LeetCode 089 Gray Code

题目

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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:

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.

给出n，写出n位的格雷码。

思路

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1 先写出n=1----n=4的格雷码，开始找规律。

2 发现不管n等于几，开头总是一样的；n越大，后面增加的数字越多。

3 发觉每次n后半部分的数字都是前半部分数字倒序后+固定数量的数，这个数是2^n-1，通过观察二进制也能够发现规律。

4 从0到1到2都是如此，所以这是普遍现象，可以完美使用循环。

ps 看到另外一种方法，前提是知道格雷码的计算特点

http://blog.youkuaiyun.com/fightforyourdream/article/details/14517973

代码

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public class Solution {
    public ArrayList<Integer> grayCode(int n) {
        ArrayList<Integer> ans = new ArrayList<Integer>();
        if(n<0){
            return ans;
        }
        ans.add(0);
        int s =0;
        while(s<n){
            int maxs = 1<<s;
            for(int i=ans.size()-1;i>=0;i--){
                int temp = ans.get(i);
                ans.add(temp+maxs);
            }
            s++;
        }
        return ans;
    }
}