leetcode-problemset/leetcode-cn/originData/maximum-rows-covered-by-columns.json

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        "question": {
            "questionId": "2482",
            "questionFrontendId": "2397",
            "categoryTitle": "Algorithms",
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            "title": "Maximum Rows Covered by Columns",
            "titleSlug": "maximum-rows-covered-by-columns",
            "content": "<p>You are given a <strong>0-indexed</strong> <code>m x n</code> binary matrix <code>matrix</code> and an integer <code>numSelect</code>, which denotes the number of <strong>distinct</strong> columns you must select from <code>matrix</code>.</p>\n\n<p>Let us consider <code>s = {c<sub>1</sub>, c<sub>2</sub>, ...., c<sub>numSelect</sub>}</code> as the set of columns selected by you. A row <code>row</code> is <strong>covered</strong> by <code>s</code> if:</p>\n\n<ul>\n\t<li>For each cell <code>matrix[row][col]</code> (<code>0 &lt;= col &lt;= n - 1</code>) where <code>matrix[row][col] == 1</code>, <code>col</code> is present in <code>s</code> or,</li>\n\t<li><strong>No cell</strong> in <code>row</code> has a value of <code>1</code>.</li>\n</ul>\n\n<p>You need to choose <code>numSelect</code> columns such that the number of rows that are covered is <strong>maximized</strong>.</p>\n\n<p>Return <em>the <strong>maximum</strong> number of rows that can be <strong>covered</strong> by a set of </em><code>numSelect</code><em> columns.</em></p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/07/14/rowscovered.png\" style=\"width: 240px; height: 400px;\" />\n<pre>\n<strong>Input:</strong> matrix = [[0,0,0],[1,0,1],[0,1,1],[0,0,1]], numSelect = 2\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> One possible way to cover 3 rows is shown in the diagram above.\nWe choose s = {0, 2}.\n- Row 0 is covered because it has no occurrences of 1.\n- Row 1 is covered because the columns with value 1, i.e. 0 and 2 are present in s.\n- Row 2 is not covered because matrix[2][1] == 1 but 1 is not present in s.\n- Row 3 is covered because matrix[2][2] == 1 and 2 is present in s.\nThus, we can cover three rows.\nNote that s = {1, 2} will also cover 3 rows, but it can be shown that no more than three rows can be covered.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/07/14/rowscovered2.png\" style=\"height: 250px; width: 84px;\" />\n<pre>\n<strong>Input:</strong> matrix = [[1],[0]], numSelect = 1\n<strong>Output:</strong> 2\n<strong>Explanation:</strong> Selecting the only column will result in both rows being covered since the entire matrix is selected.\nTherefore, we return 2.\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;= 12</code></li>\n\t<li><code>matrix[i][j]</code> is either <code>0</code> or <code>1</code>.</li>\n\t<li><code>1 &lt;= numSelect&nbsp;&lt;= n</code></li>\n</ul>\n",
            "translatedTitle": "被列覆盖的最多行数",
            "translatedContent": "<p>给你一个下标从 <strong>0 </strong>开始、大小为 <code>m x n</code> 的二进制矩阵 <code>matrix</code> ；另给你一个整数 <code>numSelect</code>，表示你必须从 <code>matrix</code> 中选择的 <strong>不同</strong> 列的数量。</p>\n\n<p>如果一行中所有的 <code>1</code> 都被你选中的列所覆盖，则认为这一行被 <strong>覆盖</strong> 了。</p>\n\n<p><strong>形式上</strong>，假设 <code>s = {c<sub>1</sub>, c<sub>2</sub>, ...., c<sub>numSelect</sub>}</code> 是你选择的列的集合。对于矩阵中的某一行 <code>row</code> ，如果满足下述条件，则认为这一行被集合 <code>s</code> <strong>覆盖</strong>：</p>\n\n<ul>\n\t<li>对于满足 <code>matrix[row][col] == 1</code> 的每个单元格 <code>matrix[row][col]</code>（<code>0 &lt;= col &lt;= n - 1</code>），<code>col</code> 均存在于 <code>s</code> 中，或者</li>\n\t<li><code>row</code> 中 <strong>不存在</strong> 值为 <code>1</code> 的单元格。</li>\n</ul>\n\n<p>你需要从矩阵中选出 <code>numSelect</code> 个列，使集合覆盖的行数最大化。</p>\n\n<p>返回一个整数，表示可以由 <code>numSelect</code> 列构成的集合 <strong>覆盖</strong> 的 <strong>最大行数</strong> 。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/07/14/rowscovered.png\" style=\"width: 250px; height: 417px;\" /></strong></p>\n\n<pre>\n<b>输入：</b>matrix = [[0,0,0],[1,0,1],[0,1,1],[0,0,1]], numSelect = 2\n<b>输出：</b>3\n<strong>解释：</strong>\n图示中显示了一种覆盖 3 行的可行办法。\n选择 s = {0, 2} 。\n- 第 0 行被覆盖，因为其中没有出现 1 。\n- 第 1 行被覆盖，因为值为 1 的两列（即 0 和 2）均存在于 s 中。\n- 第 2 行未被覆盖，因为 matrix[2][1] == 1 但是 1 未存在于 s 中。\n- 第 3 行被覆盖，因为 matrix[2][2] == 1 且 2 存在于 s 中。\n因此，可以覆盖 3 行。\n另外 s = {1, 2} 也可以覆盖 3 行，但可以证明无法覆盖更多行。</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/07/14/rowscovered2.png\" style=\"width: 83px; height: 247px;\" /></strong></p>\n\n<pre>\n<b>输入：</b>matrix = [[1],[0]], numSelect = 1\n<b>输出：</b>2\n<strong>解释：</strong>\n选择唯一的一列，两行都被覆盖了，因为整个矩阵都被覆盖了。\n所以我们返回 2 。\n</pre>\n\n<p>&nbsp;</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 &lt;= m, n &lt;= 12</code></li>\n\t<li><code>matrix[i][j]</code> 要么是 <code>0</code> 要么是 <code>1</code></li>\n\t<li><code>1 &lt;= numSelect&nbsp;&lt;= n</code></li>\n</ul>\n",
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                "Try a brute-force approach.",
                "Iterate through all possible sets of exactly <code>cols</code> columns.",
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