2571. Minimum Operations to Reduce an Integer to 0

Problem

You are given a positive integer n, you can do the following operation any number of times:

• Add or subtract a power of 2 from n.

Return **the *minimum* number of operations to make n equal to **0.

A number x is power of 2 if x == 2i where i >= 0.

Example 1:

Input: n = 39
Output: 3
Explanation: We can do the following operations:
- Add 20 = 1 to n, so now n = 40.
- Subtract 23 = 8 from n, so now n = 32.
- Subtract 25 = 32 from n, so now n = 0.
It can be shown that 3 is the minimum number of operations we need to make n equal to 0.

Example 2:

Input: n = 54
Output: 3
Explanation: We can do the following operations:
- Add 21 = 2 to n, so now n = 56.
- Add 23 = 8 to n, so now n = 64.
- Subtract 26 = 64 from n, so now n = 0.
So the minimum number of operations is 3.

Constraints:

• 1 <= n <= 105

Solution (Java)

class Solution {
    public int minOperations(int n) {
        return Integer.bitCount(n ^ (3 * n));
    }
}

Explain:

nope.

Complexity:

• Time complexity : O(n).
• Space complexity : O(n).