Partition Array for Maximum Sum — LeetCode 1043 Python Solution

The problem

Given an integer array arr, 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.

Example

Input

arr = [1,15,7,9,2,5,10], k = 3

Output

84

Explanation

arr becomes [15,15,15,9,10,10,10]

Python solution

class Solution:
    def maxSumAfterPartitioning(self, arr: List[int], k: int) -> int:
        n = len(arr)
        f = [0] * (n + 1)
        for i in range(1, n + 1):
            mx = 0
            for j in range(i, max(0, i - k), -1):
                mx = max(mx, arr[j - 1])
                f[i] = max(f[i], f[j - 1] + mx * (i - j + 1))
        return f[n]

Complexity

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 1043. Partition Array for Maximum Sum is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

Related problems