Is Partition Array for Maximum Sum easy or hard?

Partition Array for Maximum Sum is considered a medium difficulty problem. The main challenge is recognizing the dynamic programming state and efficiently evaluating partition sizes without recomputing segment maximums.

Partition Array for Maximum Sum Python/Java solution

Both Python and Java implementations follow the same DP pattern. Create a dp array of size n+1, iterate from left to right, and for each index evaluate partitions of length up to k while tracking the maximum value in the segment. Update dp[i] with the best computed sum.

How to solve Partition Array for Maximum Sum in O(n*k)?

Use dynamic programming with dp[i] representing the best result for the first i elements. For every i, iterate backward up to k elements, track the maximum value in that window, and update dp[i] using dp[i-len] + maxValue * len. This bounded backward scan keeps the complexity at O(n*k).

What is the best approach for Partition Array for Maximum Sum?

The most effective approach uses one-dimensional dynamic programming. Define dp[i] as the maximum sum achievable for the first i elements. For each index, check partitions of length 1 to k ending at that position and track the maximum value within the segment. This produces an O(n*k) time and O(n) space solution.

Is Partition Array for Maximum Sum asked at Google/Amazon/Meta?

Dynamic programming partition problems similar to this appear in interviews at companies like Amazon, Google, and Meta. The problem tests understanding of DP state design, optimal substructure, and efficient iteration over partition sizes.

What data structure is used in Partition Array for Maximum Sum?

The main structure is a one-dimensional dynamic programming array. The algorithm also uses simple variables to track the maximum element in a sliding window while iterating backward up to k elements.

What is the time complexity of Partition Array for Maximum Sum?

The optimal solution runs in O(n*k) time. For each element in the array, the algorithm checks up to k possible partition sizes while maintaining the segment maximum. Space complexity is O(n) for the dynamic programming array.

Description Hints 2 Solution Video 21:39

1043. Partition Array for Maximum Sum

Medium77.4% acceptance6 companies

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.

Return the largest sum of the given array after partitioning. Test cases are generated so that the answer fits in a 32-bit integer.

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

Asked at 6 companies

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Google Meta Bloomberg Amazon Microsoft

Topics

Array Dynamic Programming

Hints open one at a time

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 .

21:39

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