1674. Minimum Moves to Make Array Complementary

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. 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 numscomplementary.

 

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.

 

Solutions

Solution: Prefix Sum

• Time complexity: O(n+limit)
• Space complexity: O(limit)

 

JavaScript

/**
 * @param {number[]} nums
 * @param {number} limit
 * @return {number}
 */
const minMoves = function (nums, limit) {
  const moves = Array.from({length: 2 + limit * 2}).fill(0);
  const size = nums.length;
  let current = 0;
  let result = size;

  for (let index = 0; index < size / 2; index++) {
    const a = Math.min(nums[index], nums[size - 1 - index]);
    const b = Math.max(nums[index], nums[size - 1 - index]);

    moves[2] += 2;
    moves[a + 1] -= 1;
    moves[a + b] -= 1;
    moves[a + b + 1] += 1;
    moves[b + limit + 1] += 1;
  }
  for (let index = 2; index <= limit * 2; index++) {
    current += moves[index];
    result = Math.min(current, result);
  }
  return result;
};