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.

题意：长度为n的格雷码的构造。

思路：长度为2的格雷码有4个：00,01,11,10, (即：0,1,3,2)；则存在这样的关系，长度为3的格雷码有8个，前4个是 0-00, 0-01, 0-11, 0-10,(即：0,1,3,2)， 后四个是：1-00,1-01，1-11,1-10。就是在前一个长度的格雷码表示上前半段加上0（表示的数值不变），后半段加上1即可。对于从长度n-1到长度到n的变化过程也符合这个规律。

class Solution {
public:
vector<int> grayCode(int n) {
vector<int> res(1<<n, 0);
int count = 1;
for (int i = 1; i <= n; i++){
int count = 0;
for (int j = (1<<i)-1; j > (1<<i-1)-1; j--){
res[j] = res[count++] | 1 << i-1;
}
}
return res;
}
};