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.
class Solution:
def minMoves(self, nums: List[int], limit: int) -> int:
N, delta = len(nums), collections.Counter()
for i in range(N // 2):
a, b = nums[i], nums[N - 1 - i]
# 2 <= T < min(A, B) + 1, we need 2 operations to make both A, B smaller
delta[2] += 2
# min(A, B) + 1 <= T < A + B, we need 1 operation to make the larger one out of A and B smaller
delta[min(a, b) + 1] -= 1
# T = A + B, we need 0 operation
delta[a + b] -= 1
# A + B < T < max(A, B) + limit, we need 1 operation to make the smaller one out of A and B larger
delta[a + b + 1] += 1
# max(A, B) + limit < T <= 2 * limit, we need 2 operation to make both A, B larger
delta[max(a, b) + limit + 1] += 1
cur, res = 0, math.inf
for i in range(2, 2 * limit + 1):
cur += delta[i]
res = min(res, cur)
return res