Number of 1 Bits

Easy Bit Manipulation Tricks to remember Original on LeetCode

Number of 1 Bits is a easy bit manipulation problem solved with the tricks to remember pattern. The best approach, optimal (brian kernighan's trick), runs in O(number of set bits) time and O(1) space. Below are 2 approaches in Java, from check all 32 bits up.

Problem

Return the number of set bits (1s) in the binary representation of n (also called the Hamming weight).

Examples

Example 1

Input: n = 11
Output: 3
Why: 1011.

Example 2

Input: n = 128
Output: 1

Constraints

1 <= n <= 2^31 - 1

Animated walkthrough

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Solutions

Try it yourself first. Then compare: each approach lists its idea, the steps, its time and space, and the Java code.

Approach	Time	Space
Check all 32 bits	`O(32)`	`O(1)`
Optimal (Brian Kernighan's trick)	`O(number of set bits)`	`O(1)`

1Check all 32 bits

TimeO(32)

SpaceO(1)

Test the lowest bit and shift right, 32 times (or until n is 0).

count += n & 1; n >>>= 1.

Java

class Solution {
    public int hammingWeight(int n) {
        int count = 0;
        while (n != 0) {
            count += n & 1;
            n >>>= 1;
        }
        return count;
    }
}

2Optimal (Brian Kernighan's trick)

TimeO(number of set bits)

SpaceO(1)

n - 1 flips the lowest set bit and every bit below it, so n & (n - 1) removes exactly the lowest set bit. The loop runs once per set bit.

while n != 0: n &= n - 1; count++.

Java

class Solution {
    public int hammingWeight(int n) {
        int count = 0;
        while (n != 0) {
            n &= n - 1;
            count++;
        }
        return count;
    }
}

Edge cases to test

Powers of two (1)
2^31 - 1 (31 ones)

Hints

Hint 1

n & (n - 1) clears the lowest set bit. Count how many times you can do it before n becomes 0.

FAQ

What is the best time complexity for Number of 1 Bits?

Optimal (Brian Kernighan's trick) runs in O(number of set bits) time and O(1) extra space.

Which pattern does Number of 1 Bits use?

It is a bit manipulation problem that uses the tricks to remember pattern. Other problems with the same pattern: Set the rightmost unset bit, XOR of 1 to n Numbers.

Is there a brute force solution for Number of 1 Bits?

Yes. Check all 32 bits takes O(32) time and O(1) space. Test the lowest bit and shift right, 32 times (or until n is 0).

Which edge cases should I test for Number of 1 Bits?

Powers of two (1); 2^31 - 1 (31 ones).