# 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:

- 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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