Minimum Operations to Make Array Sum Divisible by K

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Question

Approach

I observe that each decrement reduces the total sum by exactly 1. Let r = sum(nums) % k be the remainder we need to remove to make the sum divisible by k. I can always perform exactly r single-unit decrements across the elements (never needing any fancy distribution beyond reducing the total by r), so the minimum number of operations is r. If r == 0 no operations are needed.

Implementation

class Solution:
    def minOperations(self, nums: List[int], k: int) -> int:
        total = sum(nums)
        return total % k

Complexities

• Time: O(n)
• Space: O(1)