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Formatted question description: https://leetcode.ca/all/1009.html

# 1009. Complement of Base 10 Integer

Easy

## Description

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 its 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:

1. 0 <= N < 10^9

## Solution

Since the complement of 0 is 1 and the complement of 1 is 0, simply deal with these two numbers first.

For the other non-negative integers, consider the number of bits in binary representation, which can be calculated by using log2N + 1 for integer N (keep the integer part of the calculated result). For a number with b bits in binary representation, the sum of the number and its complement equals 2b - 1, so the complement equals 2b - 1 minus the given number.

• class Solution {
public int bitwiseComplement(int N) {
if (N <= 1)
return 1 - N;
int power = (int) (Math.log(N) / Math.log(2));
int max = (int) (Math.pow(2, power + 1) - 1);
return max - N;
}
}

• // OJ: https://leetcode.com/problems/complement-of-base-10-integer/
// Time: O(1)
// Space: O(1)
class Solution {
public:
int bitwiseComplement(int n) {
if (n == 0) return 1;
}
};

• class Solution:
def bitwiseComplement(self, n: int) -> int:
if n == 0:
return 1
ans = 0
find = False
for i in range(30, -1, -1):
b = n & (1 << i)
if not find and b == 0:
continue
find = True
if b == 0:
ans |= 1 << i
return ans

############

# 1009. Complement of Base 10 Integer
# https://leetcode.com/problems/complement-of-base-10-integer/

class Solution:
def bitwiseComplement(self, n: int) -> int:
if n == 0: return 1

full = (1 << n.bit_length()) - 1

return full ^ n