mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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202 lines
25 KiB
JSON
202 lines
25 KiB
JSON
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"title": "Maximum Strictly Increasing Cells in a Matrix",
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"content": "<p>Given a <strong>1-indexed</strong> <code>m x n</code> integer matrix <code>mat</code>, you can select any cell in the matrix as your <strong>starting cell</strong>.</p>\n\n<p>From the starting cell, you can move to any other cell <strong>in the</strong> <strong>same row or column</strong>, but only if the value of the destination cell is <strong>strictly greater</strong> than the value of the current cell. You can repeat this process as many times as possible, moving from cell to cell until you can no longer make any moves.</p>\n\n<p>Your task is to find the <strong>maximum number of cells</strong> that you can visit in the matrix by starting from some cell.</p>\n\n<p>Return <em>an integer denoting the maximum number of cells that can be visited.</em></p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<p><strong class=\"example\"><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/04/23/diag1drawio.png\" style=\"width: 200px; height: 176px;\" /></strong></p>\n\n<pre>\n<strong>Input:</strong> mat = [[3,1],[3,4]]\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> The image shows how we can visit 2 cells starting from row 1, column 2. It can be shown that we cannot visit more than 2 cells no matter where we start from, so the answer is 2. \n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<p><strong class=\"example\"><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/04/23/diag3drawio.png\" style=\"width: 200px; height: 176px;\" /></strong></p>\n\n<pre>\n<strong>Input:</strong> mat = [[1,1],[1,1]]\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> Since the cells must be strictly increasing, we can only visit one cell in this example. \n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<p><strong class=\"example\"><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/04/23/diag4drawio.png\" style=\"width: 350px; height: 250px;\" /></strong></p>\n\n<pre>\n<strong>Input:</strong> mat = [[3,1,6],[-9,5,7]]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> The image above shows how we can visit 4 cells starting from row 2, column 1. It can be shown that we cannot visit more than 4 cells no matter where we start from, so the answer is 4. \n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>m == mat.length </code></li>\n\t<li><code>n == mat[i].length </code></li>\n\t<li><code>1 <= m, n <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= m * n <= 10<sup>5</sup></code></li>\n\t<li><code>-10<sup>5</sup> <= mat[i][j] <= 10<sup>5</sup></code></li>\n</ul>\n",
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"translatedTitle": "矩阵中严格递增的单元格数",
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"translatedContent": "<p>给你一个下标从 <strong>1</strong> 开始、大小为 <code>m x n</code> 的整数矩阵 <code>mat</code>，你可以选择任一单元格作为 <strong>起始单元格</strong> 。</p>\n\n<p>从起始单元格出发，你可以移动到 <strong>同一行或同一列</strong> 中的任何其他单元格，但前提是目标单元格的值<strong> 严格大于 </strong>当前单元格的值。</p>\n\n<p>你可以多次重复这一过程，从一个单元格移动到另一个单元格，直到无法再进行任何移动。</p>\n\n<p>请你找出从某个单元开始访问矩阵所能访问的 <strong>单元格的最大数量</strong> 。</p>\n\n<p>返回一个表示可访问单元格最大数量的整数。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/04/23/diag1drawio.png\" style=\"width: 200px; height: 176px;\"></strong></p>\n\n<pre><strong>输入：</strong>mat = [[3,1],[3,4]]\n<strong>输出：</strong>2\n<strong>解释：</strong>上图展示了从第 1 行、第 2 列的单元格开始，可以访问 2 个单元格。可以证明，无论从哪个单元格开始，最多只能访问 2 个单元格，因此答案是 2 。 \n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/04/23/diag3drawio.png\" style=\"width: 200px; height: 176px;\"></strong></p>\n\n<pre><strong>输入：</strong>mat = [[1,1],[1,1]]\n<strong>输出：</strong>1\n<strong>解释：</strong>由于目标单元格必须严格大于当前单元格，在本示例中只能访问 1 个单元格。 \n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/04/23/diag4drawio.png\" style=\"width: 350px; height: 250px;\"></strong></p>\n\n<pre><strong>输入：</strong>mat = [[3,1,6],[-9,5,7]]\n<strong>输出：</strong>4\n<strong>解释：</strong>上图展示了从第 2 行、第 1 列的单元格开始，可以访问 4 个单元格。可以证明，无论从哪个单元格开始，最多只能访问 4 个单元格，因此答案是 4 。 \n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>m == mat.length </code></li>\n\t<li><code>n == mat[i].length </code></li>\n\t<li><code>1 <= m, n <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= m * n <= 10<sup>5</sup></code></li>\n\t<li><code>-10<sup>5</sup> <= mat[i][j] <= 10<sup>5</sup></code></li>\n</ul>\n",
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"We can try to build the answer in a bottom-up fashion, starting from the smallest values and increasing to the larger values.",
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"Going through the values in sorted order, we can store the maximum path we have seen so far for a row/column.",
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