[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

这题是求格雷码, 正好上节课电路老师有提到过格雷码这东西, 不过上课没仔细听, 对格雷码的转换并不清楚, 所以就去百科找了一下格雷码的转换方法:
1位格雷码有两个码字
(n+1)位格雷码中的前2n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2n个码字等于n位格雷码的码字，按逆序书写，加前缀1
n+1位格雷码的集合 = n位格雷码集合(顺序)加前缀0 + n位格雷码集合(逆序)加前缀1
根据以上四个性质很明显使用递归去构造, 就可以得到格雷码了

class Solution {
public:
    void helper(vector<int> &ans, int n) {
        if(n == 0)
            return;
        if(n == 1) {
            ans[0] = 0;
            ans[1] = 1;
            return;
        }
        helper(ans, n - 1);
        int m = pow(2, n - 1);
        int a = pow(2, n);
        for(int i = m*2 - 1; i >= m; i--) {
            ans[i] = ans[m*2-i-1] ^ m;
        }
    }

    vector<int> grayCode(int n) {
        int m = pow(2, n);
        vector<int> ans(m, 0);
        helper(ans, n);
        return ans;
    }
};