leetcode-problemset/leetcode-cn/originData/count-total-number-of-colored-cells.json

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            "questionId": "2649",
            "questionFrontendId": "2579",
            "categoryTitle": "Algorithms",
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            "title": "Count Total Number of Colored Cells",
            "titleSlug": "count-total-number-of-colored-cells",
            "content": "<p>There exists an infinitely large two-dimensional grid of uncolored unit cells. You are given a positive integer <code>n</code>, indicating that you must do the following routine for <code>n</code> minutes:</p>\n\n<ul>\n\t<li>At the first minute, color <strong>any</strong> arbitrary unit cell blue.</li>\n\t<li>Every minute thereafter, color blue <strong>every</strong> uncolored cell that touches a blue cell.</li>\n</ul>\n\n<p>Below is a pictorial representation of the state of the grid after minutes 1, 2, and 3.</p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/01/10/example-copy-2.png\" style=\"width: 500px; height: 279px;\" />\n<p>Return <em>the number of <strong>colored cells</strong> at the end of </em><code>n</code> <em>minutes</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 1\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> After 1 minute, there is only 1 blue cell, so we return 1.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 2\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> After 2 minutes, there are 4 colored cells on the boundary and 1 in the center, so we return 5. \n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
            "translatedTitle": "统计染色格子数",
            "translatedContent": "<p>有一个无穷大的二维网格图，一开始所有格子都未染色。给你一个正整数&nbsp;<code>n</code>&nbsp;，表示你需要执行以下步骤&nbsp;<code>n</code>&nbsp;分钟：</p>\n\n<ul>\n\t<li>第一分钟，将 <strong>任一</strong> 格子染成蓝色。</li>\n\t<li>之后的每一分钟，将与蓝色格子相邻的 <strong>所有</strong> 未染色格子染成蓝色。</li>\n</ul>\n\n<p>下图分别是 1、2、3 分钟后的网格图。</p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/01/10/example-copy-2.png\" style=\"width: 500px; height: 279px;\">\n<p>请你返回 <code>n</code>&nbsp;分钟之后 <strong>被染色的格子&nbsp;</strong>数目。</p>\n\n<p>&nbsp;</p>\n\n<p><b>示例 1：</b></p>\n\n<pre><b>输入：</b>n = 1\n<b>输出：</b>1\n<b>解释：</b>1 分钟后，只有 1 个蓝色的格子，所以返回 1 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre><b>输入：</b>n = 2\n<b>输出：</b>5\n<b>解释：</b>2 分钟后，有 4 个在边缘的蓝色格子和 1 个在中间的蓝色格子，所以返回 5 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
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                "Derive a mathematical relation between total number of colored cells and the time elapsed in minutes."
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