LeetCode——Gray Code

最新推荐文章于 2022-01-08 12:27:45 发布

yjfanling

最新推荐文章于 2022-01-08 12:27:45 发布

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分类专栏：算法文章标签： java leetcode

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本文介绍两种生成格雷码序列的方法。一种是递归构造法，通过递归将n位格雷码转换为n+1位格雷码；另一种是直接计算法，利用位运算快速生成格雷码序列。

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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].

解法

当n=0时，返回{0}，当n=1时，返回{0,1}
当n==2时：
0 0-----0
0 1-----1

1 1-----3
1 0-----2

当n==3时：
0 0 0-----0
0 0 1-----1
0 1 1-----3
0 1 0-----2

1 1 0-----6
1 1 1-----7
1 0 1-----5
1 0 0-----4

由此可得n的数列为：n-1的数列加上n-1数列反过来排，并给每一个数加2的n-1次幂。
讲起来有点麻烦啊，还是偷个图吧
在这里插入图片描述

public List<Integer> grayCode(int n) {
		return grayCodecore(n);
	}

	private List<Integer> grayCodecore(int n) {
		// TODO Auto-generated method stub
		List<Integer> list = new ArrayList<Integer>();
		if (n == 0)
			list.add(0);
		else if (n == 1) {
			Integer[] array = { 0, 1};
			Collections.addAll(list, array);
		} else {
			list = grayCodecore(n - 1);
			for (int i = list.size() - 1; i >= 0; i--)
				list.add((int) (list.get(i) + Math.pow(2, n - 1)));
		}
		return list;
	}

Runtime: 1 ms, faster than 44.03% of Java online submissions for Gray Code.
Memory Usage: 33 MB, less than 100.00% of Java online submissions for Gray Code.

解法二

Int    Grey Code    Binary    Binary>>1
 0  　　  000        000         000
 1  　　  001        001         000
 2   　 　011        010         001
 3   　 　010        011         001
 4   　 　110        100         010
 5   　 　111        101         010
 6   　 　101        110         011
 7   　　 100        111         011

可见格雷码为i和i右移一位的异或

public List<Integer> grayCode(int n) {
		List<Integer> list = new ArrayList<Integer>();
		for(int i=0;i<Math.pow(2, n);i++)
			list.add((i>>1)^i);
		return list;
	}

Runtime: 0 ms, faster than 100.00% of Java online submissions for Gray Code.
Memory Usage: 32.9 MB, less than 100.00% of Java online submissions for Gray Code.