Problem Description
You are given an array nums of length n and a positive integer k. A subarray of nums is called good if the absolute difference between its first and last element is exactly k, in other words, the subarray nums[i..j] is good if |nums[i] - nums[j]| == k. Return the maximum sum of a good subarray of nums. If there are no good subarrays, return 0.
Key Insights
- The problem requires identifying subarrays where the first and last elements differ by exactly
k. - We can leverage a hash table to store indices of elements for quick access.
- The sum of the elements in the subarray needs to be calculated efficiently.
- A two-pointer or sliding window approach could be beneficial to explore subarrays while maintaining their sum.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(n)
Solution
To solve the problem, we can use a hash table to keep track of the indices of the elements in the array. As we iterate through the array, we can check if the current element plus or minus k exists in the hash table. If it does, we can identify a good subarray. We will compute the sum of the elements in this identified subarray and keep track of the maximum sum encountered. This approach ensures that we only traverse the list a limited number of times, making it efficient.