Problem URL: Minimum moves to make array complementary

First we create an overlay lookup hashmap of size 2limit+2, as our minimum boundary of change is 2 and maximum is 2limit. Then we iterate over the elements in pair, take the first and last element, and calculate the overlay value for the left and right boundary. Then we iterate over the input array, take the current move and add it to the overlay value, and keep track of a rolling minimum. We return the rolling minimum when the iteration is over.

class Solution:
    def minMoves(self, nums: List[int], limit: int) -> int:
        n = len(nums)
        overlay = [0]*((2*limit)+2)
        for i in range(n//2):
            left_boundary = min(nums[i], nums[n-1-i]) + 1
            no_move_value = nums[i] + nums[n-1-i]
            right_boundary = max(nums[i], nums[n-1-i]) + limit

            overlay[left_boundary] -= 1
            overlay[no_move_value] -= 1
            overlay[no_move_value+1] += 1
            overlay[right_boundary+1] += 1

        current_moves = n
        res = math.inf
        for i in range(2, (2*limit)+1):
            current_moves += overlay[i]
            res = min(res, current_moves)
        return res

Time Complexity: O(n+l), n is the number of items in the array, l is the limit Space Complexity: O(l)