Problem Description
You are given an integer array nums of even length n and an integer limit. In one move, you can replace any integer from nums with another integer between 1 and limit, inclusive. The array nums is complementary if for all indices i (0-indexed), nums[i] + nums[n - 1 - i] equals the same number. Return the minimum number of moves required to make nums complementary.
Key Insights
- The array length is even, which means pairs can be formed.
- Each pair
(nums[i], nums[n-1-i])should sum to a constant value across all pairs. - The maximum possible sum of any pair is
limit + limit. - The minimum possible sum of any pair is
2. - We need to count how many changes are required to meet the target sums.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(limit)
Solution
To solve the problem, we can use a frequency array to count the number of changes needed for each possible sum. We will iterate through each pair (nums[i], nums[n-1-i]) and determine the minimum number of changes required to make the sum equal to a specific target value. The frequency array will help us track how many pairs need to be adjusted for each possible sum from 2 to 2 * limit. We then find the minimum number of changes from the frequency array.