813. Largest Sum of Averages
Medium
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91

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 , [1, 2, 3], . The answer is 9 + (1 + 2 + 3) / 3 + 9 = 20.
We could have also partitioned nums into [9, 1], , [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`
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