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.

//整数n 的格雷码是n ^ (n/2)。

class Solution {
public:
    vector<int> grayCode(int n) {
        vector<int> rst;
		size_t size = 1 << n;//2^n
		rst.reserve(size);
		for (size_t i = 0; i < size; i++)
			rst.push_back(i ^ (i >> 1));
		return  rst;
    }
};

vector的reserve()与resize()函数区别:

• vector 的reserve增加了vector的capacity，但是它的size没有改变！而resize改变了vector的capacity同时也增加了它的size！
• reserve是容器预留空间，但在空间内不真正创建元素对象，所以在没有添加新的对象之前，不能引用容器内的元素。加入新的元素时，要调用push_back()/insert()函数。
• resize是改变容器的大小，且在创建对象，因此，调用这个函数之后，就可以引用容器内的对象了，因此当加入新的元素时，用operator[]操作符，或者用迭代器来引用元素对象。此时再调用push_back()函数，是加在这个新的空间后面的。