leetcode-problemset/leetcode-cn/originData/separate-squares-ii.json

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        "question": {
            "questionId": "3775",
            "questionFrontendId": "3454",
            "categoryTitle": "Algorithms",
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            "title": "Separate Squares II",
            "titleSlug": "separate-squares-ii",
            "content": "<p>You are given a 2D integer array <code>squares</code>. Each <code>squares[i] = [x<sub>i</sub>, y<sub>i</sub>, l<sub>i</sub>]</code> represents the coordinates of the bottom-left point and the side length of a square parallel to the x-axis.</p>\n\n<p>Find the <strong>minimum</strong> y-coordinate value of a horizontal line such that the total area covered by squares above the line <em>equals</em> the total area covered by squares below the line.</p>\n\n<p>Answers within <code>10<sup>-5</sup></code> of the actual answer will be accepted.</p>\n\n<p><strong>Note</strong>: Squares <strong>may</strong> overlap. Overlapping areas should be counted <strong>only once</strong> in this version.</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\">squares = [[0,0,1],[2,2,1]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">1.00000</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2025/01/15/4065example1drawio.png\" style=\"width: 269px; height: 203px;\" /></p>\n\n<p>Any horizontal line between <code>y = 1</code> and <code>y = 2</code> results in an equal split, with 1 square unit above and 1 square unit below. The minimum y-value is 1.</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\">squares = [[0,0,2],[1,1,1]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">1.00000</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2025/01/15/4065example2drawio.png\" style=\"width: 269px; height: 203px;\" /></p>\n\n<p>Since the blue square overlaps with the red square, it will not be counted again. Thus, the line <code>y = 1</code> splits the squares into two equal parts.</p>\n</div>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= squares.length &lt;= 5 * 10<sup>4</sup></code></li>\n\t<li><code>squares[i] = [x<sub>i</sub>, y<sub>i</sub>, l<sub>i</sub>]</code></li>\n\t<li><code>squares[i].length == 3</code></li>\n\t<li><code>0 &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>9</sup></code></li>\n\t<li><code>1 &lt;= l<sub>i</sub> &lt;= 10<sup>9</sup></code></li>\n\t<li>The total area of all the squares will not exceed <code>10<sup>15</sup></code>.</li>\n</ul>\n",
            "translatedTitle": "分割正方形 II",
            "translatedContent": "<p>给你一个二维整数数组 <code>squares</code>&nbsp;，其中&nbsp;<code>squares[i] = [x<sub>i</sub>, y<sub>i</sub>, l<sub>i</sub>]</code> 表示一个与 x 轴平行的正方形的左下角坐标和正方形的边长。</p>\n\n<p>找到一个<strong>最小的</strong> y 坐标，它对应一条水平线，该线需要满足它以上正方形的总面积 <strong>等于</strong> 该线以下正方形的总面积。</p>\n\n<p>答案如果与实际答案的误差在 <code>10<sup>-5</sup></code> 以内，将视为正确答案。</p>\n\n<p><strong>注意</strong>：正方形&nbsp;<strong>可能会&nbsp;</strong>重叠。重叠区域只&nbsp;<strong>统计一次&nbsp;</strong>。</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\">squares = [[0,0,1],[2,2,1]]</span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\">1.00000</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><img alt=\"\" src=\"https://pic.leetcode.cn/1739609602-zhNmeC-4065example1drawio.png\" style=\"width: 269px; height: 203px;\" /></p>\n\n<p>任何在 <code>y = 1</code> 和 <code>y = 2</code> 之间的水平线都会有 1 平方单位的面积在其上方，1 平方单位的面积在其下方。最小的 y 坐标是 1。</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\">squares = [[0,0,2],[1,1,1]]</span></p>\n\n<p><strong>输出：</strong> <span class=\"example-io\">1.00000</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><img alt=\"\" src=\"https://pic.leetcode.cn/1739609605-ezeVgk-4065example2drawio.png\" style=\"width: 269px; height: 203px;\" /></p>\n\n<p>由于蓝色正方形和红色正方形有重叠区域且重叠区域只统计一次。所以直线&nbsp;<code>y = 1</code>&nbsp;将正方形分割成两部分且面积相等。</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;= squares.length &lt;= 5 * 10<sup>4</sup></code></li>\n\t<li><code>squares[i] = [x<sub>i</sub>, y<sub>i</sub>, l<sub>i</sub>]</code></li>\n\t<li><code>squares[i].length == 3</code></li>\n\t<li><code>0 &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>9</sup></code></li>\n\t<li><code>1 &lt;= l<sub>i</sub> &lt;= 10<sup>9</sup></code></li>\n\t<li>所有正方形的总面积不超过 <code>10<sup>15</sup></code>。</li>\n</ul>\n",
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