mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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187 lines
18 KiB
JSON
187 lines
18 KiB
JSON
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"questionId": "2826",
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"title": "Find a Good Subset of the Matrix",
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"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> </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> 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> 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> 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> 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> 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> </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 <= m <= 10<sup>4</sup></code></li>\n\t<li><code>1 <= n <= 5</code></li>\n\t<li><code>grid[i][j]</code> is either <code>0</code> or <code>1</code>.</li>\n</ul>\n",
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"categoryTitle": "Algorithms",
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"code": "# @param {Integer[][]} grid\n# @return {Integer[]}\ndef good_subsetof_binary_matrix(grid)\n \nend",
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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.",
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"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.",
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"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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