【Leetcode】Grey Code

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最新推荐文章于 2025-08-16 00:47:01 发布

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本文详细介绍了灰度编码的概念及其生成算法。通过逐步分析和代码实现，展示了如何使用位移运算构建灰度编码序列。包括从n=1到n=3的实例展示，并解释了如何将灰度编码序列从n阶扩展到n+1阶。

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【题目】

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.

For example, given n = 2, return [0,1,3,2]. Its gray code sequence is:

Note:
For a given n, a gray code sequence is not uniquely defined.

For example, [0,2,3,1] is also a valid gray code sequence according to the above definition.

For now, the judge is able to judge based on one instance of gray code sequence. Sorry about that.

【分析】

n = 1

0
1

n=2

0 0
0 1
1 1
1 0

n=3

0 0 0
0 0 1
0 1 1
0 1 0
1 1 0
1 1 1
1 0 1
1 0 0

After growing some rows and cols of the table, you can tell how to build table n+1 from tablen, namely add 1 to each row of table n, reverse it and append on table n. The actual operation is easier since the output only requires a list(not a nested list), so adding bit 1 to a table row is just add 1<<(n-1) to the number that row represents.

【左移】

2<<1

2向左移一位

10--》100

2-》4

【代码】

public static ArrayList<Integer> gray(int n){
    ArrayList<Integer> arr = new ArrayList<Integer>();
    arr.add(0);
    for(int i=0;i<n;i++){
        int inc = 1<<i; //n是多少，就有多少位
        for(int j=arr.size()-1;j>=0;j--){//倒过来相加
            arr.add(arr.get(j)+inc);
        }
    }
    return arr;}