Leetcode–Gray Code

The Problem:

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.

Notes:

  1. List a few examples then a pattern reveals. The list of n is the list of n-1 appends another list created by reversing the list of n-1 and adding a leading 1 to each element.

Java Solution

public class Solution {
    public List<Integer> grayCode(int n) {
        // combo fo rn is the reverse of combo for n-1, and left append 1
        List<Integer> result = new ArrayList<Integer>();
        
        result.add(0);
        if(n==0) return result;
        result.add(1);
        if(n==1)return result;
        
        for(int j = 2; j <=n; j++){
            List<Integer> append = new ArrayList<Integer>();
            int num = 1<<(j-1);
            for(int i = result.size()-1; i>=0; i--){
                append.add( num+ result.get(i));
            }
            result.addAll(append);
        }
        return result;
    }
    
}
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