[NeetCode 150] Number of One Bits

Number of One Bits

You are given an unsigned integer n. Return the number of 1 bits in its binary representation.

You may assume n is a non-negative integer which fits within 32-bits.

Example 1:

Input: n = 00000000000000000000000000010111

Output: 4

Example 2:

Input: n = 01111111111111111111111111111101

Output: 30

Solution

A straightforward solution to this problem is to divide the number by 2 and check the remainer of mod 2 until the number turns into 0.

However, there is a cooler solution that we use n & (n-1) to transform $n$ until $n=0$. In each transform, the number of 1s in $n$ will be reduced by 1. We can discuss this property in 2 cases:

1. The binary number is ends with $1$. Let $n=0bB1$, then $n-1=0bB0$ and $n\&(n-1)=0bB0$. The tail 1 disappears.
2. The binary number is ends with $0$. Let $n=0bB10\dots 0$, then $n-1=0bB01\dots 1$ and $n\&(n-1)=0bB00\dots 0$. The tail 1 still disappears.

Therefore, we can repeat this process $T$ times until $n$ becomes 0 and $T$ is the answer.

Code

Modulo

class Solution:
    def hammingWeight(self, n: int) -> int:
        ans = 0
        while n > 0:
            ans += n%2
            n //= 2
        return ans 

Bit operation

class Solution:
    def hammingWeight(self, n: int) -> int:
        ans = 0
        while n > 0:
            n &= (n-1)
            ans += 1
        return ans