Problem Description
You are given two integer arrays of the same length nums1 and nums2. In one operation, you are allowed to swap nums1[i] with nums2[i]. Return the minimum number of needed operations to make nums1 and nums2 strictly increasing.
Key Insights
- The goal is to ensure both sequences are strictly increasing after a series of swaps.
- A strictly increasing sequence requires that each element is less than the next, which means careful tracking of both arrays after potential swaps.
- Dynamic programming can be utilized to maintain the minimum number of swaps required while iterating through the arrays.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
The solution involves using a dynamic programming approach to track the minimum number of swaps required to maintain the increasing order of both arrays. We maintain two states: one where we don't swap the current index and one where we do. The states are updated based on the comparison of elements at the current index and the previous index in both arrays. We utilize a loop to iterate through the arrays while updating our counts based on whether we choose to swap or not.