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# 89. Gray Code

### Description

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.

### Constraints

### Approach

### Links

* [GeeksforGeeks](https://www.geeksforgeeks.org/generate-n-bit-gray-codes-set-2/)
* [Leetcode](https://leetcode.com/problems/gray-code/)
* [ProgramCreek](https://www.programcreek.com/2014/05/leetcode-gray-code-java/)
* YouTube

### **Examples**

{% tabs %}
{% tab title="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
{% endtab %}

{% tab title="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].
{% endtab %}
{% endtabs %}

### **Solutions**

{% tabs %}
{% tab title="Solution 1" %}

```java
/**
 * Time complexity : 
 * Space complexity : 
 */

class Solution {
    public List<Integer> grayCode(int n) {
        int noOfGrays = (1 << n);
        return IntStream.range(0, noOfGrays)
            .mapToObj(i -> (i ^ (i>>1)))
            .collect(Collectors.toList());
    }
}
```

{% endtab %}

{% tab title="Solution 2" %}

```java
/**
 * Time complexity : 
 * Space complexity : 
 */

class Solution {
    public List<Integer> grayCode(int n) {
        // Number of possible gray codes (i.e, 2^n)
        int noOfGrays = (1 << n);
        List<Integer> grayCodes = new ArrayList<>();
        for(int i = 0; i < noOfGrays; i++) {
            grayCodes.add(i ^ (i>>1));
        }
        return grayCodes;
    }
}
```

{% endtab %}
{% endtabs %}

### **Follow up**

* A backtracking approach to generate n bit Gray Codes - [GFG](https://www.geeksforgeeks.org/backtracking-approach-generate-n-bit-gray-codes/)