{ "data": { "question": { "questionId": "699", "questionFrontendId": "699", "categoryTitle": "Algorithms", "boundTopicId": 1824, "title": "Falling Squares", "titleSlug": "falling-squares", "content": "

There are several squares being dropped onto the X-axis of a 2D plane.

\n\n

You are given a 2D integer array positions where positions[i] = [lefti, sideLengthi] represents the ith square with a side length of sideLengthi that is dropped with its left edge aligned with X-coordinate lefti.

\n\n

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 on the top side of another square or on the X-axis. 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.

\n\n

After each square is dropped, you must record the height of the current tallest stack of squares.

\n\n

Return an integer array ans where ans[i] represents the height described above after dropping the ith square.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: positions = [[1,2],[2,3],[6,1]]\nOutput: [2,5,5]\nExplanation:\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
\n\n

Example 2:

\n\n
\nInput: positions = [[100,100],[200,100]]\nOutput: [100,100]\nExplanation:\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
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "掉落的方块", "translatedContent": "

在无限长的数轴（即 x 轴）上，我们根据给定的顺序放置对应的正方形方块。

\n\n

第 i 个掉落的方块（positions[i] = (left, side_length)）是正方形，其中 left 表示该方块最左边的点位置(positions[i][0])，side_length 表示该方块的边长(positions[i][1])。

\n\n

每个方块的底部边缘平行于数轴（即 x 轴），并且从一个比目前所有的落地方块更高的高度掉落而下。在上一个方块结束掉落，并保持静止后，才开始掉落新方块。

\n\n

方块的底边具有非常大的粘性，并将保持固定在它们所接触的任何长度表面上（无论是数轴还是其他方块）。邻接掉落的边不会过早地粘合在一起，因为只有底边才具有粘性。

\n\n

 

\n\n

返回一个堆叠高度列表 ans 。每一个堆叠高度 ans[i] 表示在通过 positions[0], positions[1], ..., positions[i] 表示的方块掉落结束后，目前所有已经落稳的方块堆叠的最高高度。

\n\n

 

\n\n

 

\n\n

示例 1:

\n\n
输入: [[1, 2], [2, 3], [6, 1]]\n输出: [2, 5, 5]\n解释:\n\n第一个方块 positions[0] = [1, 2] 掉落：\n_aa\n_aa\n-------\n方块最大高度为 2 。\n\n第二个方块 positions[1] = [2, 3] 掉落：\n__aaa\n__aaa\n__aaa\n_aa__\n_aa__\n--------------\n方块最大高度为5。\n大的方块保持在较小的方块的顶部，不论它的重心在哪里，因为方块的底部边缘有非常大的粘性。\n\n第三个方块 positions[1] = [6, 1] 掉落：\n__aaa\n__aaa\n__aaa\n_aa\n_aa___a\n-------------- \n方块最大高度为5。\n\n因此，我们返回结果[2, 5, 5]。\n
\n\n

 

\n\n

示例 2:

\n\n
输入: [[100, 100], [200, 100]]\n输出: [100, 100]\n解释: 相邻的方块不会过早地卡住，只有它们的底部边缘才能粘在表面上。\n
\n\n

 

\n\n

注意:

\n\n\n\n

 

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