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# 0813. Largest Sum of Averages

<https://leetcode.com/problems/largest-sum-of-averages>

## Description

You are given an integer array `nums` and an integer `k`. You can partition the array into **at most** `k` non-empty adjacent subarrays. The **score** of a partition is the sum of the averages of each subarray.

Note that the partition must use every integer in `nums`, and that the score is not necessarily an integer.

Return *the maximum **score** you can achieve of all the possible partitions*. Answers within `10-6` of the actual answer will be accepted.

**Example 1:**

```
**Input:** nums = [9,1,2,3,9], k = 3
**Output:** 20.00000
**Explanation:** 
The best choice is to partition nums into [9], [1, 2, 3], [9]. The answer is 9 + (1 + 2 + 3) / 3 + 9 = 20.
We could have also partitioned nums into [9, 1], [2], [3, 9], for example.
That partition would lead to a score of 5 + 2 + 6 = 13, which is worse.
```

**Example 2:**

```
**Input:** nums = [1,2,3,4,5,6,7], k = 4
**Output:** 20.50000
```

**Constraints:**

* `1 <= nums.length <= 100`
* `1 <= nums[i] <= 104`
* `1 <= k <= nums.length`

## ac

```java
```