Leetcode-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:

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.

Analysis:

For num = n, suppose we know a gray sequence for number n-1, we then can construct a sequence for n like this:

1. add 0 in front of the n-1 sequence.

2. add 1 in front of the reverse of the n-1 sequence.

Because the reverse of a valid gray sequence also satisfy the rule of the gray sequence, except that ends with 0. For example,

for num==2:

00,01,11,10

for num==3

000,001,011,010, 110,111,101,100.

Change the rule to integer number, then we have:

1. add n-1 sequence to the list.

2. reversely add (each int in n-1 sequence+base), where base==2^n.

Solution:

 1 public class Solution {
 2     public List<Integer> grayCode(int n) {
 3         List<Integer> res = new ArrayList<Integer>();
 4         res.add(0);
 5         if (n==0){            
 6             return res;
 7         }
 8         res.add(1);
 9         if (n==1) return res;       
10         
11         int base = 1;
12         for (int i=2;i<=n;i++){
13             base = base*2;
14             List<Integer> newRes = new ArrayList<Integer>();
15             newRes.addAll(res);
16             
17             for (int j=res.size()-1;j>=0;j--){
18                 int temp = res.get(j)+base;
19                 newRes.add(temp);
20             }
21             res = newRes;
22         }
23         return res;
24         
25     }
26 }

NOTE: We actually does not need to create a new list for every n, since we only need to add the reverse n-1 sequence to the n-1 sequence to get n sequence.

 1 public class Solution {
 2     public List<Integer> grayCode(int n) {
 3         List<Integer> res = new ArrayList<Integer>();
 4         res.add(0);
 5         if (n==0){            
 6             return res;
 7         }
 8         res.add(1);
 9         if (n==1) return res;       
10         
11         int base = 1;
12         for (int i=2;i<=n;i++){
13             base = base*2;
14             int end = res.size()-1;
15             for (int j=end;j>=0;j--){
16                 int temp = res.get(j)+base;
17                 res.add(temp);
18             }
19         }
20         return res;
21         
22     }
23 }