Problem Description
You are given two non-increasing 0-indexed integer arrays nums1 and nums2. A pair of indices (i, j), where 0 <= i < nums1.length and 0 <= j < nums2.length, is valid if both i <= j and nums1[i] <= nums2[j]. The distance of the pair is j - i. Return the maximum distance of any valid pair (i, j). If there are no valid pairs, return 0.
Key Insights
- Both arrays are sorted in non-increasing order, which allows us to efficiently find valid pairs.
- The conditions for a valid pair only depend on the current indices and their corresponding values.
- A two-pointer approach can be utilized to explore valid pairs without needing to check every possible combination.
Space and Time Complexity
Time Complexity: O(n) - where n is the length of the smaller array, as we traverse both arrays linearly with two pointers.
Space Complexity: O(1) - since we are using a constant amount of extra space.
Solution
To solve the problem, we can use a two-pointer approach. We initialize two pointers, one for each array. The first pointer (i) will iterate through nums1, while the second pointer (j) will iterate through nums2. We will check if nums1[i] is less than or equal to nums2[j] and if the current pair is valid. If it is valid, we calculate the distance and update the maximum distance found. If not, we move the pointer j to find a larger value in nums2. This way, we efficiently find the maximum distance without nested loops.