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g3101_3200.s3102_minimize_manhattan_distances.readme.md Maven / Gradle / Ivy

3102\. Minimize Manhattan Distances

Hard

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

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

Return _the **minimum** possible value for **maximum** distance between any two points by removing exactly one point_.

**Example 1:**

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

**Output:** 12

**Explanation:**

The maximum distance after removing each point is the following:

*   After removing the 0th point the maximum distance is between points (5, 15) and (10, 2), which is `|5 - 10| + |15 - 2| = 18`.
*   After removing the 1st point the maximum distance is between points (3, 10) and (10, 2), which is `|3 - 10| + |10 - 2| = 15`.
*   After removing the 2nd point the maximum distance is between points (5, 15) and (4, 4), which is `|5 - 4| + |15 - 4| = 12`.
*   After removing the 3rd point the maximum distance is between points (5, 15) and (10, 2), which is `|5 - 10| + |15 - 2| = 18`.

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

**Example 2:**

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

**Output:** 0

**Explanation:**

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

**Constraints:**

*   3 <= points.length <= 105
*   `points[i].length == 2`
*   1 <= points[i][0], points[i][1] <= 108