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.

It is using the mirror arrangement way to calculate the gray code, because the grey code for (n-1) is already calculated, so we can calculate the next one by appending 1 to the last element in (n-1)'s grey code sequence, then the second last and so on.

for n=2: 1<<1 = 10

new gray code: 01+10=11, 00+10=10

for n=3: 1<<2 = 100

new gray code: 010+100=110, 011+100=111, 001+100=101, 000+100=100

public List<Integer> grayCode(int n) {
        List<Integer> results = new ArrayList<Integer>();
        results.add(0);
        for (int i = 0; i < n; i++) {
            int highBit = 1 << i;
            for (int j = results.size() - 1; j >= 0; j--) {
                results.add(highBit + results.get(j));
            }
        }
        return results;
    }