leetcode-problemset/leetcode-cn/originData/difference-of-number-of-distinct-values-on-diagonals.json

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            "questionId": "2801",
            "questionFrontendId": "2711",
            "categoryTitle": "Algorithms",
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            "title": "Difference of Number of Distinct Values on Diagonals",
            "titleSlug": "difference-of-number-of-distinct-values-on-diagonals",
            "content": "<p>Given a <strong>0-indexed</strong> 2D <code>grid</code> of size <code>m x n</code>, you should find the matrix <code>answer</code> of size <code>m x n</code>.</p>\n\n<p>The value of each cell <code>(r, c)</code> of the matrix <code>answer</code> is calculated in the following way:</p>\n\n<ul>\n\t<li>Let <code>topLeft[r][c]</code> be the number of <strong>distinct</strong> values in the top-left diagonal of the cell <code>(r, c)</code> in the matrix <code>grid</code>.</li>\n\t<li>Let <code>bottomRight[r][c]</code> be the number of <strong>distinct</strong> values in the bottom-right diagonal of the cell <code>(r, c)</code> in the matrix <code>grid</code>.</li>\n</ul>\n\n<p>Then <code>answer[r][c] = |topLeft[r][c] - bottomRight[r][c]|</code>.</p>\n\n<p>Return <em>the matrix</em> <code>answer</code>.</p>\n\n<p>A <strong>matrix diagonal</strong> is a diagonal line of cells starting from some cell in either the topmost row or leftmost column and going in the bottom-right direction until reaching the matrix&#39;s end.</p>\n\n<p>A cell <code>(r<sub>1</sub>, c<sub>1</sub>)</code> belongs to the top-left diagonal of the cell <code>(r, c)</code>, if both belong to the same diagonal and <code>r<sub>1</sub> &lt; r</code>. Similarly is defined bottom-right diagonal.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/04/19/ex2.png\" style=\"width: 786px; height: 121px;\" />\n<pre>\n<strong>\nInput:</strong> grid = [[1,2,3],[3,1,5],[3,2,1]]\n<strong>Output:</strong> [[1,1,0],[1,0,1],[0,1,1]]\n<strong>Explanation:</strong> The 1<sup>st</sup> diagram denotes the initial grid.&nbsp;\nThe 2<sup>nd</sup> diagram denotes a grid for cell (0,0), where blue-colored cells are cells on its bottom-right diagonal.\nThe 3<sup>rd</sup> diagram denotes a grid for cell (1,2), where red-colored cells are cells on its top-left diagonal.\nThe 4<sup>th</sup> diagram denotes a grid for cell (1,1), where blue-colored cells are cells on its bottom-right diagonal and red-colored cells are cells on its top-left diagonal.\n- The cell (0,0) contains [1,1] on its bottom-right diagonal and [] on its top-left diagonal. The answer is |1 - 0| = 1.\n- The cell (1,2) contains [] on its bottom-right diagonal and [2] on its top-left diagonal. The answer is |0 - 1| = 1.\n- The cell (1,1) contains [1] on its bottom-right diagonal and [1] on its top-left diagonal. The answer is |1 - 1| = 0.\nThe answers of other cells are similarly calculated.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> grid = [[1]]\n<strong>Output:</strong> [[0]]\n<strong>Explanation:</strong> - The cell (0,0) contains [] on its bottom-right diagonal and [] on its top-left diagonal. The answer is |0 - 0| = 0.\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, grid[i][j] &lt;= 50</code></li>\n</ul>\n",
            "translatedTitle": "对角线上不同值的数量差",
            "translatedContent": "<p>给你一个下标从 <code>0</code> 开始、大小为 <code>m x n</code> 的二维矩阵 <code>grid</code> ，请你求解大小同样为 <code>m x n</code> 的答案矩阵 <code>answer</code> 。</p>\n\n<p>矩阵 <code>answer</code> 中每个单元格 <code>(r, c)</code> 的值可以按下述方式进行计算：</p>\n\n<ul>\n\t<li>令 <code>topLeft[r][c]</code> 为矩阵 <code>grid</code> 中单元格 <code>(r, c)</code> 左上角对角线上 <strong>不同值</strong> 的数量。</li>\n\t<li>令 <code>bottomRight[r][c]</code> 为矩阵 <code>grid</code> 中单元格 <code>(r, c)</code> 右下角对角线上 <strong>不同值</strong> 的数量。</li>\n</ul>\n\n<p>然后 <code>answer[r][c] = |topLeft[r][c] - bottomRight[r][c]|</code> 。</p>\n\n<p>返回矩阵 <code>answer</code> 。</p>\n\n<p><strong>矩阵对角线</strong> 是从最顶行或最左列的某个单元格开始，向右下方向走到矩阵末尾的对角线。</p>\n\n<p>如果单元格 <code>(r1, c1)</code> 和单元格 <code>(r, c) </code>属于同一条对角线且 <code>r1 &lt; r</code> ，则单元格 <code>(r1, c1)</code> 属于单元格 <code>(r, c)</code> 的左上对角线。类似地，可以定义右下对角线。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/04/19/ex2.png\" style=\"width: 786px; height: 121px;\" />\n<pre>\n<strong>输入：</strong>grid = [[1,2,3],[3,1,5],[3,2,1]]\n<strong>输出：</strong>[[1,1,0],[1,0,1],[0,1,1]]\n<strong>解释：</strong>第 1 个图表示最初的矩阵 grid 。&nbsp;\n第 2 个图表示对单元格 (0,0) 计算，其中蓝色单元格是位于右下对角线的单元格。\n第 3 个图表示对单元格 (1,2) 计算，其中红色单元格是位于左上对角线的单元格。\n第 4 个图表示对单元格 (1,1) 计算，其中蓝色单元格是位于右下对角线的单元格，红色单元格是位于左上对角线的单元格。\n- 单元格 (0,0) 的右下对角线包含 [1,1] ，而左上对角线包含 [] 。对应答案是 |1 - 0| = 1 。\n- 单元格 (1,2) 的右下对角线包含 [] ，而左上对角线包含 [2] 。对应答案是 |0 - 1| = 1 。\n- 单元格 (1,1) 的右下对角线包含 [1] ，而左上对角线包含 [1] 。对应答案是 |1 - 1| = 0 。\n其他单元格的对应答案也可以按照这样的流程进行计算。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>grid = [[1]]\n<strong>输出：</strong>[[0]]\n<strong>解释：</strong>- 单元格 (0,0) 的右下对角线包含 [] ，左上对角线包含 [] 。对应答案是 |0 - 0| = 0 。\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>1 &lt;= m, n, grid[i][j] &lt;= 50</code></li>\n</ul>\n",
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