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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 [0,1,3,2]
. Its gray code sequence is:
00 - 001 - 111 - 310 - 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.
二进制码->格雷码(编码):从最右边一位起,依次将每一位与左边一位异或(XOR),作为对应格雷码该位的值,最左边一位不变(相当于左边是0);
格雷码->二进制码(解码):从左边第二位起,将每位与左边一位解码后的值异或,作为该位解码后的值(最左边一位依然不变)。
Gray Code 0 = 0, 下一项是toggle最右边的bit(LSB), 再下一项是toggle最右边值为 “1” bit的左边一个bit,然后重复。直到最右边值为 “1” 的bit在最左边了,结束。
C++代码实现:
#include<iostream>#include<vector>#include<cmath>using namespace std;class Solution {public: vector<int> grayCode(int n) { vector<int> ret; int i; for(i=0;i<pow(2,n);i++) { ret.push_back((i>>1)^i); } return ret; }};int main(){ Solution s; vector<int> result=s.grayCode(4); for(auto v:result) cout<<v<<" "; cout<<endl;}
运行结果:
Gray Code