leetcode-problemset/leetcode-cn/originData/rank-transform-of-a-matrix.json

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        "question": {
            "questionId": "1257",
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            "categoryTitle": "Algorithms",
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            "title": "Rank Transform of a Matrix",
            "titleSlug": "rank-transform-of-a-matrix",
            "content": "<p>Given an <code>m x n</code> <code>matrix</code>, return <em>a new matrix </em><code>answer</code><em> where </em><code>answer[row][col]</code><em> is the </em><em><strong>rank</strong> of </em><code>matrix[row][col]</code>.</p>\n\n<p>The <strong>rank</strong> is an <strong>integer</strong> that represents how large an element is compared to other elements. It is calculated using the following rules:</p>\n\n<ul>\n\t<li>The rank is an integer starting from <code>1</code>.</li>\n\t<li>If two elements <code>p</code> and <code>q</code> are in the <strong>same row or column</strong>, then:\n\t<ul>\n\t\t<li>If <code>p &lt; q</code> then <code>rank(p) &lt; rank(q)</code></li>\n\t\t<li>If <code>p == q</code> then <code>rank(p) == rank(q)</code></li>\n\t\t<li>If <code>p &gt; q</code> then <code>rank(p) &gt; rank(q)</code></li>\n\t</ul>\n\t</li>\n\t<li>The <strong>rank</strong> should be as <strong>small</strong> as possible.</li>\n</ul>\n\n<p>The test cases are generated so that <code>answer</code> is unique under the given rules.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/10/18/rank1.jpg\" style=\"width: 442px; height: 162px;\" />\n<pre>\n<strong>Input:</strong> matrix = [[1,2],[3,4]]\n<strong>Output:</strong> [[1,2],[2,3]]\n<strong>Explanation:</strong>\nThe rank of matrix[0][0] is 1 because it is the smallest integer in its row and column.\nThe rank of matrix[0][1] is 2 because matrix[0][1] &gt; matrix[0][0] and matrix[0][0] is rank 1.\nThe rank of matrix[1][0] is 2 because matrix[1][0] &gt; matrix[0][0] and matrix[0][0] is rank 1.\nThe rank of matrix[1][1] is 3 because matrix[1][1] &gt; matrix[0][1], matrix[1][1] &gt; matrix[1][0], and both matrix[0][1] and matrix[1][0] are rank 2.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/10/18/rank2.jpg\" style=\"width: 442px; height: 162px;\" />\n<pre>\n<strong>Input:</strong> matrix = [[7,7],[7,7]]\n<strong>Output:</strong> [[1,1],[1,1]]\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/10/18/rank3.jpg\" style=\"width: 601px; height: 322px;\" />\n<pre>\n<strong>Input:</strong> matrix = [[20,-21,14],[-19,4,19],[22,-47,24],[-19,4,19]]\n<strong>Output:</strong> [[4,2,3],[1,3,4],[5,1,6],[1,3,4]]\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>m == matrix.length</code></li>\n\t<li><code>n == matrix[i].length</code></li>\n\t<li><code>1 &lt;= m, n &lt;= 500</code></li>\n\t<li><code>-10<sup>9</sup> &lt;= matrix[row][col] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
            "translatedTitle": "矩阵转换后的秩",
            "translatedContent": "<p>给你一个 <code>m x n</code> 的矩阵 <code>matrix</code> ，请你返回一个新的矩阵<em> </em><code>answer</code> ，其中<em> </em><code>answer[row][col]</code> 是 <code>matrix[row][col]</code> 的秩。</p>\n\n<p>每个元素的 <b>秩</b> 是一个整数，表示这个元素相对于其他元素的大小关系，它按照如下规则计算：</p>\n\n<ul>\n\t<li>秩是从 1 开始的一个整数。</li>\n\t<li>如果两个元素 <code>p</code> 和 <code>q</code> 在 <strong>同一行</strong> 或者 <strong>同一列</strong> ，那么：\n\t<ul>\n\t\t<li>如果 <code>p < q</code> ，那么 <code>rank(p) < rank(q)</code></li>\n\t\t<li>如果 <code>p == q</code> ，那么 <code>rank(p) == rank(q)</code></li>\n\t\t<li>如果 <code>p > q</code> ，那么 <code>rank(p) > rank(q)</code></li>\n\t</ul>\n\t</li>\n\t<li><b>秩</b> 需要越 <strong>小</strong> 越好。</li>\n</ul>\n\n<p>题目保证按照上面规则 <code>answer</code> 数组是唯一的。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/10/25/rank1.jpg\" style=\"width: 442px; height: 162px;\" />\n<pre>\n<b>输入：</b>matrix = [[1,2],[3,4]]\n<b>输出：</b>[[1,2],[2,3]]\n<strong>解释：</strong>\nmatrix[0][0] 的秩为 1 ，因为它是所在行和列的最小整数。\nmatrix[0][1] 的秩为 2 ，因为 matrix[0][1] > matrix[0][0] 且 matrix[0][0] 的秩为 1 。\nmatrix[1][0] 的秩为 2 ，因为 matrix[1][0] > matrix[0][0] 且 matrix[0][0] 的秩为 1 。\nmatrix[1][1] 的秩为 3 ，因为 matrix[1][1] > matrix[0][1]， matrix[1][1] > matrix[1][0] 且 matrix[0][1] 和 matrix[1][0] 的秩都为 2 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/10/25/rank2.jpg\" style=\"width: 442px; height: 162px;\" />\n<pre>\n<b>输入：</b>matrix = [[7,7],[7,7]]\n<b>输出：</b>[[1,1],[1,1]]\n</pre>\n\n<p><strong>示例 3：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/10/25/rank3.jpg\" style=\"width: 601px; height: 322px;\" />\n<pre>\n<b>输入：</b>matrix = [[20,-21,14],[-19,4,19],[22,-47,24],[-19,4,19]]\n<b>输出：</b>[[4,2,3],[1,3,4],[5,1,6],[1,3,4]]\n</pre>\n\n<p><strong>示例 4：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/10/25/rank4.jpg\" style=\"width: 601px; height: 242px;\" />\n<pre>\n<b>输入：</b>matrix = [[7,3,6],[1,4,5],[9,8,2]]\n<b>输出：</b>[[5,1,4],[1,2,3],[6,3,1]]\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>m == matrix.length</code></li>\n\t<li><code>n == matrix[i].length</code></li>\n\t<li><code>1 <= m, n <= 500</code></li>\n\t<li><code>-10<sup>9</sup> <= matrix[row][col] <= 10<sup>9</sup></code></li>\n</ul>\n",
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