Find the Integer Added to Array II

Problem Description

You are given two integer arrays nums1 and nums2. From nums1 two elements have been removed, and all other elements have been increased (or decreased in the case of negative) by an integer, represented by the variable x. As a result, nums1 becomes equal to nums2. Two arrays are considered equal when they contain the same integers with the same frequencies. Return the minimum possible integer x that achieves this equivalence.

Key Insights

• We need to find two elements in nums1 that can be removed to make the modified nums1 equal to nums2.
• The modification involves adding a constant integer x to the remaining elements of nums1.
• The solution can be approached using sorting and a two-pointer technique to efficiently find the required x.

Space and Time Complexity

Time Complexity: O(n log n) due to sorting the array.
Space Complexity: O(1) if we ignore the input arrays, as we are using only a fixed amount of extra space.

Solution

To solve the problem, we can follow these steps:

1. Sort both nums1 and nums2.
2. Use a two-pointer technique to iterate through the sorted nums1, trying to remove each possible pair of elements.
3. For each pair removed, compute the value of x that would make the modified nums1 equal to nums2.
4. Track the minimum value of x found during the iterations.

We will use sorting to bring the elements into order and make it easier to compare the two arrays after removing elements.

Code Solutions