{ "data": { "question": { "questionId": "3344", "questionFrontendId": "3102", "categoryTitle": "Algorithms", "boundTopicId": 2673010, "title": "Minimize Manhattan Distances", "titleSlug": "minimize-manhattan-distances", "content": "

You are given an array points representing integer coordinates of some points on a 2D plane, where points[i] = [xi, yi].

\n\n

The distance between two points is defined as their Manhattan distance.

\n\n

Return the minimum possible value for maximum distance between any two points by removing exactly one point.

\n\n

 

\n

Example 1:

\n\n
\n

Input: points = [[3,10],[5,15],[10,2],[4,4]]

\n\n

Output: 12

\n\n

Explanation:

\n\n

The maximum distance after removing each point is the following:

\n\n\n\n

12 is the minimum possible maximum distance between any two points after removing exactly one point.

\n
\n\n

Example 2:

\n\n
\n

Input: points = [[1,1],[1,1],[1,1]]

\n\n

Output: 0

\n\n

Explanation:

\n\n

Removing any of the points results in the maximum distance between any two points of 0.

\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "最小化曼哈顿距离", "translatedContent": "

给你一个下标从 0 开始的数组 points ，它表示二维平面上一些点的整数坐标，其中 points[i] = [xi, yi] 。

\n\n

两点之间的距离定义为它们的曼哈顿距离。

\n\n

请你恰好移除一个点，返回移除后任意两点之间的 最大 距离可能的 最小 值。

\n\n

 

\n\n

示例 1：

\n\n
\n输入：points = [[3,10],[5,15],[10,2],[4,4]]\n输出：12\n解释：移除每个点后的最大距离如下所示：\n- 移除第 0 个点后，最大距离在点 (5, 15) 和 (10, 2) 之间，为 |5 - 10| + |15 - 2| = 18 。\n- 移除第 1 个点后，最大距离在点 (3, 10) 和 (10, 2) 之间，为 |3 - 10| + |10 - 2| = 15 。\n- 移除第 2 个点后，最大距离在点 (5, 15) 和 (4, 4) 之间，为 |5 - 4| + |15 - 4| = 12 。\n- 移除第 3 个点后，最大距离在点 (5, 15) 和 (10, 2) 之间的，为 |5 - 10| + |15 - 2| = 18 。\n在恰好移除一个点后，任意两点之间的最大距离可能的最小值是 12 。\n
\n\n

示例 2：

\n\n
\n输入：points = [[1,1],[1,1],[1,1]]\n输出：0\n解释：移除任一点后，任意两点之间的最大距离都是 0 。\n
\n\n

 

\n\n

提示：

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"Racket", "langSlug": "racket", "code": "(define/contract (minimum-distance points)\n (-> (listof (listof exact-integer?)) exact-integer?)\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec minimum_distance(Points :: [[integer()]]) -> integer().\nminimum_distance(Points) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec minimum_distance(points :: [[integer]]) :: integer\n def minimum_distance(points) do\n \n end\nend", "__typename": "CodeSnippetNode" }, { "lang": "Cangjie", "langSlug": "cangjie", "code": "class Solution {\n func minimumDistance(points: Array>): Int64 {\n\n }\n}", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"12.6K\", \"totalSubmission\": \"23.3K\", \"totalAcceptedRaw\": 12597, \"totalSubmissionRaw\": 23314, \"acRate\": \"54.0%\"}", "hints": [ "Notice that the Manhattan distance between two points [xi, yi] and [xj, yj] is max({xi - xj + yi - yj, xi - xj - yi + yj, - xi + xj + yi - yj, - xi + xj - yi + yj}).", "If you replace points as [xi - yi, xi + yi] then the Manhattan distance is max(max(xi) - min(xi), max(yi) - min(yi)) over all i.", "After those observations, the problem just becomes a simulation. Create multiset of points [xi - yi, xi + yi], you can iterate on a point you might remove and get the maximum Manhattan distance over all other points." ], "solution": null, "status": null, "sampleTestCase": "[[3,10],[5,15],[10,2],[4,4]]", "metaData": "{\n \"name\": \"minimumDistance\",\n \"params\": [\n {\n \"name\": \"points\",\n \"type\": \"integer[][]\"\n }\n ],\n \"return\": {\n \"type\": \"integer\"\n }\n}", "judgerAvailable": true, "judgeType": "large", "mysqlSchemas": [], "enableRunCode": true, "envInfo": "{\"cpp\":[\"C++\",\"

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