Partition Array for Maximum Sum
The problem asks us to partition the array into contiguous subarrays of length at most k
. After partitioning, each subarray’s values will be changed to become the maximum value of that subarray. We need to return the largest sum of the given array after partitioning.
Solution
We can solve this problem using dynamic programming. We’ll create a DP array dp
of size n
, where dp[i]
represents the maximum sum for the subarray arr[0], arr[1], ..., arr[i]
.
 Initialization: Initialize
dp[0] = arr[0]
.  Loop Through the Array: For each
i
from 1 ton1
, computedp[i]
as the maximum value by considering all possible subarray lengths from 1 tok
ending ati
.  Result: The result will be in
dp[n1]
.


Explanation
max_val
keeps track of the maximum value in the lastj
elements. We multiply
max_val
withj
and add it to the DP value ati  j
.  We repeat this for all
j
from 1 tok
, and take the maximum.
The time complexity of this solution is O(n * k), where n
is the length of the array and k
is the given parameter. The space complexity is O(n), considering the DP array storage.