leetcode格雷编码_swift编码查询

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].

题源：here；完整实现：here

思路：

两种思路，一种事手动生成需要的格雷码，一种事根据公式（来自维基百科）。

1 手动生成

我们建立一个hash表，里面存放已经生成的gray码，生成gray码很简单：与当前gray码有一个位置不同。代码如下：

vector<int> grayCode(int n) {
	string grayCode(n, '0');
	vector<int> result;
	unordered_map<string, int> records;
	result.push_back(0);
	records[grayCode]++;
	int total = int(pow(2, n));
	for (int i = 0; i < total; i++){			
		for (int j = 0; j < n; j++){
			string temp = grayCode;
			temp[j] = temp[j] == '0' ? '1' : '0';
			if (records[temp] == 0){
				records[temp]++;
				int num = strtol(temp.data(), NULL, 2);
				result.push_back(num);
				grayCode = temp;
				break;
			}
		}
	}

	return result;
}

2 公式

vector<int> grayCode2(int n){
	vector<int> result;
	int size = 1 << n;
	for (int i = 0; i < size; i++){
		result.push_back(i ^ (i >> 1));
	}
	return result;
}

纪念贴图：

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