Gray Code 解答

Question

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.

Solution

Key to the solution is to find that we can get grey code of n by grey code of (n - 1).

A simple illustration of from 2 to 3

When input is n, grey code size is 2ⁿ.

1. For first 2^{n - 1}, we just get from grey code of (n - 1)

2. For second 2^{n - 1}, we traverse grey code of (n - 1) in back order, and add 1 to head for each element.

public class Solution {
    public List<Integer> grayCode(int n) {
        if (n == 0) {
            List<Integer> result = new ArrayList<Integer>();
            result.add(0);
            return result;
        }
        
        List<Integer> result = grayCode(n - 1);
        int length = result.size();
        int addNumber = 1 << (n - 1);
        for (int i = length - 1; i >= 0; i--) {
            int tmp = result.get(i);
            result.add(addNumber + tmp);
        }
        return result;
    }
}