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49 lines
2.4 KiB
HTML
49 lines
2.4 KiB
HTML
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<p>You are given an <code>m x n</code> integer matrix <code>grid</code>.</p>
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<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>
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<img alt="" src="https://assets.leetcode.com/uploads/2021/04/23/pc73-q4-desc-2.png" style="width: 385px; height: 385px;" />
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<p>Note that the rhombus can have an area of 0, which is depicted by the purple rhombus in the bottom right corner.</p>
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<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>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2021/04/23/pc73-q4-ex1.png" style="width: 360px; height: 361px;" />
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<pre>
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<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]]
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<strong>Output:</strong> [228,216,211]
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<strong>Explanation:</strong> The rhombus shapes for the three biggest distinct rhombus sums are depicted above.
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- Blue: 20 + 3 + 200 + 5 = 228
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- Red: 200 + 2 + 10 + 4 = 216
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- Green: 5 + 200 + 4 + 2 = 211
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</pre>
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<p><strong>Example 2:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2021/04/23/pc73-q4-ex2.png" style="width: 217px; height: 217px;" />
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<pre>
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<strong>Input:</strong> grid = [[1,2,3],[4,5,6],[7,8,9]]
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<strong>Output:</strong> [20,9,8]
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<strong>Explanation:</strong> The rhombus shapes for the three biggest distinct rhombus sums are depicted above.
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- Blue: 4 + 2 + 6 + 8 = 20
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- Red: 9 (area 0 rhombus in the bottom right corner)
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- Green: 8 (area 0 rhombus in the bottom middle)
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</pre>
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<p><strong>Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> grid = [[7,7,7]]
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<strong>Output:</strong> [7]
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<strong>Explanation:</strong> All three possible rhombus sums are the same, so return [7].
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>m == grid.length</code></li>
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<li><code>n == grid[i].length</code></li>
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<li><code>1 <= m, n <= 50</code></li>
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<li><code>1 <= grid[i][j] <= 10<sup>5</sup></code></li>
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</ul>
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