Find Minimum Operations to Make All Elements Divisible by Three

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Question

Approach

For each number, I only care about its remainder mod 3:

• If num % 3 == 0, cost = 0 (already divisible).
• If num % 3 == 1, I can subtract 1 → cost = 1.
• If num % 3 == 2, I can add 1 → cost = 1.

Since adding/subtracting 1 always brings the number directly to a multiple of 3, every non-divisible number costs exactly 1 operation. So I simply count how many numbers have remainder 1 or 2.

Implementation

class Solution:
    def minimumOperations(self, nums: List[int]) -> int:
        ans = 0
        for x in nums:
            if x % 3 != 0:
                ans += 1
        return ans

Complexities

• Time: O(n)
• Space: O(1)