Minimum Array Length After Pair Removals

Problem Description

Given an integer array nums sorted in non-decreasing order, you can perform the following operation any number of times: choose two indices i and j where nums[i] < nums[j], and then remove the elements at indices i and j. The goal is to return the minimum length of nums after applying the operation zero or more times.

Key Insights

• The array is sorted in non-decreasing order, which means that any two elements can only be removed if they are distinct.
• If all elements are the same, no removals can occur, and the array length remains unchanged.
• The minimum length of the array is determined by the number of unique elements.
• If there are k distinct elements, we can remove pairs of them, and the minimum length will be n - 2 * (count of removable pairs).

Space and Time Complexity

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

Solution

To solve the problem:

1. Count the unique elements in the array.
2. If the count of unique elements is less than or equal to 1, the minimum length is the original length.
3. Otherwise, the minimum length can be calculated as the remainder when the total count is reduced by the maximum pairs we can form.

The algorithm primarily relies on a linear scan to count unique elements, thus ensuring efficiency.

Code Solutions