LeetCode 89. Gray Code

89. Gray Code

Difficulty: Medium

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.

Example 1:

Input: 2
Output: [0,1,3,2]
Explanation:
00 - 0
01 - 1
11 - 3
10 - 2

For a given n, a gray code sequence may not be uniquely defined.
For example, [0,2,3,1] is also a valid gray code sequence.

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

Example 2:

Input: 0
Output: [0]
Explanation: We define the gray code sequence to begin with 0.
             A gray code sequence of n has size = 2n, which for n = 0 the size is 20 = 1.
             Therefore, for n = 0 the gray code sequence is [0].

Solution

Language: Java

class Solution {
    public List<Integer> grayCode(int n) {
        List<Integer> result = new ArrayList<>();
        result.add(0);
        if (n == 0) {
            return result;
        }
        boolean[] visited = new boolean[1 << n];
        visited[0] = true;
        dfsHelper(result, visited, n);
        return result;
    }
    
    private boolean dfsHelper(List<Integer> result, boolean[] visited, int n) {
        if (result.size() == (1 << n)) {
            return true;
        }
        int last = result.get(result.size() - 1);
        int cur = last;
        for (int i = 0; i < n; i++) {
            cur = last ^ (1 << i);
            if (!visited[cur]) {
                result.add(cur);
                visited[cur] = true;
                if (dfsHelper(result, visited, n)) {
                    return true;
                }
                visited[cur] = false;
                result.remove(result.size() - 1);
            }
        }
        return false;
    }
}