leetcode-problemset/leetcode-cn/originData/find-a-good-subset-of-the-matrix.json

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            "questionId": "2826",
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            "categoryTitle": "Algorithms",
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            "title": "Find a Good Subset of the Matrix",
            "titleSlug": "find-a-good-subset-of-the-matrix",
            "content": "<p>You are given a <strong>0-indexed</strong> <code>m x n</code> binary matrix <code>grid</code>.</p>\n\n<p>Let us call a <strong>non-empty</strong> subset of rows <strong>good</strong> if the sum of each column of the subset is at most half of the length of the subset.</p>\n\n<p>More formally, if the length of the chosen subset of rows is <code>k</code>, then the sum of each column should be at most <code>floor(k / 2)</code>.</p>\n\n<p>Return <em>an integer array that contains row indices of a good subset sorted in <strong>ascending</strong> order.</em></p>\n\n<p>If there are multiple good subsets, you can return any of them. If there are no good subsets, return an empty array.</p>\n\n<p>A <strong>subset</strong> of rows of the matrix <code>grid</code> is any matrix that can be obtained by deleting some (possibly none or all) rows from <code>grid</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> grid = [[0,1,1,0],[0,0,0,1],[1,1,1,1]]\n<strong>Output:</strong> [0,1]\n<strong>Explanation:</strong> We can choose the 0<sup>th</sup> and 1<sup>st</sup> rows to create a good subset of rows.\nThe length of the chosen subset is 2.\n- The sum of the 0<sup>th</sup>&nbsp;column is 0 + 0 = 0, which is at most half of the length of the subset.\n- The sum of the 1<sup>st</sup>&nbsp;column is 1 + 0 = 1, which is at most half of the length of the subset.\n- The sum of the 2<sup>nd</sup>&nbsp;column is 1 + 0 = 1, which is at most half of the length of the subset.\n- The sum of the 3<sup>rd</sup>&nbsp;column is 0 + 1 = 1, which is at most half of the length of the subset.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> grid = [[0]]\n<strong>Output:</strong> [0]\n<strong>Explanation:</strong> We can choose the 0<sup>th</sup> row to create a good subset of rows.\nThe length of the chosen subset is 1.\n- The sum of the 0<sup>th</sup>&nbsp;column is 0, which is at most half of the length of the subset.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> grid = [[1,1,1],[1,1,1]]\n<strong>Output:</strong> []\n<strong>Explanation:</strong> It is impossible to choose any subset of rows to create a good subset.\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 &lt;= 10<sup>4</sup></code></li>\n\t<li><code>1 &lt;= n &lt;= 5</code></li>\n\t<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>\n</ul>\n",
            "translatedTitle": "找到矩阵中的好子集",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong>&nbsp;开始大小为&nbsp;<code>m x n</code>&nbsp;的二进制矩阵&nbsp;<code>grid</code>&nbsp;。</p>\n\n<p>从原矩阵中选出若干行构成一个行的 <strong>非空&nbsp;</strong>子集，如果子集中任何一列的和至多为子集大小的一半，那么我们称这个子集是 <strong>好子集</strong>。</p>\n\n<p>更正式的，如果选出来的行子集大小（即行的数量）为 k，那么每一列的和至多为&nbsp;<code>floor(k / 2)</code>&nbsp;。</p>\n\n<p>请你返回一个整数数组，它包含好子集的行下标，请你将子集中的元素&nbsp;<b>升序</b>&nbsp;返回。</p>\n\n<p>如果有多个好子集，你可以返回任意一个。如果没有好子集，请你返回一个空数组。</p>\n\n<p>一个矩阵 <code>grid</code>&nbsp;的行 <strong>子集</strong> ，是删除 <code>grid</code>&nbsp;中某些（也可能不删除）行后，剩余行构成的元素集合。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>grid = [[0,1,1,0],[0,0,0,1],[1,1,1,1]]\n<b>输出：</b>[0,1]\n<b>解释：</b>我们可以选择第 0 和第 1 行构成一个好子集。\n选出来的子集大小为 2 。\n- 第 0&nbsp;列的和为 0 + 0 = 0 ，小于等于子集大小的一半。\n- 第 1&nbsp;列的和为 1 + 0 = 1 ，小于等于子集大小的一半。\n- 第 2&nbsp;列的和为 1 + 0 = 1 ，小于等于子集大小的一半。\n- 第 3&nbsp;列的和为 0 + 1 = 1 ，小于等于子集大小的一半。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>grid = [[0]]\n<b>输出：</b>[0]\n<strong>解释：</strong>我们可以选择第 0 行构成一个好子集。\n选出来的子集大小为 1 。\n- 第 0 列的和为 0 ，小于等于子集大小的一半。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<b>输入：</b>grid = [[1,1,1],[1,1,1]]\n<b>输出：</b>[]\n<b>解释：</b>没有办法得到一个好子集。\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 &lt;= 10<sup>4</sup></code></li>\n\t<li><code>1 &lt;= n &lt;= 5</code></li>\n\t<li><code>grid[i][j]</code>&nbsp;要么是&nbsp;<code>0</code>&nbsp;，要么是&nbsp;<code>1</code> 。</li>\n</ul>\n",
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                "It can be proven, that if there exists a good subset of rows then there exists a good subset of rows with the size of either 1 or 2.",
                "To check if there exists a good subset of rows of size 1, we check if there exists a row containing only zeros, if it does, we return its index as a good subset.",
                "To check if there exists a good subset of rows of size 2, we iterate over two bit-masks, check if both are presented in the array and if they form a good subset, if they do, return their indices as a good subset."
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