, n <= 100</code></li>\n\t<li><code>1 <= grid[i][j] <= 10<sup>5</sup></code></li>\n</ul>\n",
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