medie2005 发表于 2008-12-2 18:49:21

G(n)表示第n个Gray code的十进制形式.
则,G(n)=n^(n/2)。[^表示异或]
记Gray code a_{n-1}a_{n-2}...a_{1}a_{0} 的对应的序号是G^{-1}(a_{n-1}a_{n-2}...a_{1}a_{0}),设G^{-1}(a_{n-1}a_{n-2}...a_{1}a_{0})=b_{n-1}b_{n-2}...b_{1}b_{0}
则,
b_{i}=a_{i}^a_{i+1}^...^a_{n-1}   0<=i<=n-1
比如,15      8       1000
b_{0}=0^0^0^1=1
b_{1}=0^0^1=1
b_{2}=0^1=1
b_{3}=1
于是,G^{-1}(8)=(1111)_2=15.
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