89. Gray Code

原创于 2019-04-30 18:50:34 发布 · 166 阅读

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#Gray Code #Leetcode #Java #格雷码

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本文介绍了一种生成格雷码的算法，格雷码是一种二进制数系统，其中两个连续的数值仅在一个位上不同。文章提供了算法实现，展示了如何为给定的位数n生成格雷码序列，并通过实例解释了算法的工作原理。

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Medium

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:

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].格雷码生成公式：g(i)= i^(i/2)

i g(i)

0 0

1 1

2 3

3 2

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