Problem Description
You are given two sorted arrays of distinct integers nums1 and nums2. A valid path is defined as choosing one of the arrays to traverse from index-0 and moving left to right. If you encounter any value that is present in both arrays, you can switch to the other array. The score is defined as the sum of unique values in a valid path. Return the maximum score obtainable from all possible valid paths, modulo (10^9 + 7).
Key Insights
- Both arrays are sorted and contain distinct integers.
- You can switch between the two arrays upon encountering a common element.
- The problem can be approached using two pointers to traverse both arrays efficiently.
- The use of a prefix sum can help quickly calculate the sum of unique elements encountered.
Space and Time Complexity
Time Complexity: O(n + m), where n is the length of nums1 and m is the length of nums2.
Space Complexity: O(1), as no extra space proportional to the input sizes is used.
Solution
To solve the problem, we can use the two-pointer technique to traverse both arrays simultaneously. We maintain two pointers, one for each array, and a running total of the score. We also keep track of the last common element encountered to switch arrays effectively. When encountering a common element, we compute the score for the current path and decide whether to continue on the current array or switch to the other. We utilize prefix sums to efficiently calculate scores without redundant calculations.