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"categoryTitle": "Algorithms",
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"title": "Build a Matrix With Conditions",
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"content": "<p>You are given a <strong>positive</strong> integer <code>k</code>. You are also given:</p>\n\n<ul>\n\t<li>a 2D integer array <code>rowConditions</code> of size <code>n</code> where <code>rowConditions[i] = [above<sub>i</sub>, below<sub>i</sub>]</code>, and</li>\n\t<li>a 2D integer array <code>colConditions</code> of size <code>m</code> where <code>colConditions[i] = [left<sub>i</sub>, right<sub>i</sub>]</code>.</li>\n</ul>\n\n<p>The two arrays contain integers from <code>1</code> to <code>k</code>.</p>\n\n<p>You have to build a <code>k x k</code> matrix that contains each of the numbers from <code>1</code> to <code>k</code> <strong>exactly once</strong>. The remaining cells should have the value <code>0</code>.</p>\n\n<p>The matrix should also satisfy the following conditions:</p>\n\n<ul>\n\t<li>The number <code>above<sub>i</sub></code> should appear in a <strong>row</strong> that is strictly <strong>above</strong> the row at which the number <code>below<sub>i</sub></code> appears for all <code>i</code> from <code>0</code> to <code>n - 1</code>.</li>\n\t<li>The number <code>left<sub>i</sub></code> should appear in a <strong>column</strong> that is strictly <strong>left</strong> of the column at which the number <code>right<sub>i</sub></code> appears for all <code>i</code> from <code>0</code> to <code>m - 1</code>.</li>\n</ul>\n\n<p>Return <em><strong>any</strong> matrix that satisfies the conditions</em>. If no answer exists, return an empty matrix.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/07/06/gridosdrawio.png\" style=\"width: 211px; height: 211px;\" />\n<pre>\n<strong>Input:</strong> k = 3, rowConditions = [[1,2],[3,2]], colConditions = [[2,1],[3,2]]\n<strong>Output:</strong> [[3,0,0],[0,0,1],[0,2,0]]\n<strong>Explanation:</strong> The diagram above shows a valid example of a matrix that satisfies all the conditions.\nThe row conditions are the following:\n- Number 1 is in row <u>1</u>, and number 2 is in row <u>2</u>, so 1 is above 2 in the matrix.\n- Number 3 is in row <u>0</u>, and number 2 is in row <u>2</u>, so 3 is above 2 in the matrix.\nThe column conditions are the following:\n- Number 2 is in column <u>1</u>, and number 1 is in column <u>2</u>, so 2 is left of 1 in the matrix.\n- Number 3 is in column <u>0</u>, and number 2 is in column <u>1</u>, so 3 is left of 2 in the matrix.\nNote that there may be multiple correct answers.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> k = 3, rowConditions = [[1,2],[2,3],[3,1],[2,3]], colConditions = [[2,1]]\n<strong>Output:</strong> []\n<strong>Explanation:</strong> From the first two conditions, 3 has to be below 1 but the third conditions needs 3 to be above 1 to be satisfied.\nNo matrix can satisfy all the conditions, so we return the empty matrix.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= k &lt;= 400</code></li>\n\t<li><code>1 &lt;= rowConditions.length, colConditions.length &lt;= 10<sup>4</sup></code></li>\n\t<li><code>rowConditions[i].length == colConditions[i].length == 2</code></li>\n\t<li><code>1 &lt;= above<sub>i</sub>, below<sub>i</sub>, left<sub>i</sub>, right<sub>i</sub> &lt;= k</code></li>\n\t<li><code>above<sub>i</sub> != below<sub>i</sub></code></li>\n\t<li><code>left<sub>i</sub> != right<sub>i</sub></code></li>\n</ul>\n",
