1043. Partition Array for Maximum Sum

Given an integer array arr, you should partition the array into (contiguous) subarrays of length at most k. After partitioning, each subarray has their values changed to become the maximum value of that subarray.

Return the largest sum of the given array after partitioning.

Example 1:

Input: arr = [1,15,7,9,2,5,10], k = 3
Output: 84
Explanation: arr becomes [15,15,15,9,10,10,10]

Example 2:

Input: arr = [1,4,1,5,7,3,6,1,9,9,3], k = 4
Output: 83

Example 3:

Input: arr = [1], k = 1
Output: 1

Constraints:

• 1 <= arr.length <= 500
• 0 <= arr[i] <= 109
• 1 <= k <= arr.length

# @lc code=start
using LeetCode

function max_sum_after_partitioning(arr::Vector{Int}, k::Int)
    n = length(arr)
    dp = OffsetArray(zeros(Int, n + 1), -1)
    for i in 1:n
        maxn = arr[i]
        dp[i] = maxn + dp[i - 1]
        for j in (i - 1):-1:max(1, i - k + 1)
            maxn = max(maxn, arr[j])
            dp[i] = max(dp[i], (i - j + 1) * maxn + dp[j - 1])
        end
    end
    return dp[n]
end

# @lc code=end

max_sum_after_partitioning (generic function with 1 method)

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