Serial lock Gray Code knowledge + large number

Serial lock

Title Abstract: One gray code to another gray code the minimum number of conversion steps required.

Idea: Directly find the corresponding decimal, subtract the absolute value.

When n=2 , the sequence of transformations is xx,

The sequence of transformations when n=3 is 001,011,010,111, 101,

......

Careful observation found that this is the gray code, adjacent to two states only one difference (in fact, the title description has said this condition)!

Decimal number	Natural binary Number	Gray Code
0	0000	0000
1	0001	0001
2	0010	0011
3	0011	0010
4	0100	0110
5	0101	0111
6	0110	0101
7	0111	0100
8	1000	1100
9	1001	1101
10	1010	1111
11	1011	1110
12	1100	1010
13	1101	1011
14	1110	1001
15	1111	1000

Ps:

Generally, the ordinary binary code and gray code can be converted to each other in the following ways:

Binary code-- Gray Code (code): From the rightmost one, and then each one with the left one XOR (XOR), as the corresponding Gray code that bit value, the leftmost one unchanged (equivalent to the left is 0);

Gray Code ---binary code (decoding): From the second left, each bit with the left one decoded value XOR, as the bit decoded value (the leftmost one remains unchanged).

1 ImportJava.io.*;2 Importjava.math.*;3 ImportJava.util.*;4 5 classMain6 {7      Public Static intms=128;8      Public StaticBiginteger[] Base=NewBiginteger[ms];9      Public Static voidInit ()Ten     { Onebase[0]=Biginteger.one; A          for(inti=1;i<128;i++) -Base[i]=base[i-1].multiply (Biginteger.valueof (2)); -     } the      Public Static voidMain (string[] args) -     { -Scanner cin=NewScanner (NewBufferedinputstream (system.in)); - init (); +         intt=cin.nextint (); -         intN; +         int[] A=New int[MS]; A         int[] b=New int[MS]; at          while(t-->0) -         { -n=cin.nextint (); -              for(inti=0;i<n;i++) -             { -a[i]=cin.nextint (); in                 if(i!=0) -a[i]=a[i-1]^A[i]; to             } +              for(inti=0;i<n;i++) -             { theb[i]=cin.nextint (); *                 if(i!=0) $b[i]=b[i-1]^B[i];Panax Notoginseng             } -BigInteger s=Biginteger.zero; theBigInteger t=Biginteger.zero; +              for(inti=0;i<n;i++) A             { the                 if(a[n-1-i]!=0) +s=S.add (Base[i]); -                 if(b[n-1-i]!=0) $t=T.add (Base[i]); $             } - System.out.println (T.max (s). Subtract (T.min (s))); -         } the cin.close (); -     }Wuyi}

Serial lock Gray Code knowledge + large number