Leetcode Problem 1043. Partition Array for Maximum Sum

1043. Partition Array for Maximum Sum

Leetcode Solutions

Dynamic Programming Approach

  1. Initialize a list dp of length n + 1 with all elements as 0, where n is the length of the input array arr. dp[i] will store the maximum sum we can achieve for the subarray ending at position i - 1.
  2. Iterate over the array from the first element to the last.
  3. For each position i, iterate over all possible lengths of the subarray ending at i, from 1 to k.
  4. For each length l, find the maximum value in the subarray arr[i - l + 1] to arr[i].
  5. Calculate the sum of the current subarray as the maximum value multiplied by the length l.
  6. Add the sum of the current subarray to the maximum sum we have already calculated for the position i - l, which is dp[i - l].
  7. Update dp[i] with the maximum of its current value and the new sum calculated.
  8. After the iteration, the last element in dp will contain the maximum sum of the array after partitioning.
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Recursive Approach with Memoization

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