1793 Minimum Moves To Make Array Complementary

Minimum Moves to Make Array Complementary

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.

 

Constraints:

n == nums.length
2 <= n <= 105
1 <= nums[i] <= limit <= 105
n is even.

impl Solution {
    pub fn min_moves(nums: Vec<i32>, limit: i32) -> i32 {
        let n = nums.len();
        let mut diff = vec![0; (2 * limit + 2) as usize];

        for i in 0..n / 2 {
            let a = nums[i].min(nums[n - 1 - i]);
            let b = nums[i].max(nums[n - 1 - i]);

            diff[2] += 2;
            diff[(a + 1) as usize] -= 1;
            diff[(a + b) as usize] -= 1;
            diff[(a + b + 1) as usize] += 1;
            diff[(b + limit + 1) as usize] += 1;
        }

        let mut min_ops = n as i32;
        let mut current_ops = 0;

        for c in 2..=(2 * limit) as usize {
            current_ops += diff[c];
            min_ops = min_ops.min(current_ops);
        }

        min_ops
    }
}