LeetCode 3190: Find Minimum Operations to Make All Elements Divisible by Three Solution

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3190. Find Minimum Operations to Make All Elements Divisible by Three

Problem Explanation

Explanation

To solve this problem, we need to find the minimum number of operations required to make all elements in the given array divisible by 3. We can achieve this by iterating through each element in the array and calculating the remainder when divided by 3. Based on the remainder, we can determine how many operations are needed to make the element divisible by 3.

Algorithm:

  1. Initialize variables to count the number of operations needed for each remainder (rem1, rem2) where rem1 represents the remainder 1 when divided by 3 and rem2 represents the remainder 2.
  2. Iterate through the array and calculate the remainder of each element.
  3. Update the count of operations needed based on the remainder:
    • If the remainder is 1, we need to either subtract 1 or add 2 to make it divisible by 3.
    • If the remainder is 2, we need to either subtract 2 or add 1 to make it divisible by 3.
  4. Return the total number of operations required.

Time Complexity: The time complexity of this algorithm is O(N) where N is the number of elements in the input array.

Space Complexity: The space complexity of this algorithm is O(1) as we are using only a constant amount of extra space.

Solution Code

class Solution {
    public int minOperations(int[] nums) {
        int operations = 0;
        int rem1 = 0, rem2 = 0;
        
        for (int num : nums) {
            if (num % 3 == 1) {
                rem1++;
            } else if (num % 3 == 2) {
                rem2++;
            }
        }
        
        if (rem1 > rem2) {
            operations += rem1;
            operations += (rem1 - rem2) / 3;
        } else {
            operations += rem2;
            operations += (rem2 - rem1) / 3;
        }
        
        return operations;
    }
}

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