Complement of Base 10 Integer

Introduction Link to heading

Every non-negative integer N has a binary representation. For example, 5 can be represented as “101” in binary, 11 as “1011” in binary, and so on. Note that except for N = 0, there are no leading zeroes in any binary representation.

The complement of a binary representation is the number in binary you get when changing every 1 to a 0 and 0 to a 1. For example, the complement of “101” in binary is “010” in binary.

For a given number N in base-10, return the complement of it’s binary representation as a base-10 integer.

Example 1:

Input: 5
Output: 2
Explanation: 5 is "101" in binary, with complement "010" in binary, which is 2 in base-10.

Example 2:

Input: 7
Output: 0
Explanation: 7 is "111" in binary, with complement "000" in binary, which is 0 in base-10.

Example 3:

Input: 10
Output: 5
Explanation: 10 is "1010" in binary, with complement "0101" in binary, which is 5 in base-10.

Note:

0 <= N < 10^9

Solution Link to heading

Xor solution:

func bitwiseComplement(N int) int {
    if N == 0 {
        return 1
    }
    n := N
    mask := 0
    for n > 0 {
        if mask != 0 {
            mask <<= 1
        }
        mask |= 1
        n >>= 1
    }
    return N ^ mask
}

Explanation Link to heading

Lets first check for 0, because it is a special case. After that lets create a mask of ones for the size of the number and finally xor with this mask. It will invert all binary digits in the number.