巧用位运算规律 Flags

找规律

(1 ) &1 =1
(1 ) &2 =0
(1 ) &3 =1
(1 ) &4 =0
(1 ) &5 =1
(1 ) &6 =0
(1 ) &7 =1
(1 ) &8 =0
(1 ) &9 =1
(1 ) &10 =0
(1 ) &11 =1
(1 ) &12 =0
(1 ) &13 =1
(1 ) &14 =0
(1 ) &15 =1
(1 ) &16 =0
(1 ) &17 =1
(1 ) &18 =0
(1 ) &19 =1

(1 | 2 ) &1 =1
(1 | 2 ) &2 =2
(1 | 2 ) &3 =3
(1 | 2 ) &4 =0
(1 | 2 ) &5 =1
(1 | 2 ) &6 =2
(1 | 2 ) &7 =3
(1 | 2 ) &8 =0
(1 | 2 ) &9 =1
(1 | 2 ) &10 =2
(1 | 2 ) &11 =3
(1 | 2 ) &12 =0
(1 | 2 ) &13 =1
(1 | 2 ) &14 =2
(1 | 2 ) &15 =3
(1 | 2 ) &16 =0
(1 | 2 ) &17 =1
(1 | 2 ) &18 =2
(1 | 2 ) &19 =3

(1 | 2 | 4 ) &1 =1
(1 | 2 | 4 ) &2 =2
(1 | 2 | 4 ) &3 =3
(1 | 2 | 4 ) &4 =4
(1 | 2 | 4 ) &5 =5
(1 | 2 | 4 ) &6 =6
(1 | 2 | 4 ) &7 =7
(1 | 2 | 4 ) &8 =0
(1 | 2 | 4 ) &9 =1
(1 | 2 | 4 ) &10 =2
(1 | 2 | 4 ) &11 =3
(1 | 2 | 4 ) &12 =4
(1 | 2 | 4 ) &13 =5
(1 | 2 | 4 ) &14 =6
(1 | 2 | 4 ) &15 =7
(1 | 2 | 4 ) &16 =0
(1 | 2 | 4 ) &17 =1
(1 | 2 | 4 ) &18 =2
(1 | 2 | 4 ) &19 =3

(1 | 2 | 4 | 8) &1 =1
(1 | 2 | 4 | 8) &2 =2
(1 | 2 | 4 | 8) &3 =3
(1 | 2 | 4 | 8) &4 =4
(1 | 2 | 4 | 8) &5 =5
(1 | 2 | 4 | 8) &6 =6
(1 | 2 | 4 | 8) &7 =7
(1 | 2 | 4 | 8) &8 =8
(1 | 2 | 4 | 8) &9 =9
(1 | 2 | 4 | 8) &10 =10
(1 | 2 | 4 | 8) &11 =11
(1 | 2 | 4 | 8) &12 =12
(1 | 2 | 4 | 8) &13 =13
(1 | 2 | 4 | 8) &14 =14
(1 | 2 | 4 | 8) &15 =15
(1 | 2 | 4 | 8) &16 =0
(1 | 2 | 4 | 8) &17 =1
(1 | 2 | 4 | 8) &18 =2
(1 | 2 | 4 | 8) &19 =3

找到的规律就是数组  [1、2、4、8]   满足任意一个成员 Xn  = 任意多个不同成员异或运算的结果 y([X1-Xn]) & Xn

即  y([X1-Xn]) & Xn  =Xn

再看下 这个规律

(1 ) =1
(1 | 2 ) =3
(1 | 2 | 4 ) =7
(1 | 2 | 4 | 8) =15

2 的等比数列