题目

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.

题解

这道题是要考我知不知道格雷码么。。反正我自己单看找不出规律。。。

可以看到n位的格雷码由两部分构成,一部分是n-1位格雷码,再加上 1<<(n-1)和n-1位格雷码的逆序(整个格雷码逆序0132变成2310这种)的和。

1位格雷码有两个码字
(n+1)位格雷码中的前2^n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2^n个码字等于n位格雷码的码字,按逆序书写,加前缀1。

由于是二进制,在最高位加0跟原来的数本质没有改变,所以取得上一位算出的格雷码结果,再加上逆序添1的方法就是当前这位格雷码的结果了。

n = 0时,[0]

n = 1时,[0,1]

n = 2时,[00,01,11,10]

n = 3时,[000,001,011,010,110,111,101,100]

当n=1时,0,1

当n=2时,原来的list 0,1不变,只是前面形式上加了个0变成00,01。然后加数是1<<1为10,依次:10+1=11 10+0=10。结果为:00 01 11 10

当n=3时,原来的list 00,01,11, 10(倒序为:10,11,01,00)。加数1<<2为100。倒序相加为:100+10=110, 100+11=,100+01=, 100+00= 100。

最终结果为000 001 011 010 110 111 101 100

代码如下:

 1     public ArrayList<Integer> grayCode(int n) {  
 2         if(n==0) {  
 3             ArrayList<Integer> result = new ArrayList<Integer>();  
 4             result.add(0);  
 5             return result;  
 6         }  
 7           
 8         ArrayList<Integer> result = grayCode(n-1);  
 9         int addNumber = 1 << (n-1);
         int originalsize=result.size();
         
         for(int i=originalsize-1;i>=0;i--) {  
             result.add(addNumber + result.get(i));  
         }  
         return result;  
     }

Gray Code leetcode java的更多相关文章

  1. 89. Gray Code - LeetCode

    Question 89. Gray Code Solution 思路: n = 0 0 n = 1 0 1 n = 2 00 01 10 11 n = 3 000 001 010 011 100 10 ...

  2. Gray Code -- LeetCode

    原标题链接: http://oj.leetcode.com/problems/gray-code/  这道题要求求出n位的格雷码相应的二进制数,主要在于找到一种格雷码的递增方法(格雷码并非唯一的,能够 ...

  3. Java for LeetCode 089 Gray Code

    The gray code is a binary numeral system where two successive values differ in only one bit. Given a ...

  4. [LeetCode] 89. Gray Code 格雷码

    The gray code is a binary numeral system where two successive values differ in only one bit. Given a ...

  5. [LeetCode] Gray Code 格雷码

    The gray code is a binary numeral system where two successive values differ in only one bit. Given a ...

  6. [LeetCode]题解(python):089 Gray Code

    题目来源 https://leetcode.com/problems/gray-code/ The gray code is a binary numeral system where two suc ...

  7. 【一天一道LeetCode】#89. Gray Code

    一天一道LeetCode 本系列文章已全部上传至我的github,地址:ZeeCoder's Github 欢迎大家关注我的新浪微博,我的新浪微博 欢迎转载,转载请注明出处 (一)题目 The gra ...

  8. [leetcode]Gray Code @ Python

    原题地址:https://oj.leetcode.com/problems/gray-code/ 题意: The gray code is a binary numeral system where ...

  9. LeetCode: Gray Code 解题报告

    Gray CodeThe gray code is a binary numeral system where two successive values differ in only one bit ...

随机推荐

  1. hdu 1116 敌兵布阵(树状数组区间求和)

    题意: 给出一行数字,然后可以修改其中第i个数字,并且可以询问第i至第j个数字的和(i <= j). 输入: 首行输入一个t,表示共有t组数据. 接下来每行首行输入一个整数n,表示共有n个数字. ...

  2. 【BZOJ-3456】城市规划 CDQ分治 + NTT

    题目链接 http://www.lydsy.com/JudgeOnline/problem.php?id=3456 Solution 这个问题可以考虑dp,利用补集思想 N个点的简单图总数量为$2^{ ...

  3. Moment.js 一款JS时间封装库

    链接地址:http://momentjs.cn/docs/#/displaying/difference/

  4. Codeforces Round #373 (Div. 2) B. Anatoly and Cockroaches 水题

    B. Anatoly and Cockroaches 题目连接: http://codeforces.com/contest/719/problem/B Description Anatoly liv ...

  5. Moscow Subregional 2013. 部分题题解 (6/12)

    Moscow Subregional 2013. 比赛连接 http://opentrains.snarknews.info/~ejudge/team.cgi?contest_id=006570 总叙 ...

  6. Educational Codeforces Round 14 A. Fashion in Berland 水题

    A. Fashion in Berland 题目连接: http://www.codeforces.com/contest/691/problem/A Description According to ...

  7. springMvc Velocity tool 源码分析

    在公司使用pandoraboot配置了velocity tool,一直不明白官方支持的init方法没有调用,而且不支持velocity tool 1.x版本的定义(1.x和2.x的定义见下面),而另一 ...

  8. STM32 F4 GPIO Modes

    STM32 F4 GPIO Modes Goal: creating a visual summary of GPIO configuration modes. The summary at the ...

  9. How to properly set clock speed for STM32F4xx devices

    http://stm32f4-discovery.com/2015/01/properly-set-clock-speed-stm32f4xx-devices/ I see that you have ...

  10. C#Winform将WebBowser控件替换为Chrome内核

    摘要 由于最近要做一个浏览器式的软件,其中有不少地方需要使用到jQuery和BootStrap,但是在C#中,默认的WebBrowser控件默认使用的是IE的core,而低版本的IE在JS加载上总是容 ...