Sum of K Subarrays With Length at Least M

Problem Description

You are given an integer array nums and two integers, k and m. Return the maximum sum of k non-overlapping subarrays of nums, where each subarray has a length of at least m.

Key Insights

• We need to choose k subarrays that do not overlap.
• Each subarray must be at least m elements long.
• We can leverage prefix sums to efficiently calculate subarray sums.
• Dynamic programming can be used to keep track of the maximum sums achievable with the given constraints.

Space and Time Complexity

Time Complexity: O(n * k)
Space Complexity: O(n)

Solution

To tackle this problem, we can use a dynamic programming approach combined with prefix sums. We will create a prefix sum array to quickly compute the sum of any subarray. The dynamic programming table will keep track of the maximum sums for k subarrays, ensuring that each subarray has a length of at least m.

1. Compute the prefix sum of the array nums to allow O(1) sum retrieval for any subarray.
2. Use a dynamic programming array dp where dp[j] represents the maximum sum achievable using j subarrays.
3. Iterate through the possible end indices of the subarrays, updating the dp array based on previous sums and ensuring that the subarray length is at least m.
4. Finally, return the maximum sum obtained using k subarrays.

Code Solutions