Lintcode365 Count 1 in Binary solution 题解

【题目描述】

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

计算在一个 32 位的整数的二进制表示中有多少个1.

【题目链接】

www.lintcode.com/en/problem/count-1-in-binary/

【题目解析】

最容易想到的方法是对数字依次右移，判断每一位是否为1,时间复杂度为o(n),n为数字有效位数，但是这个方法不够简洁。

更优的方法是使用n&(n-1),时间复杂度是o(m),m为1的位数，

具体实现原理可假设一个数为

num = 00010 10000

关注点放在后5位,

num-1 = 0001001111,可观察到，对一个数进行-1操作，会使最后一位1变0，高于最后一位1的位不变，低于最后一位1的位全变1，于是我们可以通过与操作，使原来最后一位1所在位变成0。并通过这个方法来判断总共有多少个1

【参考答案】

www.jiuzhang.com/solutions/count-1-in-binary/

原文地址：https://www.cnblogs.com/qiangqingci/p/8660953.html

时间： 2024-10-14 21:02:27

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