Gray Code

lc 89

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.

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

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

当n=3时，正确的GrayCode应该是

000
001
011
010
110
111 //如果按照题意的话，只是要求有一位不同，这里也可以是100
101
100

GrayCode的规律就出来了，n=k时的Gray Code，相当于n=k-1时的Gray Code的逆序 加上 1<<k。

    public List<Integer> grayCode(int n) {
        List<Integer> res = new ArrayList<Integer>();
        if(n == 0){
            res.add(0);
            return res;
        } 
        if( n == 1){
            res.add(0);
            res.add(1);
            return res;
        }
        List<Integer> last = grayCode(n - 1);
        for(int i = 0; i < last.size(); i++){
            res.add(last.get(i));
        }
        for(int i = last.size() - 1; i >= 0; i--){
            int cur = (1 << (n- 1)) + last.get(i);
            res.add(cur);
        }        
        return res;
    }