Solution to Leetcode problem 1012: Complement of Base 10 Integer

In this Leetcode problem, we are given an integer N and we should return the integer representing the complement of its base 2 representation. For instance, with the input 5, the binary representation of 5 is 101, the complement of 101 is 010, which represents the integer 2. Therefore for input 5 the output should be 2.

Problem statement

One idea would be to take N, find its binary representation bin_str, then change all the ‘0’s in ‘1’s and the ‘1’s in ‘0’s. Then find the int_val of the binary string obtained, and return it. That would be the most natural solution and I encourage you to try it out.

Another way, that is commonly applied for solution where we use binary representation of integers, is to find a ‘clever’ mask and apply it for a bitwise operation. Here, we will find out that once we analyze the problem correctly the mask isn’t that clever.

As mentioned before, we want to turn each 1 in the binary string representation into 0 and vice versa. In other words we want an operation corresponding to the truth table:

input   |  output
-----------------
   0    |    1
   1    |    0

To do this we are given this set of bitwise operations in Go:

&   bitwise AND
 |   bitwise OR
 ^   bitwise XOR
&^   AND NOT
<<   left shift
>>…