Problem

Solution

Intuition

This problem requires us to perform operations on each number in a list of numbers to make each number divisible by 3. The operations that we can perform are adding or subtracting 1 from each number. We can perform this operation as many times as necessary in order to set each number to being divisible by 3.

Because we are looking for a number divisible by 3, there are only 3 cases to consider.

1. The number is already divisible by 3 and requires 0 operations.
2. The number is 1 greater than a multiple of 3 and requires 1 subtraction operation.
3. The number is 2 greater than a multiple fo 3 and requires 2 subtraction operations.

For the last case however, we can understand that if a number is 2 greater than a multiple of 3 it must also be 1 less than a multiple of three. Thus we can re-write our rules as follows:

1. The number is already divisible by 3 and requires 0 operations.
2. The number is 1 greater than a multiple of 3 and requires 1 subtraction operation.
3. The number is 2 greater than a multiple fo 3 and requires 1 addition operation.

Therefore, we have found our solution for the minimum number of operations. If the number is not divisible by 3, we simply increment our counter of operations.

Approach

1. For each num in nums. If num is not divisible by 3, increment our counter res.
2. Return res when we have traversed through each number in nums.

Complexity

• Time complexity: $O(n)$. We iterate through the full list and perform constant time operations on each iteration.
• Space complexity: $O(1)$. We utilize constant space for our return variable.

Code

```python3 [] class Solution: def minimumOperations(self, nums: List[int]) -> int: res = 0

    for num in nums:
        if num % 3 != 0:
            res += 1
    
    return res ```