Largest Sum of Averages

arraydynamic programmingprefix sum

Problem Statement

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.

Examples

Example 1

Input: nums = [9,1,2,3,9], k = 3
Output: 20.00000
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] <= 10 ^4

1 <= k <= nums.length

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Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicDynamic Programming