3190. Find Minimum Operations to Make All Elements Divisible by Three
Description
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
Solution 1: Mathematics
We directly iterate through the array $\textit{nums}$. For each element $x$, we calculate the remainder of $x$ divided by 3, $x \bmod 3$. If the remainder is not 0, we need to make $x$ divisible by 3 with the minimum number of operations. Therefore, we can choose to either decrease $x$ by $x \bmod 3$ or increase $x$ by $3 - x \bmod 3$, and we accumulate the minimum of these two values to the answer.
The time complexity is $O(n)$, where $n$ is the length of the array $\textit{nums}$. The space complexity is $O(1)$.
1 2 3 4 5 6 7 |
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1 2 3 4 5 6 7 8 9 10 11 12 |
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1 2 3 4 5 6 7 8 9 10 11 12 13 |
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1 2 3 4 5 6 7 8 |
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1 2 3 4 5 6 7 8 9 10 |
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