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

• Leetcode

• ProgramCreek

• YouTube

Examples

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

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].

Solutions

Solution 1

/**
 * 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());
    }
}

Solution 2

/**
 * 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;
    }
}

Follow up

• A backtracking approach to generate n bit Gray Codes - GFG