LeetCode Gray Code

最新推荐文章于 2025-09-11 19:19:55 发布

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本文介绍了一种生成灰码序列的方法，灰码是一种特殊的二进制数系统，相邻两个数只有一位不同。文中提供了Java实现代码，能够根据输入的位数生成相应的灰码序列。

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.

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.

Solution:

首先将0到2^n - 1的数字对应的二进制得到，然后通过

公式表示：

（G：格雷码，B：二进制码）

公式，将二进制的数字转化为格雷码，最高位（位数从0到n-1)，第n位补0，再将最后得到的格雷码当作二进制数字，转化为十进制。

import java.util.*;

public class Solution {
	List<Integer> list = new ArrayList<Integer>();

	public List<Integer> grayCode(int n) {
		if (n == 0) {
			list.add(0);
			return list;
		}

		String binary, grey;
		int limit = 1 << n;

		for (int i = 0; i < (1 << n); i++) {
			binary = Integer.toBinaryString((limit - 1) & i | limit);
			binary = "0" + binary.substring(1);
			grey = "";
			for (int j = 1; j < binary.length(); j++) {
				grey = grey
						+ ((binary.charAt(j - 1) - '0') ^ (binary.charAt(j) - '0'));
			}
			list.add(Integer.parseInt(grey, 2));

		}

		return list;
	}

	public static void main(String[] args) {
		Solution s = new Solution();
		s.grayCode(3);
	}
}