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# 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`

## ac

```java
```