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【leetcode】Gray Code

时间:2014-06-10 19:38:39      阅读:199      评论:0      收藏:0      [点我收藏+]

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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.

For example, given n = 2, return [0,1,3,2]. Its gray code sequence is:

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00 - 0
01 - 1
11 - 3
10 - 2
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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.


题解:查了资料才发现,原来可以从二进制码转成gray码。比如说二进制码1101,要转成gray码,过程如下:

(1)左边第一位保留:1

(2)第二位与第一位异或得到第二位:1^1 = 0

(3)第三位与第二位异或得到第三位:0^1 = 1

(4)第四位与第三位异或得到第四位:1^0 = 1

所以最后得到的gray码是1011

有一个简单的公式,二进制码x对应的gray码为(x>>1)^x,上情况就是(1101>>1)^1101=1011,原理就是上述描述的过程,把x右移一位,然后错位相异或。至于第一位,如果原来是1,那么右移后得到的0和这个1相异或得到的还是1;如果原来是0,那么右移后得到的0与这个0相异或得到的还是0.

代码如下:

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 1 class Solution {
 2 public:
 3     vector<int> grayCode(int n) {
 4         int total_number = 1 << n;
 5         vector<int> answer;
 6         
 7         for(int i = 0;i < total_number;i++){
 8             answer.push_back((i>>1)^i);
 9         }
10         return answer;
11     }
12 };
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【leetcode】Gray Code,布布扣,bubuko.com

【leetcode】Gray Code

标签:style   class   blog   code   java   http   

原文地址:http://www.cnblogs.com/sunshineatnoon/p/3779603.html

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