# number-complement

## Problem

Number Complement

## Problem Description

``````Given a positive integer, output its complement number. The complement strategy is to flip the bits of its binary representation.

Example 1:

Input: 5
Output: 2
Explanation: The binary representation of 5 is 101 (no leading zero bits), and its complement is 010. So you need to output 2.

Example 2:

Input: 1
Output: 0
Explanation: The binary representation of 1 is 1 (no leading zero bits), and its complement is 0. So you need to output 0.

Note:

The given integer is guaranteed to fit within the range of a 32-bit signed integer.
You could assume no leading zero bit in the integer’s binary representation.
This question is the same as 1009: https://leetcode.com/problems/complement-of-base-10-integer/``````

## Solution

To find complement number, observe that complete number, the binary only has 1s.

ie.`7 (111)` `15(1111)`

if we can find complete number, then the number complete = complete number - num.

to find complete number:

• complete start from 1, loop while num > complete, each iterate, `complete = complete * 2 + 1`

• when num <= complete, meaning complete found

• return complete - num;

### Code

``````class Solution {
public int findComplement(int num) {
int complete = 1;
while (num > complete) {
complete = complete * 2 + 1;
}
return complete - num;
}
}``````

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