[leetcode] 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 - 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.

https://oj.leetcode.com/problems/gray-code/

思路：格雷码的 定义

思路1：递归生成码表法。先将n-1的序列加入结果集中（相当于最高位是0），然后填上最高位1，再将n-1的序列倒序加入结果集。

思路2：公式法。gray = (binary) xor (binary >> 1)

import java.util.ArrayList;
import java.util.List;

public class Solution {

    public List<Integer> grayCode(int n) {
        List<Integer> res = new ArrayList<Integer>();
        if (n == 0) {
            res.add(0);
            return res;
        }
        List<Integer> pre = grayCode(n - 1);
        res.addAll(pre);
        int high = 1 << n - 1;
        for (int i = pre.size() - 1; i >= 0; i--)
            res.add(high + pre.get(i));

        return res;

    }

    public List<Integer> grayCode2(int n) {
        List<Integer> res = new ArrayList<Integer>();
        int count = 1 << n;
        for (int i = 0; i < count; i++) {
            res.add(i ^ (i >> 1));
        }
        return res;
    }

    public static void main(String[] args) {
        System.out.println(new Solution().grayCode(3));
    }

}

第二遍记录：

学会递归生成法，注意n=0时候终止条件的处理。

参考：

http://blog.csdn.net/worldwindjp/article/details/21536103