Count 1 in Binary

Question

• lintcode: (365) Count 1 in Binary

Count how many 1 in binary representation of a 32-bit integer.

Example
Given 32, return 1

Given 5, return 2

Given 1023, return 9

Challenge
If the integer is n bits with m 1 bits. Can you do it in O(m) time?

题解

题 O1 Check Power of 2 的进阶版，x & (x - 1) 的含义为去掉二进制数中1的最后一位，无论 x 是正数还是负数都成立。

C++

class Solution {
public:
    /**
     * @param num: an integer
     * @return: an integer, the number of ones in num
     */
    int countOnes(int num) {
        int count=0;
        while (num) {
            num &= num-1;
            count++;
        }
        return count;
    }
};

Java

public class Solution {
    /**
     * @param num: an integer
     * @return: an integer, the number of ones in num
     */
    public int countOnes(int num) {
        int count = 0;
        while (num != 0) {
            num = num & (num - 1);
            count++;
        }

        return count;
    }
}

源码分析

累加计数器即可。

复杂度分析

这种算法依赖于数中1的个数，时间复杂度为 $O(m)$. 空间复杂度 $O(1)$.

Reference

• Number of 1 bits | LeetCode - 评论中有关于不同算法性能的讨论