Tuesday, November 18, 2014

[LeetCode] 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:

例举grey code序列,并找规律 :
n = 0: 0
n = 1: 0, 1
n = 2: 00, 01, 11, 10  (0, 1, 3, 2)
n = 3: 000, 001, 011, 010, 110, 111, 101, 100 (0, 1, 3, 2, 6, 7, 5, 4)
以n = 3为例,grey code中前4个包括了n = 2的所有gray code。后4个则是前4个逆序后加上2^2。

推广:n = i的grey code的前一半包括了n = i-1的所有grey code,而后一半则为前一半逆序后家上2^(i-1)。


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

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