LintCode 411: Gray Code (二进制操作)

最新推荐文章于 2020-05-03 04:06:23 发布

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本文介绍了一种基于异或操作生成格雷码序列的高效算法。格雷码是一种二进制数系统，其中任意两个连续数值仅在一个位上不同。文章详细解释了如何使用(i^(i<<1))的异或操作来生成长度为2^n的格雷码序列，适用于n个比特的编码需求。

Gray Code
The gray code is a binary numeral system where two successive values differ in only one bit.

Given a non-negative integer n representing the total number of bits in the code, find the sequence of gray code. A gray code sequence must begin with 0 and with cover all 2n integers.

Example
Given n = 2, return [0,1,3,2]. Its gray code sequence is:

00 - 0
01 - 1
11 - 3
10 - 2
Challenge
O(2n) time.

Notice
For a given n, a gray code sequence is not uniquely defined.

[0,2,3,1] is also a valid gray code sequence according to the above definition.

解法：
基于(i ^ (i << 1))的异或操作。
代码如下：

class Solution {
public:
    /**
     * @param n: a number
     * @return: Gray code
     */
    vector<int> grayCode(int n) {
        vector<int> result;
        int len = 1 << n;
       // result.reserve(len);
        for (int i = 0; i < len; ++i) {
            result.push_back(i ^ (i >> 1));
        }
        return result;
    }
};