leetcode-problemset/leetcode-cn/originData/minimum-sensors-to-cover-grid.json

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            "questionId": "3945",
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            "categoryTitle": "Algorithms",
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            "title": "Minimum Sensors to Cover Grid",
            "titleSlug": "minimum-sensors-to-cover-grid",
            "content": "<p>You are given <code>n &times; m</code> grid and an integer <code>k</code>.</p>\n\n<p>A sensor placed on cell <code>(r, c)</code> covers all cells whose <strong>Chebyshev distance</strong> from <code>(r, c)</code> is <strong>at most</strong> <code>k</code>.</p>\n\n<p>The <strong>Chebyshev distance</strong> between two cells <code>(r<sub>1</sub>, c<sub>1</sub>)</code> and <code>(r<sub>2</sub>, c<sub>2</sub>)</code> is <code>max(|r<sub>1</sub> &minus; r<sub>2</sub>|,|c<sub>1</sub> &minus; c<sub>2</sub>|)</code>.</p>\n\n<p>Your task is to return the <strong>minimum</strong> number of sensors required to cover every cell of the grid.</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 = 5, m = 5, k = 1</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">4</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>Placing sensors at positions <code>(0, 3)</code>, <code>(1, 0)</code>, <code>(3, 3)</code>, and <code>(4, 1)</code> ensures every cell in the grid is covered. Thus, the answer is 4.</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 = 2, m = 2, k = 2</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">1</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>With <code>k = 2</code>, a single sensor can cover the entire <code>2 * 2</code> grid regardless of its position. Thus, the answer is 1.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 10<sup>3</sup></code></li>\n\t<li><code>1 &lt;= m &lt;= 10<sup>3</sup></code></li>\n\t<li><code>0 &lt;= k &lt;= 10<sup>3</sup></code></li>\n</ul>\n",
            "translatedTitle": "覆盖网格的最少传感器数目",
            "translatedContent": "<p>给你一个 <code>n × m</code> 的网格和一个整数 <code>k</code>。</p>\n\n<p>一个放置在单元格 <code>(r, c)</code> 的传感器可以覆盖所有与 <code>(r, c)</code> 的&nbsp;<strong>切比雪夫距离</strong><strong>不超过</strong> <code>k</code> 的单元格。</p>\n\n<p>两个单元格 <code>(r<sub>1</sub>, c<sub>1</sub>)</code> 和 <code>(r<sub>2</sub>, c<sub>2</sub>)</code> 之间的&nbsp;<strong>切比雪夫距离&nbsp;</strong>为 <code>max(|r<sub>1</sub> − r<sub>2</sub>|,|c<sub>1</sub> − c<sub>2</sub>|)</code>。</p>\n\n<p>你的任务是返回覆盖整个网格所需传感器的&nbsp;<strong>最少&nbsp;</strong>数量。</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 = 5, m = 5, k = 1</span></p>\n\n<p><strong>输出:</strong> <span class=\"example-io\">4</span></p>\n\n<p><strong>解释:</strong></p>\n\n<p>在位置 <code>(0, 3)</code>、<code>(1, 0)</code>、<code>(3, 3)</code> 和 <code>(4, 1)</code> 放置传感器可以确保网格中的每个单元格都被覆盖。因此，答案是 4。</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 = 2, m = 2, k = 2</span></p>\n\n<p><strong>输出:</strong> <span class=\"example-io\">1</span></p>\n\n<p><strong>解释:</strong></p>\n\n<p>当 <code>k = 2</code> 时，无论传感器放在哪个位置，单个传感器都可以覆盖整个 <code>2 * 2</code> 的网格。因此，答案是 1。</p>\n</div>\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>3</sup></code></li>\n\t<li><code>1 &lt;= m &lt;= 10<sup>3</sup></code></li>\n\t<li><code>0 &lt;= k &lt;= 10<sup>3</sup></code></li>\n</ul>\n",
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