[LeetCode] 89. Gray Code

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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.

Example 1:

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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:

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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].

Explanation

  1. We list the first couple of grey code and its corresponding binary number.

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     Int    Grey Code    Binary
  0  　　  000        000
  1  　　  001        001
  2   　 　011        010
  3   　 　010        011
  4   　 　110        100
  5   　 　111        101
  6   　 　101        110
  7   　　 100        111

  2. There is a formula to convert binary number to its grey code, and formula to convert grey code to its binary.

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     unsigned int binaryToGray(unsigned int num) {
         return (num >> 1) ^ num;
 }

 unsigned int grayToBinary(unsigned int num) {
     unsigned int mask;
     for (mask = num >> 1; mask != 0; mask = mask >> 1) {
         num = num ^ mask;
     }
     return num;
 }

Solution

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class Solution {
    public List<Integer> grayCode(int n) {
        List<Integer> res = new ArrayList<>();
        for (int i = 0; i < 1<<n; i++) {
            res.add(i>>1 ^ i);
        }

        return res;
    }
}