[leetcode]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

Gray Code， 每次看每次都不记得。写下来让自己好温习。

Gray Code 0 = 0, 下一项是toggle最右边的bit(LSB), 再下一项是toggle最右边值为 “1” bit的左边一个bit。然后重复

如： 3bit

Gray Code:  000, 001, 011, 010, 110, 111, 101, 100, 最右边值为 “1” 的bit在最左边了，结束。

Binary      :  000, 001, 010, 011, 100, 101, 110, 111

再者就是Binary Code 转换为Gray Code了。

如：

　　Binary Code ：1011 要转换成Gray Code

　　1011 = 1（照写第一位）, 1(第一位与第二位异或 1^0 = 1), 1(第二位异或第三位， 0^1=1), 0 (1^1 =0) = 1110

　　其实就等于 (1011 >> 1) ^ 1011 = 1110

有了上面的等式写code就简单了

class Solution {
public:
    vector<int> grayCode(int n) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        int size = 1<<n;
        vector<int> grayCodes;
        grayCodes.resize(size);

        for (int i = 0; i < size; i++){
            int gCode = i ^ i>>1;
            grayCodes[i] = gCode;
        }

        return grayCodes;
    }
};

EOF