leetcode-problemset/leetcode-cn/originData/falling-squares.json

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            "questionId": "699",
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            "title": "Falling Squares",
            "titleSlug": "falling-squares",
            "content": "<p>There are several squares being dropped onto the X-axis of a 2D plane.</p>\n\n<p>You are given a 2D integer array <code>positions</code> where <code>positions[i] = [left<sub>i</sub>, sideLength<sub>i</sub>]</code> represents the <code>i<sup>th</sup></code> square with a side length of <code>sideLength<sub>i</sub></code> that is dropped with its left edge aligned with X-coordinate <code>left<sub>i</sub></code>.</p>\n\n<p>Each square is dropped one at a time from a height above any landed squares. It then falls downward (negative Y direction) until it either lands <strong>on the top side of another square</strong> or <strong>on the X-axis</strong>. A square brushing the left/right side of another square does not count as landing on it. Once it lands, it freezes in place and cannot be moved.</p>\n\n<p>After each square is dropped, you must record the <strong>height of the current tallest stack of squares</strong>.</p>\n\n<p>Return <em>an integer array </em><code>ans</code><em> where </em><code>ans[i]</code><em> represents the height described above after dropping the </em><code>i<sup>th</sup></code><em> square</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/04/28/fallingsq1-plane.jpg\" style=\"width: 500px; height: 505px;\" />\n<pre>\n<strong>Input:</strong> positions = [[1,2],[2,3],[6,1]]\n<strong>Output:</strong> [2,5,5]\n<strong>Explanation:</strong>\nAfter the first drop, the tallest stack is square 1 with a height of 2.\nAfter the second drop, the tallest stack is squares 1 and 2 with a height of 5.\nAfter the third drop, the tallest stack is still squares 1 and 2 with a height of 5.\nThus, we return an answer of [2, 5, 5].\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> positions = [[100,100],[200,100]]\n<strong>Output:</strong> [100,100]\n<strong>Explanation:</strong>\nAfter the first drop, the tallest stack is square 1 with a height of 100.\nAfter the second drop, the tallest stack is either square 1 or square 2, both with heights of 100.\nThus, we return an answer of [100, 100].\nNote that square 2 only brushes the right side of square 1, which does not count as landing on it.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= positions.length &lt;= 1000</code></li>\n\t<li><code>1 &lt;= left<sub>i</sub> &lt;= 10<sup>8</sup></code></li>\n\t<li><code>1 &lt;= sideLength<sub>i</sub> &lt;= 10<sup>6</sup></code></li>\n</ul>\n",
            "translatedTitle": "掉落的方块",
            "translatedContent": "<p>在二维平面上的 x 轴上，放置着一些方块。</p>\n\n<p>给你一个二维整数数组 <code>positions</code> ，其中 <code>positions[i] = [left<sub>i</sub>, sideLength<sub>i</sub>]</code> 表示：第 <code>i</code> 个方块边长为 <code>sideLength<sub>i</sub></code> ，其左侧边与 x 轴上坐标点&nbsp;<code>left<sub>i</sub></code> 对齐。</p>\n\n<p>每个方块都从一个比目前所有的落地方块更高的高度掉落而下。方块沿 y 轴负方向下落，直到着陆到 <strong>另一个正方形的顶边</strong> 或者是 <strong>x 轴上</strong> 。一个方块仅仅是擦过另一个方块的左侧边或右侧边不算着陆。一旦着陆，它就会固定在原地，无法移动。</p>\n\n<p>在每个方块掉落后，你必须记录目前所有已经落稳的 <strong>方块堆叠的最高高度</strong> 。</p>\n\n<p>返回一个整数数组 <code>ans</code> ，其中 <code>ans[i]</code> 表示在第 <code>i</code> 块方块掉落后堆叠的最高高度。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/04/28/fallingsq1-plane.jpg\" style=\"width: 500px; height: 505px;\" />\n<pre>\n<strong>输入：</strong>positions = [[1,2],[2,3],[6,1]]\n<strong>输出：</strong>[2,5,5]\n<strong>解释：</strong>\n第 1 个方块掉落后，最高的堆叠由方块 1 组成，堆叠的最高高度为 2 。\n第 2 个方块掉落后，最高的堆叠由方块 1 和 2 组成，堆叠的最高高度为 5 。\n第 3 个方块掉落后，最高的堆叠仍然由方块 1 和 2 组成，堆叠的最高高度为 5 。\n因此，返回 [2, 5, 5] 作为答案。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>positions = [[100,100],[200,100]]\n<strong>输出：</strong>[100,100]\n<strong>解释：</strong>\n第 1 个方块掉落后，最高的堆叠由方块 1 组成，堆叠的最高高度为 100 。\n第 2 个方块掉落后，最高的堆叠可以由方块 1 组成也可以由方块 2 组成，堆叠的最高高度为 100 。\n因此，返回 [100, 100] 作为答案。\n注意，方块 2 擦过方块 1 的右侧边，但不会算作在方块 1 上着陆。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= positions.length &lt;= 1000</code></li>\n\t<li><code>1 &lt;= left<sub>i</sub> &lt;= 10<sup>8</sup></code></li>\n\t<li><code>1 &lt;= sideLength<sub>i</sub> &lt;= 10<sup>6</sup></code></li>\n</ul>\n",
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                    "code": "class Solution {\npublic:\n    vector<int> fallingSquares(vector<vector<int>>& positions) {\n\n    }\n};",
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                "If positions = [[10, 20], [20, 30]], this is the same as [[1, 2], [2, 3]].  Currently, the values of positions are very large.  Can you generalize this approach so as to make the values in positions manageable?"
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