89. 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.

Example 1:

Input: 2
Output: [0,1,3,2]
Explanation:
00 - 0
01 - 1
11 - 3
10 - 2

For a given n, a gray code sequence may not be uniquely defined.
For example, [0,2,3,1] is also a valid gray code sequence.

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

Example 2:

Input: 0
Output: [0]
Explanation: We define the gray code sequence to begin with 0.
             A gray code sequence of n has size = 2n, which for n = 0 the size is 20 = 1.
             Therefore, for n = 0 the gray code sequence is [0].

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Submissions

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class Solution {
public:
    vector<int> grayCode(int n) {
        vector<int> res;
        res.push_back(0);
        for(int i=0;i<n;++i)
        {
            int n=res.size();
            for(int j=n-1;j>=0;--j)
                res.push_back(res[j]|1<<i);
        }
        return res;
    }
};

这题要求给定n,生成所有二进制长度为n的数字, 并且在他们当中每两个连续的数字的二进制形式只有一bit不同, 其实最后数组的内容就是从0到2的n次方所有数字,但是排序上有讲究.

采用的方法是迭代,如果拥有了n的结果,那么n+1的结果也可以得到.

这只是gray code的方法之一.毕竟只要符合要求有多种答案