Partition Array for Maximum Sum
Partition DP & MCM DSA practice problem on Onlearn.
Difficulty: hard.
Topics: Partition Array for Maximum Sum (DP Partitioning Problem), Dynamic Programming, Recursion, Memoization, Tabulation, Optimal Substructure, Overlapping Subproblems, Partition DP, Arrays, Subarray, Time Complexity, Space Complexity, Base Cases, complexity analysis, dynamic programming, memoization, array partitioning, divide and conquer, tabulation, recursion.
Partition Array for Maximum Sum Problem Statement Given an integer array arr, partition the array into (contiguous) subarrays of length at most k. After partitioning, each subarray has its values changed to become the maximum value of that subarray. Return the largest sum of the given array after partitioning. Examples Example 1: Input: arr = [1, 15, 7, 9, 2, 5, 10], k = 3 Output: 84 Explanation: The partition will be the following to get the largest sum: [1, 15, 7 | 9 | 2, 5, 10]. After replacing the elements of each subarray with its maximum, the array will look like this: [15, 15, 15, 9, 10, 10, 10] and the sum will be 84. Example 2: Input: arr = [1], k = 1 Output: 1 Explanation: only one partition is possible like this: [1] and the sum will be 1.