leetcode-problemset/leetcode-cn/originData/find-the-minimum-area-to-cover-all-ones-ii.json

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            "questionId": "3459",
            "questionFrontendId": "3197",
            "categoryTitle": "Algorithms",
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            "title": "Find the Minimum Area to Cover All Ones II",
            "titleSlug": "find-the-minimum-area-to-cover-all-ones-ii",
            "content": "<p>You are given a 2D <strong>binary</strong> array <code>grid</code>. You need to find 3 <strong>non-overlapping</strong> rectangles having <strong>non-zero</strong> areas with horizontal and vertical sides such that all the 1&#39;s in <code>grid</code> lie inside these rectangles.</p>\n\n<p>Return the <strong>minimum</strong> possible sum of the area of these rectangles.</p>\n\n<p><strong>Note</strong> that the rectangles are allowed to touch.</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\">grid = [[1,0,1],[1,1,1]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">5</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/05/14/example0rect21.png\" style=\"padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; width: 280px; height: 198px;\" /></p>\n\n<ul>\n\t<li>The 1&#39;s at <code>(0, 0)</code> and <code>(1, 0)</code> are covered by a rectangle of area 2.</li>\n\t<li>The 1&#39;s at <code>(0, 2)</code> and <code>(1, 2)</code> are covered by a rectangle of area 2.</li>\n\t<li>The 1 at <code>(1, 1)</code> is covered by a rectangle of area 1.</li>\n</ul>\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\">grid = [[1,0,1,0],[0,1,0,1]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">5</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/05/14/example1rect2.png\" style=\"padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; width: 356px; height: 198px;\" /></p>\n\n<ul>\n\t<li>The 1&#39;s at <code>(0, 0)</code> and <code>(0, 2)</code> are covered by a rectangle of area 3.</li>\n\t<li>The 1 at <code>(1, 1)</code> is covered by a rectangle of area 1.</li>\n\t<li>The 1 at <code>(1, 3)</code> is covered by a rectangle of area 1.</li>\n</ul>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= grid.length, grid[i].length &lt;= 30</code></li>\n\t<li><code>grid[i][j]</code> is either 0 or 1.</li>\n\t<li>The input is generated such that there are at least three 1&#39;s in <code>grid</code>.</li>\n</ul>\n",
            "translatedTitle": "包含所有 1 的最小矩形面积 II",
            "translatedContent": "<p>给你一个二维 <strong>二进制 </strong>数组 <code>grid</code>。你需要找到 3 个<strong> 不重叠</strong>、面积 <strong>非零</strong> 、边在水平方向和竖直方向上的矩形，并且满足 <code>grid</code> 中所有的 1 都在这些矩形的内部。</p>\n\n<p>返回这些矩形面积之和的<strong> 最小 </strong>可能值。</p>\n\n<p><strong>注意</strong>，这些矩形可以相接。</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\">grid = [[1,0,1],[1,1,1]]</span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\">5</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/05/14/example0rect21.png\" style=\"padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; width: 280px; height: 198px;\" /></p>\n\n<ul>\n\t<li>位于 <code>(0, 0)</code> 和 <code>(1, 0)</code> 的 1 被一个面积为 2 的矩形覆盖。</li>\n\t<li>位于 <code>(0, 2)</code> 和 <code>(1, 2)</code> 的 1 被一个面积为 2 的矩形覆盖。</li>\n\t<li>位于 <code>(1, 1)</code> 的 1 被一个面积为 1 的矩形覆盖。</li>\n</ul>\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\">grid = [[1,0,1,0],[0,1,0,1]]</span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\">5</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/05/14/example1rect2.png\" style=\"padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem; width: 356px; height: 198px;\" /></p>\n\n<ul>\n\t<li>位于 <code>(0, 0)</code> 和 <code>(0, 2)</code> 的 1 被一个面积为 3 的矩形覆盖。</li>\n\t<li>位于 <code>(1, 1)</code> 的 1 被一个面积为 1 的矩形覆盖。</li>\n\t<li>位于 <code>(1, 3)</code> 的 1 被一个面积为 1 的矩形覆盖。</li>\n</ul>\n</div>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= grid.length, grid[i].length &lt;= 30</code></li>\n\t<li><code>grid[i][j]</code> 是 0 或 1。</li>\n\t<li>输入保证 <code>grid</code> 中至少有三个 1 。</li>\n</ul>\n",
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            "hints": [
                "Consider covering using 2 rectangles. As the rectangles don’t overlap, one of the rectangles must either be vertically above or horizontally left to the other.",
                "To find the minimum area, check all possible vertical and horizontal splits.",
                "For 3 rectangles, extend the idea to first covering using one rectangle, and then try splitting leftover ones both horizontally and vertically."
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