Find Minimum Operations to Make All Elements Divisible by Three

Problem Statement

You are given an integer array nums. In one operation, you can add or subtract 1 from any element of nums.

Return the minimum number of operations to make all elements of nums divisible by 3.

Example 1:

Input: nums = [1, 2, 3, 4] Output: 3

Explanation: All array elements can be made divisible by 3 using 3 operations:

• Subtract 1 from 1.
• Add 1 to 2.
• Subtract 1 from 4.

Example 2:

Input: nums = [3, 6, 9] Output: 0

Constraints:

• 1 <= nums.length <= 50
• 1 <= nums[i] <= 50

Solutions

Intuition

To make all elements divisible by 3, we need to adjust each element by either adding or subtracting 1 until its remainder when divided by 3 is zero. Each adjustment operation (either adding or subtracting 1) counts as one operation.

Approach

1. Iterate through each element in the array.
2. For each element, check its remainder when divided by 3.
3. If the remainder is 1 or 2, it means we need one operation to make it divisible by 3 (subtract 1 if the remainder is 1, or add 1 if the remainder is 2).
4. Sum up the number of operations required for each element.

Implementation

The provided code effectively implements the above approach. Here's the breakdown:

1. Iteration and Remainder Check:
   • Iterate through each element in the nums array.
   • Check the remainder of each element when divided by 3.
   • Increment the operations counter based on the remainder.

Java

class Solution {
    public int minimumOperations(int[] nums) {
        int operations = 0;
        for (int n : nums) {
            if (n % 3 == 1 || n % 3 == 2) {
                operations++;
            }
        }
        return operations;
    }
}

Python

class Solution:
    def minimumOperations(self, nums: List[int]) -> int:
        operations = 0
        for n in nums:
            if n % 3 == 1 or n % 3 == 2:
                operations += 1
        return operations

Conclusion

This implementation efficiently computes the minimum operations required to make all elements of nums divisible by 3 by iterating through the array and counting adjustments needed based on remainders.