Problem Description
Given an integer array nums and two integers firstLen and secondLen, return the maximum sum of elements in two non-overlapping subarrays with lengths firstLen and secondLen. The array with length firstLen could occur before or after the array with length secondLen, but they have to be non-overlapping. A subarray is a contiguous part of an array.
Key Insights
- We need to calculate the maximum sum of two non-overlapping subarrays of given lengths.
- The two subarrays can be arranged in two ways: firstLen followed by secondLen or secondLen followed by firstLen.
- A sliding window approach can be employed to efficiently compute the sums of the subarrays.
- We can maintain a running maximum of the first subarray's sum while iterating through the second subarray to ensure they do not overlap.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
To solve this problem, we can use a sliding window technique along with a prefix sum approach. We will compute the maximum sums of subarrays of lengths firstLen and secondLen as we iterate through the array. We will maintain two scenarios: one where the first subarray comes before the second subarray and the other where the second subarray comes before the first. By keeping track of the maximum sums dynamically, we can efficiently arrive at the final solution.