89. 格雷编码

　　　　知识点：格雷编码的生成过程， G(i) = i ^ (i/2);

        如 n = 3: 
        G(0) = 000, 
        G(1) = 1 ^ 0 = 001 ^ 000 = 001
        G(2) = 2 ^ 1 = 010 ^ 001 = 011 
        G(3) = 3 ^ 1 = 011 ^ 001 = 010
        G(4) = 4 ^ 2 = 100 ^ 010 = 110
        G(5) = 5 ^ 2 = 101 ^ 010 = 111
        G(6) = 6 ^ 3 = 110 ^ 011 = 101
        G(7) = 7 ^ 3 = 111 ^ 011 = 100

class Solution {
    
    List<Integer> res = new ArrayList<>();
    public List<Integer> grayCode(int n) {
        for(int i = 0; i < 1 << n; i++) {
            res.add(i ^ (i / 2));
        }
        return res;
    }
}

方法二：dfs

class Solution {
    List<Integer> res = new ArrayList<>();
    public List<Integer> grayCode(int n) {
        int total = 1 << n;
        boolean[] st = new boolean[total];
        st[0] = true;
        dfs(0,n,st);
        return res;
    }
    public void dfs(int cur, int n, boolean[] st) {
        if(cur < 1 << n) res.add(cur);

        for(int i = 0; i < n; i++) {
            int next = cur ^ (1 << i);
            if(st[next]) continue;
            st[next] = true;
            dfs(next,n,st);
        }
    }
}