leetcode-problemset/leetcode-cn/originData/fill-a-special-grid.json

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        "question": {
            "questionId": "3822",
            "questionFrontendId": "3537",
            "categoryTitle": "Algorithms",
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            "title": "Fill a Special Grid",
            "titleSlug": "fill-a-special-grid",
            "content": "<p>You are given a non-negative integer <code><font face=\"monospace\">n</font></code> representing a <code>2<sup>n</sup> x 2<sup>n</sup></code> grid. You must fill the grid with integers from 0 to <code>2<sup>2n</sup> - 1</code> to make it <strong>special</strong>. A grid is <strong>special</strong> if it satisfies <strong>all</strong> the following conditions:</p>\n\n<ul>\n\t<li>All numbers in the top-right quadrant are smaller than those in the bottom-right quadrant.</li>\n\t<li>All numbers in the bottom-right quadrant are smaller than those in the bottom-left quadrant.</li>\n\t<li>All numbers in the bottom-left quadrant are smaller than those in the top-left quadrant.</li>\n\t<li>Each of its quadrants is also a special grid.</li>\n</ul>\n\n<p>Return the <strong>special</strong> <code>2<sup>n</sup> x 2<sup>n</sup></code> grid.</p>\n\n<p><strong>Note</strong>: Any 1x1 grid is special.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">n = 0</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">[[0]]</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The only number that can be placed is 0, and there is only one possible position in the grid.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">n = 1</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">[[3,0],[2,1]]</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>The numbers in each quadrant are:</p>\n\n<ul>\n\t<li>Top-right: 0</li>\n\t<li>Bottom-right: 1</li>\n\t<li>Bottom-left: 2</li>\n\t<li>Top-left: 3</li>\n</ul>\n\n<p>Since <code>0 &lt; 1 &lt; 2 &lt; 3</code>, this satisfies the given constraints.</p>\n</div>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">n = 2</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">[[15,12,3,0],[14,13,2,1],[11,8,7,4],[10,9,6,5]]</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2025/03/05/4123example3p1drawio.png\" style=\"width: 161px; height: 161px;\" /></p>\n\n<p>The numbers in each quadrant are:</p>\n\n<ul>\n\t<li>Top-right: 3, 0, 2, 1</li>\n\t<li>Bottom-right: 7, 4, 6, 5</li>\n\t<li>Bottom-left: 11, 8, 10, 9</li>\n\t<li>Top-left: 15, 12, 14, 13</li>\n\t<li><code>max(3, 0, 2, 1) &lt; min(7, 4, 6, 5)</code></li>\n\t<li><code>max(7, 4, 6, 5) &lt; min(11, 8, 10, 9)</code></li>\n\t<li><code>max(11, 8, 10, 9) &lt; min(15, 12, 14, 13)</code></li>\n</ul>\n\n<p>This satisfies the first three requirements. Additionally, each quadrant is also a special grid. Thus, this is a special grid.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>0 &lt;= n &lt;= 10</code></li>\n</ul>\n",
            "translatedTitle": "填充特殊网格",
            "translatedContent": "<p>给你一个非负整数 <code><font face=\"monospace\">N</font></code>，表示一个 <code>2<sup>N</sup> x 2<sup>N</sup></code> 的网格。你需要用从 0 到 <code>2<sup>2N</sup> - 1</code> 的整数填充网格，使其成为一个&nbsp;<strong>特殊&nbsp;</strong>网格。一个网格当且仅当满足以下&nbsp;<strong>所有&nbsp;</strong>条件时，才能称之为 <strong>特殊</strong> 网格：</p>\n\n<ul>\n\t<li>右上角象限中的所有数字都小于右下角象限中的所有数字。</li>\n\t<li>右下角象限中的所有数字都小于左下角象限中的所有数字。</li>\n\t<li>左下角象限中的所有数字都小于左上角象限中的所有数字。</li>\n\t<li>每个象限也都是一个特殊网格。</li>\n</ul>\n\n<p>返回一个&nbsp;<code>2<sup>N</sup> x 2<sup>N</sup></code>&nbsp;的特殊网格。</p>\n\n<p><strong>注意：</strong>任何 1x1 的网格都是特殊网格。