Leetcode 1674 — Minimum Moves to Make Array Complementary
Link: Leetcode 1674
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. For example, the array [1,2,3,4] is complementary because for all indices i, nums[i] + nums[n — 1 — i] = 5.
Return the minimum number of moves required to make nums complementary.
Example 1:
Input: nums = [1,2,4,3], limit = 4
Output: 1
Explanation: In 1 move, you can change nums to [1,2,2,3] (underlined elements are changed).
nums[0] + nums[3] = 1 + 3 = 4.
nums[1] + nums[2] = 2 + 2 = 4.
nums[2] + nums[1] = 2 + 2 = 4.
nums[3] + nums[0] = 3 + 1 = 4.
Therefore, nums[i] + nums[n-1-i] = 4 for every i, so nums is complementary.Example 2:
Input: nums = [1,2,2,1], limit = 2
Output: 2
Explanation: In 2 moves, you can change nums to [2,2,2,2]. You cannot change any number to 3 since 3 > limit.Example 3:
Input: nums = [1,2,1,2], limit = 2
Output: 0
Explanation: nums is already complementary.Solution
Let’s call the sum of any pair (A[i], A[A.size() - 1 - i]) the target value. Given a pair (a, b) with a ≤b, if the target value is a + b, then we don’t need to modify this pair and it contributes zero to the final cost. It’s obvious that the maximum contribution of a pair is two. So we just need to figure out when the cost is one. We observe that with one change the lower bound of a + b is a + 1 and upper bound of a + b is b + limit. Therefore if a+1≤target≤b+limit, then the cost contribution of the pair (a, b) is one.
Now we can see that three values are important: (1) a + 1 (2) a + b and (3) limit + b. For this problem, we can view them as a segment with three points. We will call them left point, middle point and right point.
We will use the first example in the problem description to explain the solution.
