README_EN.md

89. Gray Code

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Description

An n-bit gray code sequence is a sequence of 2n integers where:

• Every integer is in the inclusive range [0, 2n - 1],
• The first integer is 0,
• An integer appears no more than once in the sequence,
• The binary representation of every pair of adjacent integers differs by exactly one bit, and
• The binary representation of the first and last integers differs by exactly one bit.

Given an integer n, return any valid n-bit gray code sequence.

 

Example 1:

Input: n = 2
Output: [0,1,3,2]
Explanation:
The binary representation of [0,1,3,2] is [00,01,11,10].
- 00 and 01 differ by one bit
- 01 and 11 differ by one bit
- 11 and 10 differ by one bit
- 10 and 00 differ by one bit
[0,2,3,1] is also a valid gray code sequence, whose binary representation is [00,10,11,01].
- 00 and 10 differ by one bit
- 10 and 11 differ by one bit
- 11 and 01 differ by one bit
- 01 and 00 differ by one bit

Example 2:

Input: n = 1
Output: [0,1]

 

Constraints:

• 1 <= n <= 16

Solutions

G(i) = i ^ (i/2).

Python3

class Solution:
    def grayCode(self, n: int) -> List[int]:
        return [i ^ (i >> 1) for i in range(1 << n)]

Java

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

C++

class Solution {
public:
    vector<int> grayCode(int n) {
        vector<int> ans;
        for (int i = 0; i < 1 << n; ++i) {
            ans.push_back(i ^ (i >> 1));
        }
        return ans;
    }
};

Go

func grayCode(n int) (ans []int) {
	for i := 0; i < 1<<n; i++ {
		ans = append(ans, i^(i>>1))
	}
	return
}

JavaScript

/**
 * @param {number} n
 * @return {number[]}
 */
var grayCode = function (n) {
    const ans = [];
    for (let i = 0; i < 1 << n; ++i) {
        ans.push(i ^ (i >> 1));
    }
    return ans;
};

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