get-biggest-three-rhombus-sums-in-a-grid

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Algorithms

You are given an <code>m x n</code> integer matrix <code>grid</code>​​​.

A rhombus sum is the sum of the elements that form the border 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 rhombus sum:
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/23/pc73-q4-desc-2.png" style="width: 385px; height: 385px;" />
Note that the rhombus can have an area of 0, which is depicted by the purple rhombus in the bottom right corner.

Return the biggest three distinct rhombus sums in the <code>grid</code> in descending order. If there are less than three distinct values, return all of them.

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/23/pc73-q4-ex1.png" style="width: 360px; height: 361px;" />
<pre>
Input: 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]]
Output: [228,216,211]
Explanation: The rhombus shapes for the three biggest distinct rhombus sums are depicted above.
- Blue: 20 + 3 + 200 + 5 = 228
- Red: 200 + 2 + 10 + 4 = 216
- Green: 5 + 200 + 4 + 2 = 211
</pre>

Example 2:
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/23/pc73-q4-ex2.png" style="width: 217px; height: 217px;" />
<pre>
Input: grid = [[1,2,3],[4,5,6],[7,8,9]]
Output: [20,9,8]
Explanation: The rhombus shapes for the three biggest distinct rhombus sums are depicted above.
- Blue: 4 + 2 + 6 + 8 = 20
- Red: 9 (area 0 rhombus in the bottom right corner)
- Green: 8 (area 0 rhombus in the bottom middle)
</pre>

Example 3:

<pre>
Input: grid = [[7,7,7]]
Output: [7]
Explanation: All three possible rhombus sums are the same, so return [7].
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 50</code></li>
	<li><code>1 &lt;= grid[i][j] &lt;= 105</code></li>
</ul>

getBiggestThree

Get Biggest Three Rhombus Sums in a Grid

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给你一个 <code>m x n</code> 的整数矩阵 <code>grid</code> 。

菱形和 指的是 <code>grid</code> 中一个正菱形 边界 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。
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/23/pc73-q4-desc-2.png" style="width: 385px; height: 385px;" />
 

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。

请你按照 降序 返回 <code>grid</code> 中三个最大的 互不相同的菱形和 。如果不同的和少于三个，则将它们全部返回。

 

示例 1：
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/23/pc73-q4-ex1.png" style="width: 360px; height: 361px;" />
<pre>
输入：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]]
输出：[228,216,211]
解释：最大的三个菱形和如上图所示。
- 蓝色：20 + 3 + 200 + 5 = 228
- 红色：200 + 2 + 10 + 4 = 216
- 绿色：5 + 200 + 4 + 2 = 211
</pre>

示例 2：
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/23/pc73-q4-ex2.png" style="width: 217px; height: 217px;" />
<pre>
输入：grid = [[1,2,3],[4,5,6],[7,8,9]]
输出：[20,9,8]
解释：最大的三个菱形和如上图所示。
- 蓝色：4 + 2 + 6 + 8 = 20
- 红色：9 （右下角红色的面积为 0 的菱形）
- 绿色：8 （下方中央面积为 0 的菱形）
</pre>

示例 3：

<pre>
输入：grid = [[7,7,7]]
输出：[7]
解释：所有三个可能的菱形和都相同，所以返回 [7] 。
</pre>

 

提示：

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 <= m, n <= 100</code></li>
	<li><code>1 <= grid[i][j] <= 105</code></li>
</ul>