leetcode——89——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, 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.

镜射排列
n位元的格雷码可以从n-1位元的格雷码以上下镜射后加上新位元的方式快速的得到。这种方法基于格雷码是反射码的事实，利用递归的如下规则来构造：

1位格雷码有两个码字
(n+1)位格雷码中的前2^n个码字等于n位格雷码的码字，按顺序书写，加前缀0
(n+1)位格雷码中的后2^n个码字等于n位格雷码的码字，按逆序书写，加前缀1

class Solution {
public:
vector<int> grayCode(int n) {
if (n == 0)
return vector<int>(1, 0);
vector<int> pre_result = grayCode(n - 1);
vector<int> cur_result(pre_result);
for (int i = pre_result.size() - 1; i >=0; --i) {
cur_result.push_back((1<<(n - 1)) + pre_result[i]);
}
return cur_result;
}
};

二进制数转格雷码
（假设以二进制为0的值做为格雷码的0）
G：格雷码 B：二进制码
G(N) = (B(n)/2) XOR B(n)

class Solution {
public:
vector<int> grayCode(int n) {

vector<int> v;
for(int i = 0; i < 1 << n; ++ i)
v.push_back(i ^ i >> 1);
return v;
}
};