0774. Minimize Max Distance to Gas Station

https://leetcode.com/problems/minimize-max-distance-to-gas-station

Description

You are given an integer array stations that represents the positions of the gas stations on the x-axis. You are also given an integer k.

You should add k new gas stations. You can add the stations anywhere on the x-axis, and not necessarily on an integer position.

Let penalty() be the maximum distance between adjacent gas stations after adding the k new stations.

Return the smallest possible value of penalty(). Answers within 10-6 of the actual answer will be accepted.

Example 1:

**Input:** stations = [1,2,3,4,5,6,7,8,9,10], k = 9
**Output:** 0.50000

Example 2:

**Input:** stations = [23,24,36,39,46,56,57,65,84,98], k = 1
**Output:** 14.00000

Constraints:

• 10 <= stations.length <= 2000

• 0 <= stations[i] <= 108

• stations is sorted in a strictly increasing order.

• 1 <= k <= 106

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