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong> <span class=\"example-io\">N = 0</span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\">[[0]]</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>唯一可以放置的数字是 0，并且网格中只有一个位置。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong> <span class=\"example-io\">N = 1</span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\">[[3,0],[2,1]]</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p>每个象限的数字如下：</p>\n\n<ul>\n\t<li>右上角：0</li>\n\t<li>右下角：1</li>\n\t<li>左下角：2</li>\n\t<li>左上角：3</li>\n</ul>\n\n<p>由于 <code>0 &lt; 1 &lt; 2 &lt; 3</code>，该网格满足给定的约束条件。</p>\n</div>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<div class=\"example-block\">\n<p><strong>输入：</strong> <span class=\"example-io\">N = 2</span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\">[[15,12,3,0],[14,13,2,1],[11,8,7,4],[10,9,6,5]]</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><img alt=\"\" src=\"https://pic.leetcode.cn/1746289512-jpANZH-4123example3p1drawio.png\" style=\"width: 161px; height: 161px;\" /></p>\n\n<p>每个象限的数字如下：</p>\n\n<ul>\n\t<li>右上角：3, 0, 2, 1</li>\n\t<li>右下角：7, 4, 6, 5</li>\n\t<li>左下角：11, 8, 10, 9</li>\n\t<li>左上角：15, 12, 14, 13</li>\n\t<li><code>max(3, 0, 2, 1) &lt; min(7, 4, 6, 5)</code></li>\n\t<li><code>max(7, 4, 6, 5) &lt; min(11, 8, 10, 9)</code></li>\n\t<li><code>max(11, 8, 10, 9) &lt; min(15, 12, 14, 13)</code></li>\n</ul>\n\n<p>这满足前三个要求。此外，每个象限也是一个特殊网格。因此，这是一个特殊网格。</p>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>0 &lt;= N &lt;= 10</code></li>\n</ul>\n",
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target=\\\"_blank\\\">sortedcontainers<\\/a> \\u5e93\\u3002<\\/p>\"],\"scala\":[\"Scala\",\"<p>\\u7248\\u672c\\uff1a<code>Scala 3.3.1<\\/code><\\/p>\"],\"kotlin\":[\"Kotlin\",\"<p>\\u7248\\u672c\\uff1a<code>Kotlin 2.1.10<\\/code><\\/p>\"],\"rust\":[\"Rust\",\"<p>\\u7248\\u672c\\uff1a<code>rust 1.85.0<\\/code><\\/p>\\r\\n\\r\\n<p>\\u652f\\u6301 crates.io \\u7684 <a href=\\\"https:\\/\\/crates.io\\/crates\\/rand\\\" target=\\\"_blank\\\">rand<\\/a>\\u3001<a href=\\\"https:\\/\\/crates.io\\/crates\\/regex\\\" target=\\\"_blank\\\">regex<\\/a> \\u548c <a href=\\\"https:\\/\\/crates.io\\/crates\\/itertools\\\" target=\\\"_blank\\\">itertools<\\/a><\\/p>\"],\"php\":[\"PHP\",\"<p><code>PHP 8.2<\\/code>.<\\/p>\\r\\n\\r\\n<p>With bcmath module.<\\/p>\"],\"typescript\":[\"TypeScript\",\"<p>TypeScript 5.7.3<\\/p>\\r\\n\\r\\n<p>Compile Options: --alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2024<\\/p>\\r\\n\\r\\n<p><a href=\\\"https:\\/\\/lodash.com\\\" target=\\\"_blank\\\">lodash.js<\\/a> \\u5e93\\u5df2\\u7ecf\\u9ed8\\u8ba4\\u88ab\\u5305\\u542b\\u3002<\\/p>\\r\\n\\r\\n<p> \\u5982\\u9700\\u4f7f\\u7528\\u961f\\u5217\\/\\u4f18\\u5148\\u961f\\u5217\\uff0c\\u60a8\\u53ef\\u4f7f\\u7528 <a href=\\\"https:\\/\\/github.com\\/datastructures-js\\/priority-queue\\/tree\\/v6.3.2\\\" target=\\\"_blank\\\"> datastructures-js\\/priority-queue@6.3.2<\\/a>\\uff0c<a href=\\\"https:\\/\\/github.com\\/datastructures-js\\/queue\\/tree\\/v4.2.3\\\" target=\\\"_blank\\\"> datastructures-js\\/queue@4.2.3<\\/a> \\u4ee5\\u53ca <a href=\\\"https:\\/\\/github.com\\/datastructures-js\\/deque\\/tree\\/v1.0.4\\\" target=\\\"_blank\\\"> datastructures-js\\/deque@1.0.4<\\/a>\\u3002<\\/p>\"],\"racket\":[\"Racket\",\"<p><a href=\\\"https:\\/\\/docs.racket-lang.org\\/guide\\/performance.html#%28tech._c%29\\\" target=\\\"_blank\\\">Racket CS<\\/a> v8.15<\\/p>\\r\\n\\r\\n<p>\\u4f7f\\u7528 #lang racket<\\/p>\\r\\n\\r\\n<p>\\u5df2\\u9884\\u5148 (require data\\/gvector 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target=\\\"_blank\\\">\\u300c\\u4ed3\\u9889\\u7f16\\u7a0b\\u8bed\\u8a00\\u5f00\\u53d1\\u6307\\u5357\\u300d<\\/a><\\/p>\"]}",
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