状态压缩DP常遇到的位运算的6种形式

整理

位操作一共有6种形式:<<,>>,&,|,^,~;

1.左移操作符<<:左移操作符将整数的二进制向左移若干位,将最高若干位挤掉,并在低位补0

如:

int a=3;            //a=000000000000000000000000000000011=3
int b=a<<1;         //b=000000000000000000000000000000110=6
int c=a<<3;         //c=000000000000000000000000000001100=12

实际上:a<<1,a右移1位表示a*2,a<<m表示a*2^m

2.右移操作符>>:右移操作符将整数的二进制向右移若干位,将最低若干位挤掉,并在高位补0或者1

int a =10;         //a=000000000000000000000000000001010=10
int b = a>>1; //b=000000000000000000000000000000101=5 int c = a >> 2; //c=000000000000000000000000000000010=2

右移操作符就是不断的做除2^m的运算。

3.位与操作&:位与操作是将两个数的二进制的每一位左与操作:例如:

int a = 6, b = 10;
int c = a&b; //则 c = 2;
//(000000000000000000000000000000110)
 &(000000000000000000000000000001010)
//=000000000000000000000000000000010

4.位或操作符|:将两个整数二进制的每一位做或操作运算。

int a = 6, b = 10;
int c = a|b;         //则 c=14;
//(000000000000000000000000000000110)
 |(000000000000000000000000000001010)
//=000000000000000000000000000001110

5.位异或操作符^:将两个操作数每一位做异或操作(相同为0,不同为1)

int a = 6, b = 10;
int c = a^b;         //则 =12;
//(000000000000000000000000000000110)
 ^(000000000000000000000000000001010)
//=000000000000000000000000000001100

6位反操作~:将操作数的二进制每一位按位取反,0变为1,1变为0.

int a = 6;
int b = ~a; //b=-7
//b=~(000000000000000000000000000000110)
   =   11111111111111111111111111111001

位操作相对乘法快很多,将所有对2的乘法运算转换为位移运算,可提高程序的运行效率。在C/C++中还有一类复合的位运算符:&=、!=、>>=、<<=和^=

其实a&=b;等价于a=a&b;依次类推。

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转载自blog.csdn.net/qq_41668093/article/details/80427923