1674. 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.

Rust Solution

struct Solution;

impl Solution {
    fn min_moves(nums: Vec<i32>, limit: i32) -> i32 {
        let n = nums.len();
        let limit = limit as usize;
        let mut delta = vec![0; limit * 2 + 2];
        for i in 0..n / 2 {
            let a = nums[i] as usize;
            let b = nums[n - 1 - i] as usize;
            delta[2] += 2;
            delta[a.min(b) + 1] -= 1;
            delta[a + b] -= 1;
            delta[a + b + 1] += 1;
            delta[a.max(b) + limit + 1] += 1;
        }

        let mut res = std::i32::MAX;
        let mut cur = 0;
        for sum in 2..=limit * 2 {
            cur += delta[sum];
            res = res.min(cur);
        }
        res
    }
}

#[test]
fn test() {
    let nums = vec![1, 2, 4, 3];
    let limit = 4;
    let res = 1;
    assert_eq!(Solution::min_moves(nums, limit), res);
    let nums = vec![1, 2, 2, 1];
    let limit = 2;
    let res = 2;
    assert_eq!(Solution::min_moves(nums, limit), res);
    let nums = vec![1, 2, 1, 2];
    let limit = 2;
    let res = 0;
    assert_eq!(Solution::min_moves(nums, limit), res);
}

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