leetcode-problemset/leetcode-cn/originData/movement-of-robots.json

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        "question": {
            "questionId": "2787",
            "questionFrontendId": "2731",
            "categoryTitle": "Algorithms",
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            "title": "Movement of Robots",
            "titleSlug": "movement-of-robots",
            "content": "<p>Some robots are standing on an infinite number line with their initial coordinates given by a <strong>0-indexed</strong> integer array <code>nums</code> and will start moving once given the command to move. The robots will move a unit distance each second.</p>\n\n<p>You are given a string <code>s</code> denoting the direction in which robots will move on command. <code>&#39;L&#39;</code> means the robot will move towards the left side or negative side of the number line, whereas <code>&#39;R&#39;</code> means the robot will move towards the right side or positive side of the number line.</p>\n\n<p>If two robots collide, they will start moving in opposite directions.</p>\n\n<p>Return <em>the sum of distances between all the&nbsp;pairs of robots </em><code>d</code> <em>seconds after&nbsp;the command. </em>Since the sum can be very large, return it modulo <code>10<sup>9</sup> + 7</code>.</p>\n\n<p><b>Note: </b></p>\n\n<ul>\n\t<li>For two robots at the index <code>i</code> and <code>j</code>, pair <code>(i,j)</code> and pair <code>(j,i)</code> are considered the same pair.</li>\n\t<li>When robots collide, they <strong>instantly change</strong> their directions without wasting any time.</li>\n\t<li>Collision happens&nbsp;when two robots share the same place in a&nbsp;moment.\n\t<ul>\n\t\t<li>For example, if a robot is positioned in 0 going to the right and another is positioned in 2 going to the left, the next second they&#39;ll be both in 1 and they will change direction and the next second the first one will be in 0, heading left, and another will be in 2, heading right.</li>\n\t\t<li>For example,&nbsp;if a robot is positioned in 0 going to the right and another is positioned in 1&nbsp;going to the left, the next second the first one will be in 0, heading left, and another will be in 1, heading right.</li>\n\t</ul>\n\t</li>\n</ul>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [-2,0,2], s = &quot;RLL&quot;, d = 3\n<strong>Output:</strong> 8\n<strong>Explanation:</strong> \nAfter 1 second, the positions are [-1,-1,1]. Now, the robot at index 0 will move left, and the robot at index 1 will move right.\nAfter 2 seconds, the positions are [-2,0,0]. Now, the robot at index 1 will move left, and the robot at index 2 will move right.\nAfter 3 seconds, the positions are [-3,-1,1].\nThe distance between the robot at index 0 and 1 is abs(-3 - (-1)) = 2.\nThe distance between the robot at index 0 and 2 is abs(-3 - 1) = 4.\nThe distance between the robot at index 1 and 2 is abs(-1 - 1) = 2.\nThe sum of the pairs of all distances = 2 + 4 + 2 = 8.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,0], s = &quot;RL&quot;, d = 2\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> \nAfter 1 second, the positions are [2,-1].\nAfter 2 seconds, the positions are [3,-2].\nThe distance between the two robots is abs(-2 - 3) = 5.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>-2 * 10<sup>9</sup>&nbsp;&lt;= nums[i] &lt;= 2 * 10<sup>9</sup></code></li>\n\t<li><code>0 &lt;= d &lt;= 10<sup>9</sup></code></li>\n\t<li><code>nums.length == s.length&nbsp;</code></li>\n\t<li><code>s</code> consists of &#39;L&#39; and &#39;R&#39; only</li>\n\t<li><code>nums[i]</code>&nbsp;will be unique.</li>\n</ul>\n",
