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.

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.

思路:

0000 0

0001 1

0011 3

0010 2

0110 6

0111 7

0101 5

0100 4

可以看出，第i个值等于第2i-pow(2,count2bit(i))的值加上pow(2,count2bit(i))

代码如下(已通过leetcode)

public List<Integer> grayCode(int n) {

List<Integer> list=new ArrayList<Integer>();

if(n==0) {

list.add(0);

return list;

}

list.add(0);

list.add(1);

int i=2;

while(i<=n) {

int length=list.size();

for(int j=length-1;j>=0;j--) {

list.add(list.get(j)+(int)Math.pow(2, i-1));

}

i++;

}

return list;

}

}