Minimum Operations to Maximize Last Elements in Arrays

Problem Description

You are given two 0-indexed integer arrays, nums1 and nums2, both having length n. You are allowed to perform a series of operations (possibly none). In an operation, you select an index i in the range [0, n - 1] and swap the values of nums1[i] and nums2[i]. Your task is to find the minimum number of operations required to satisfy the conditions that nums1[n - 1] is equal to the maximum value among all elements of nums1 and nums2[n - 1] is equal to the maximum value among all elements of nums2. Return an integer denoting the minimum number of operations needed to meet both conditions, or -1 if it is impossible to satisfy both conditions.

Key Insights

• The last elements of both arrays must be the maximum values in their respective arrays.
• Swapping can only occur at the same index for both arrays, providing limited flexibility.
• The last elements can only be modified through swaps involving their indices.
• If the maximum value is already in position, no swap is needed for that array.
• If both maximum values are present in the opposite arrays, swaps need to be counted.

Space and Time Complexity

Time Complexity: O(n)
Space Complexity: O(1)

Solution

To solve the problem, we need to:

1. Identify the maximum values of both nums1 and nums2.
2. Check if the last elements of nums1 and nums2 are already the maximum values. If so, no operations are needed.
3. If not, determine if we can swap elements to bring the maximum values to the last index. We count the necessary swaps.
4. If the maximum values are not reachable, return -1.

The algorithm primarily uses linear scans to determine maximum values and conditions, which ensures efficiency.

Code Solutions