            "translatedTitle": "移动机器人",
            "translatedContent": "<p>有一些机器人分布在一条无限长的数轴上，他们初始坐标用一个下标从 <strong>0</strong>&nbsp;开始的整数数组&nbsp;<code>nums</code>&nbsp;表示。当你给机器人下达命令时，它们以每秒钟一单位的速度开始移动。</p>\n\n<p>给你一个字符串&nbsp;<code>s</code>&nbsp;，每个字符按顺序分别表示每个机器人移动的方向。<code>'L'</code>&nbsp;表示机器人往左或者数轴的负方向移动，<code>'R'</code>&nbsp;表示机器人往右或者数轴的正方向移动。</p>\n\n<p>当两个机器人相撞时，它们开始沿着原本相反的方向移动。</p>\n\n<p>请你返回指令重复执行 <code>d</code>&nbsp;秒后，所有机器人之间两两距离之和。由于答案可能很大，请你将答案对&nbsp;<code>10<sup>9</sup> + 7</code>&nbsp;取余后返回。</p>\n\n<p><b>注意：</b></p>\n\n<ul>\n\t<li>对于坐标在&nbsp;<code>i</code> 和&nbsp;<code>j</code>&nbsp;的两个机器人，<code>(i,j)</code>&nbsp;和&nbsp;<code>(j,i)</code>&nbsp;视为相同的坐标对。也就是说，机器人视为无差别的。</li>\n\t<li>当机器人相撞时，它们 <strong>立即改变</strong>&nbsp;它们的前进方向，这个过程不消耗任何时间。</li>\n\t<li>\n\t<p>当两个机器人在同一时刻占据相同的位置时，就会相撞。</p>\n\n\t<ul>\n\t\t<li>\n\t\t<p>例如，如果一个机器人位于位置 0 并往右移动，另一个机器人位于位置 2 并往左移动，下一秒，它们都将占据位置 1，并改变方向。再下一秒钟后，第一个机器人位于位置 0 并往左移动，而另一个机器人位于位置 2 并往右移动。</p>\n\t\t</li>\n\t\t<li>\n\t\t<p>例如，如果一个机器人位于位置 0 并往右移动，另一个机器人位于位置 1 并往左移动，下一秒，第一个机器人位于位置 0 并往左行驶，而另一个机器人位于位置 1 并往右移动。</p>\n\t\t</li>\n\t</ul>\n\t</li>\n</ul>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [-2,0,2], s = \"RLL\", d = 3\n<b>输出：</b>8\n<b>解释：</b>\n1 秒后，机器人的位置为 [-1,-1,1] 。现在下标为 0 的机器人开始往左移动，下标为 1 的机器人开始往右移动。\n2 秒后，机器人的位置为 [-2,0,0] 。现在下标为 1 的机器人开始往左移动，下标为 2 的机器人开始往右移动。\n3 秒后，机器人的位置为 [-3,-1,1] 。\n下标为 0 和 1 的机器人之间距离为 abs(-3 - (-1)) = 2 。\n下标为 0 和 2 的机器人之间的距离为 abs(-3 - 1) = 4 。\n下标为 1 和 2 的机器人之间的距离为 abs(-1 - 1) = 2 。\n所有机器人对之间的总距离为 2 + 4 + 2 = 8 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<b>输入：</b>nums = [1,0], s = \"RL\", d = 2\n<b>输出：</b>5\n<b>解释：</b>\n1 秒后，机器人的位置为 [2,-1] 。\n2 秒后，机器人的位置为 [3,-2] 。\n两个机器人的距离为 abs(-2 - 3) = 5 。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>-2 * 10<sup>9</sup>&nbsp;&lt;= nums[i] &lt;= 2 * 10<sup>9</sup></code></li>\n\t<li><code>0 &lt;= d &lt;= 10<sup>9</sup></code></li>\n\t<li><code>nums.length == s.length&nbsp;</code></li>\n\t<li><code>s</code>&nbsp;只包含&nbsp;<code>'L'</code> 和 <code>'R'</code>&nbsp;。</li>\n\t<li><code>nums[i]</code>&nbsp;互不相同。</li>\n</ul>\n",
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href=\\\"https:\\/\\/github.com\\/emirpasic\\/gods\\/tree\\/v1.18.1\\\" target=\\\"_blank\\\">https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods@v1.18.1<\\/a> \\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\"<p>\\u7248\\u672c\\uff1a<code>Python 3.10<\\/code><\\/p>\\r\\n\\r\\n<p>\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982<a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/array.html\\\" target=\\\"_blank\\\">array<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/bisect.html\\\" target=\\\"_blank\\\">bisect<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/collections.html\\\" target=\\\"_blank\\\">collections<\\/a>\\u3002 \\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n<p>\\u5982\\u9700\\u4f7f\\u7528 Map\\/TreeMap 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