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 – 2Note: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.
gray code中文名叫格雷码，一看题就知道是模拟类型，写几个例子出来找规律。以3位格雷码为例。0 0 00 0 10 1 10 1 01 1 01 1 11 0 11 0 0可以看到第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位格雷码的逆序的和。找到规律后就好办了，轻松AC。
public class Solution {public ArrayList<Integer> grayCode(int n) {if(n==0) {ArrayList<Integer> result = new ArrayList<Integer>();result.add(0);return result;}ArrayList<Integer> tmp = grayCode(n-1);int addNumber = 1 << (n-1);ArrayList<Integer> result = new ArrayList<Integer>(tmp);for(int i=tmp.size()-1;i>=0;i–) {result.add(addNumber + tmp.get(i));}return result;}}
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