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.

Problem

1. What to return if n = 0

Analysis

We can construct gray code from i = 1 to i = n. Each time, we use (1 << i - 1) to bit-or the exsiting numbers from the last one to the first one. Supposed n = 3.

1. Initially, {0}
2. bit = 1 << 0, {0, 1}
3. bit = 1 << 1, {00, 01, 11, 10}
4. bit = 1 << 2, {000, 001, 011, 010, 110, 111, 101, 100}

Code

Java

public class Solution {
  public List<Integer> grayCode(int n) {
    assert n >= 0;
    List<Integer> result = new ArrayList<>();
    result.add(0);
    for (int i = 0; i < n; ++i) {
      int size = result.size();
      int bit = 1 << i;
      for (int j = size - 1; j >= 0; --j) {
        result.add(result.get(j) | bit);
      }
    }
    return result;
  }
}