LeetCode: Gray Code 解题报告
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.
SOLUTION 1:
我们可以使用递归来做。规律是:
一部分是n-1位格雷码,再加上 1<<(n-1)和n-1位格雷码的逆序的和。
具体可以看维基的解释: http://zh.wikipedia.org/wiki/格雷码
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" 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格雷碼能避免訊號傳送錯誤的原理
傳統的二進位系統例如數字3的表示法為011,要切換為鄰近的數字4,也就是100時,裝置中的三個位元都得要轉換,因此於未完全轉換的過程時裝置會經歷短暫的,010,001,101,110,111等其中數種狀態,也就是代表著2、1、5、6、7,因此此種數字編碼方法於鄰近數字轉換時有比較大的誤差可能範圍。葛雷碼的發明即是用來將誤差之可能性縮減至最小,編碼的方式定義為每個鄰近數字都只相差一個位元,因此也稱為最小差異碼,可以使裝置做數字步進時只更動最少的位元數以提高穩定性。 數字0~7的編碼比較如下:
十進位 葛雷碼 二進位
0 000 000
1 001 001
2 011 010
3 010 011
4 110 100
5 111 101
6 101 110
7 100 111
public class Solution {
public List<Integer> grayCode(int n) {
List<Integer> ret = new ArrayList<Integer>();
if (n == ) {
ret.add();
return ret;
} ret = grayCode(n - ); for (int i = ret.size() - ; i >= ; i--) {
int num = ret.get(i);
num += << (n - );
ret.add(num);
} return ret;
}
}
JAVA 运算符优先级:
需要注意的是 << 的优先级 还不如+,所以,运算时,要记得加括号:
ret.add(ret.get(i) + (1 << (n - 1)));
在实际的开发中,可能在一个运算符中出现多个运算符,那么计算时,就按照优先级级别的高低进行计算,级别高的运算符先运算,级别低的运算符后计算,具体运算符的优先级见下表:
优先级 | 运算符 | 结合性 |
1 | () [] . | 从左到右 |
2 | ! +(正) -(负) ~ ++ -- | 从右向左 |
3 | * / % | 从左向右 |
4 | +(加) -(减) | 从左向右 |
5 | << >> >>> | 从左向右 |
6 | < <= > >= instanceof | 从左向右 |
7 | == != | 从左向右 |
8 | &(按位与) | 从左向右 |
9 | ^ | 从左向右 |
10 | | | 从左向右 |
11 | && | 从左向右 |
12 | || | 从左向右 |
13 | ?: | 从右向左 |
14 | = += -= *= /= %= &= |= ^= ~= <<= >>= >>>= | 从右向左 |
http://blog.csdn.net/xiaoli_feng/article/details/4567184
GITHUB:
https://github.com/yuzhangcmu/LeetCode_algorithm/blob/master/recursion/GrayCode.java
REF:
http://blog.csdn.net/fightforyourdream/article/details/14517973
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