[leetcode] Gray Code
2015-06-24 14:51
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From : https://leetcode.com/problems/gray-code/
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
is:
Note:
For a given n, a gray code sequence is not uniquely defined.
For example,
For now, the judge is able to judge based on one instance of gray code sequence. Sorry about that.
Solution 1:
Binary Code :1011 要转换成Gray Code
1011 = 1(照写第一位), 1(第一位与第二位异或 1^0 = 1), 1(第二位异或第三位, 0^1=1), 0 (1^1 =0) = 1110
其实就等于 (1011 >> 1) ^ 1011 = 1110
Solution 2:
这种方法基于格雷码是反射码的事实,利用递归的如下规则来构造:
1位格雷码有两个码字,
(n+1)位格雷码中的前2n个码字等于n位格雷码的码字,按顺序书写,加前缀0,
(n+1)位格雷码中的后2n个码字等于n位格雷码的码字,按逆序书写,加前缀1.
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:
00 - 0 01 - 1 11 - 3 10 - 2
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 1:
Binary Code :1011 要转换成Gray Code
1011 = 1(照写第一位), 1(第一位与第二位异或 1^0 = 1), 1(第二位异或第三位, 0^1=1), 0 (1^1 =0) = 1110
其实就等于 (1011 >> 1) ^ 1011 = 1110
class Solution { public: vector<int> grayCode(int n) { int size = 1<<n; vector<int> grayCodes(size); for (int i = 0; i < size; i++){ grayCodes[i] = (i>>1) ^i; } return grayCodes; } };
Solution 2:
递归生成码表
这种方法基于格雷码是反射码的事实,利用递归的如下规则来构造:1位格雷码有两个码字,
(n+1)位格雷码中的前2n个码字等于n位格雷码的码字,按顺序书写,加前缀0,
(n+1)位格雷码中的后2n个码字等于n位格雷码的码字,按逆序书写,加前缀1.
2位格雷码 | 3位格雷码 | 4位格雷码 | 4位自然二进制码 |
---|---|---|---|
00 01 11 10 | 000 001 011 010 110 111 101 100 | 0000 0001 0011 0010 0110 0111 0101 0100 1100 1101 1111 1110 1010 1011 1001 1000 | 0000 0001 0010 0011 0100 0101 0110 0111 1000 1001 1010 1011 1100 1101 1110 |
class Solution { public: vector<int> grayCode(int n) { vector<int> result; result.push_back(0); for(int i=0; i<n; i++){ int highest = 1<<i; int len = result.size(); for(int i=len-1; i>=0; i--){ result.push_back(highest+result[i]); } } return result; } };
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