Leetcode 之 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.

题目要求n个0或1的组合，每对组合只能变换其中的一位。所以就是2^n个01串的顺序问题喽。

n=1时，只有0，1两种排序，用黄色标注

n=2时，在前面加0或者1，由于要求只能变一位，发现后一位从01变成了10，顺序反过来了。

n=3时，在n=2的4个序列前面加0或1，最高位为0时跟n=2是相同的，最高位为时n=2的序列要变成逆序。



上代码吧。

public List<Integer> grayCode(int n) {
List<Integer> value = new ArrayList<Integer>();
if(n == 0){
value.add(0);
return value;
}
value = code(n);
return value;
}

public List<Integer> code(int n){
List<Integer> value = new ArrayList<Integer>();
if(n == 1){
value.add(0);
value.add(1);
return value;
}
List<Integer> last = code(n - 1);

value.addAll(last);
for(int i = last.size() - 1 ;i >= 0; i--){
value.add((int)(Math.pow(2, n - 1)) + last.get(i));
}

return value;
}

12 / 12 test cases passed.

Status: Accepted

Runtime: 240 ms