【Gray Code】cpp

题目：

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, print the sequence of gray code. A gray code sequence must begin with 0.

For example, given n = 2, return [0,1,3,2]. Its gray code sequence is:

00 - 0
01 - 1
11 - 3
10 - 2

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

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

For now, the judge is able to judge based on one instance of gray code sequence. Sorry about that.

代码：

class Solution {
public:
    vector<int> grayCode(int n) {
        std::vector<int> result;
        const size_t size = 1 << n;
        result.reserve(size);
        for (size_t i = 0; i < size; ++i)
        {
            result.push_back(i ^ ( i >> 1));
        }
        return result;
    }
};

Tips:

1. gray code与binary code之间的转换公式 “i 异或 (i右移1位)”

2. 这个代码鲁棒性比较强，即使n非常大（比如100000000）也只会返回0，不会crash

3. 另外调研了一下size_t的用法，后面再深入看看。

==========================================

第二次过Gray Code大概能想起来思路，但是记不牢了。看了一下之前的笔记，这道题考察的是位运算。

class Solution {
public:
    vector<int> grayCode(int n) {
            vector<int> ret;
            const size_t N = 1 << n;
            ret.reserve(N);
            for ( int i=0; i<N; ++i ) ret.push_back(i ^ (i >> 1));
            return ret;
    }
};

这里的核心是算2的N次幂可以用1左移N位来计算；反之，除以2，或许也可以用右移1位来操作。