"translatedTitle": "给定条件下构造矩阵",
"translatedContent": "<p>给你一个 <strong>正</strong>&nbsp;整数&nbsp;<code>k</code>&nbsp;,同时给你:</p>\n\n<ul>\n\t<li>一个大小为 <code>n</code>&nbsp;的二维整数数组&nbsp;<code>rowConditions</code>&nbsp;,其中&nbsp;<code>rowConditions[i] = [above<sub>i</sub>, below<sub>i</sub>]</code>&nbsp;和</li>\n\t<li>一个大小为 <code>m</code>&nbsp;的二维整数数组&nbsp;<code>colConditions</code>&nbsp;,其中&nbsp;<code>colConditions[i] = [left<sub>i</sub>, right<sub>i</sub>]</code>&nbsp;。</li>\n</ul>\n\n<p>两个数组里的整数都是&nbsp;<code>1</code>&nbsp;到&nbsp;<code>k</code>&nbsp;之间的数字。</p>\n\n<p>你需要构造一个&nbsp;<code>k x k</code>&nbsp;的矩阵,<code>1</code>&nbsp;到&nbsp;<code>k</code>&nbsp;每个数字需要&nbsp;<strong>恰好出现一次</strong>&nbsp;。剩余的数字都是<b>&nbsp;</b><code>0</code>&nbsp;。</p>\n\n<p>矩阵还需要满足以下条件:</p>\n\n<ul>\n\t<li>对于所有 <code>0</code>&nbsp;到&nbsp;<code>n - 1</code>&nbsp;之间的下标&nbsp;<code>i</code>&nbsp;,数字&nbsp;<code>above<sub>i</sub></code>&nbsp;所在的 <strong>行</strong>&nbsp;必须在数字&nbsp;<code>below<sub>i</sub></code>&nbsp;所在行的上面。</li>\n\t<li>对于所有 <code>0</code>&nbsp;到 <code>m - 1</code>&nbsp;之间的下标&nbsp;<code>i</code>&nbsp;,数字&nbsp;<code>left<sub>i</sub></code>&nbsp;所在的 <b>列</b>&nbsp;必须在数字&nbsp;<code>right<sub>i</sub></code>&nbsp;所在列的左边。</li>\n</ul>\n\n<p>返回满足上述要求的 <strong>任意</strong>&nbsp;矩阵。如果不存在答案,返回一个空的矩阵。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/07/06/gridosdrawio.png\" style=\"width: 211px; height: 211px;\"></p>\n\n<pre><b>输入:</b>k = 3, rowConditions = [[1,2],[3,2]], colConditions = [[2,1],[3,2]]\n<b>输出:</b>[[3,0,0],[0,0,1],[0,2,0]]\n<b>解释:</b>上图为一个符合所有条件的矩阵。\n行要求如下\n- 数字 1 在第 <strong>1</strong> 行,数字 2 在第 <strong>2</strong>&nbsp;行1 在 2 的上面。\n- 数字 3 在第 <strong>0</strong>&nbsp;行,数字 2 在第 <strong>2</strong>&nbsp;行3 在 2 的上面。\n列要求如下\n- 数字 2 在第 <strong>1</strong>&nbsp;列,数字 1 在第 <strong>2</strong>&nbsp;列2 在 1 的左边。\n- 数字 3 在第 <strong>0</strong>&nbsp;列,数字 2 在第 <strong>1</strong>&nbsp;列3 在 2 的左边。\n注意可能有多种正确的答案。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre><b>输入:</b>k = 3, rowConditions = [[1,2],[2,3],[3,1],[2,3]], colConditions = [[2,1]]\n<b>输出:</b>[]\n<b>解释:</b>由前两个条件可以得到 3 在 1 的下面,但第三个条件是 3 在 1 的上面。\n没有符合条件的矩阵存在所以我们返回空矩阵。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= k &lt;= 400</code></li>\n\t<li><code>1 &lt;= rowConditions.length, colConditions.length &lt;= 10<sup>4</sup></code></li>\n\t<li><code>rowConditions[i].length == colConditions[i].length == 2</code></li>\n\t<li><code>1 &lt;= above<sub>i</sub>, below<sub>i</sub>, left<sub>i</sub>, right<sub>i</sub> &lt;= k</code></li>\n\t<li><code>above<sub>i</sub> != below<sub>i</sub></code></li>\n\t<li><code>left<sub>i</sub> != right<sub>i</sub></code></li>\n</ul>\n",
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