【leetcode】89. Gray Code
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一、题目描述
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 - 001 - 111 - 310 - 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:需要先找出规律,试着写几个用例就可以发现了。当n=0 时,[0],当n=1 时, [0, 1],当n=2时,[00, 01, 11, 10],当n=3 时,[000, 001, 011, 010, 110, 111, 101, 100]。可以发现000, 001, 011, 010 正好是n=2 的数值在第一位加了一个0,而110, 111, 101, 100,正好是n=2 的数值按逆序在每个数的第一位加了一个1。
c++代码(3ms,100%)
class Solution {public: vector<int> grayCode(int n) { vector<int> res; if(n==0){ res.push_back(0); return res; } vector<int> last_res = grayCode(n-1); //获取之前的数值 res.insert(res.end(),last_res.begin(),last_res.end()); for(int i=(int)last_res.size()-1;i>=0; i--){ res.push_back(last_res[i]+(1<<n-1)); } return res; }};
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