Complement of Base 10 Integer

Problem Description

The complement of an integer is the integer you get when you flip all the 0's to 1's and all the 1's to 0's in its binary representation. Given an integer n, return its complement.

Key Insights

• The binary representation of a number can be manipulated using bitwise operations.
• To find the complement, we can use the XOR operation with a mask that has all bits set to 1 for the length of the binary representation of n.
• The mask can be constructed by finding the highest power of 2 less than or equal to n.

Space and Time Complexity

Time Complexity: O(log n) - The number of bits in the binary representation of n. Space Complexity: O(1) - We are using a constant amount of space.

Solution

To solve this problem, we can utilize bit manipulation techniques. The steps are as follows:

1. Determine the number of bits in the binary representation of the integer n.
2. Create a mask that has the same number of bits as n, with all bits set to 1.
3. Use the XOR operation to flip the bits of n by XORing it with the mask.
4. Return the result.

The primary data structure used here is an integer, and the algorithmic approach involves bitwise operations (specifically, the XOR operation).

Code Solutions