{ "data": { "question": { "questionId": "2554", "questionFrontendId": "2463", "categoryTitle": "Algorithms", "boundTopicId": 1946379, "title": "Minimum Total Distance Traveled", "titleSlug": "minimum-total-distance-traveled", "content": "

There are some robots and factories on the X-axis. You are given an integer array robot where robot[i] is the position of the ith robot. You are also given a 2D integer array factory where factory[j] = [positionj, limitj] indicates that positionj is the position of the jth factory and that the jth factory can repair at most limitj robots.

\n\n

The positions of each robot are unique. The positions of each factory are also unique. Note that a robot can be in the same position as a factory initially.

\n\n

All the robots are initially broken; they keep moving in one direction. The direction could be the negative or the positive direction of the X-axis. When a robot reaches a factory that did not reach its limit, the factory repairs the robot, and it stops moving.

\n\n

At any moment, you can set the initial direction of moving for some robot. Your target is to minimize the total distance traveled by all the robots.

\n\n

Return the minimum total distance traveled by all the robots. The test cases are generated such that all the robots can be repaired.

\n\n

Note that

\n\n\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: robot = [0,4,6], factory = [[2,2],[6,2]]\nOutput: 4\nExplanation: As shown in the figure:\n- The first robot at position 0 moves in the positive direction. It will be repaired at the first factory.\n- The second robot at position 4 moves in the negative direction. It will be repaired at the first factory.\n- The third robot at position 6 will be repaired at the second factory. It does not need to move.\nThe limit of the first factory is 2, and it fixed 2 robots.\nThe limit of the second factory is 2, and it fixed 1 robot.\nThe total distance is |2 - 0| + |2 - 4| + |6 - 6| = 4. It can be shown that we cannot achieve a better total distance than 4.\n
\n\n

Example 2:

\n\"\"\n
\nInput: robot = [1,-1], factory = [[-2,1],[2,1]]\nOutput: 2\nExplanation: As shown in the figure:\n- The first robot at position 1 moves in the positive direction. It will be repaired at the second factory.\n- The second robot at position -1 moves in the negative direction. It will be repaired at the first factory.\nThe limit of the first factory is 1, and it fixed 1 robot.\nThe limit of the second factory is 1, and it fixed 1 robot.\nThe total distance is |2 - 1| + |(-2) - (-1)| = 2. It can be shown that we cannot achieve a better total distance than 2.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "最小移动总距离", "translatedContent": "

X 轴上有一些机器人和工厂。给你一个整数数组 robot ，其中 robot[i] 是第 i 个机器人的位置。再给你一个二维整数数组 factory ，其中 factory[j] = [positionj, limitj] ，表示第 j 个工厂的位置在 positionj ，且第 j 个工厂最多可以修理 limitj 个机器人。

\n\n

每个机器人所在的位置 互不相同 。每个工厂所在的位置也 互不相同 。注意一个机器人可能一开始跟一个工厂在 相同的位置 。

\n\n

所有机器人一开始都是坏的，他们会沿着设定的方向一直移动。设定的方向要么是 X 轴的正方向，要么是 X 轴的负方向。当一个机器人经过一个没达到上限的工厂时，这个工厂会维修这个机器人，且机器人停止移动。

\n\n

任何时刻，你都可以设置 部分 机器人的移动方向。你的目标是最小化所有机器人总的移动距离。

\n\n

请你返回所有机器人移动的最小总距离。测试数据保证所有机器人都可以被维修。

\n\n

注意：

\n\n\n\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
\n输入：robot = [0,4,6], factory = [[2,2],[6,2]]\n输出：4\n解释：如上图所示：\n- 第一个机器人从位置 0 沿着正方向移动，在第一个工厂处维修。\n- 第二个机器人从位置 4 沿着负方向移动，在第一个工厂处维修。\n- 第三个机器人在位置 6 被第二个工厂维修，它不需要移动。\n第一个工厂的维修上限是 2 ，它维修了 2 个机器人。\n第二个工厂的维修上限是 2 ，它维修了 1 个机器人。\n总移动距离是 |2 - 0| + |2 - 4| + |6 - 6| = 4 。没有办法得到比 4 更少的总移动距离。\n
\n\n

示例 2：

\n\n

\"\"

\n\n
\n输入：robot = [1,-1], factory = [[-2,1],[2,1]]\n输出：2\n解释：如上图所示：\n- 第一个机器人从位置 1 沿着正方向移动，在第二个工厂处维修。\n- 第二个机器人在位置 -1 沿着负方向移动，在第一个工厂处维修。\n第一个工厂的维修上限是 1 ，它维修了 1 个机器人。\n第二个工厂的维修上限是 1 ，它维修了 1 个机器人。\n总移动距离是 |2 - 1| + |(-2) - (-1)| = 2 。没有办法得到比 2 更少的总移动距离。\n
\n\n

 

\n\n

提示：

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