problem1043

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1043. Partition Array for Maximum Sum (Medium)

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

Related Topics

[Dynamic Programming]

Hints

Hint 1

Think dynamic programming: dp[i] will be the answer for array A[0], ..., A[i-1].

Hint 2

For j = 1 .. k that keeps everything in bounds, dp[i] is the maximum of dp[i-j] + max(A[i-1], ..., A[i-j]) * j .