C++中的位运算和位图bitmap解析

-x = ~x + 1 = ~(x-1)
-(~x) = x+1
~(-x) = x-1
x+y = x - ~y - 1 = (x|y)+(x&y)
x-y = x + ~y + 1 = (x|~y)-(~x&y)
x^y = (x|y)-(x&y)
x|y = (x&~y)+y
x&y = (~x|y)-~x
x==y:    ~(x-y|y-x)
x!=y:    x-y|y-x
x< y:    (x-y)^((x^y)&((x-y)^x))
x<=y:    (x|~y)&((x^y)|~(y-x))
x< y:    (~x&y)|((~x|y)&(x-y))//无符号x,y比较
x<=y:    (~x|y)&((x^y)|~(y-x))//无符号x,y比较

a&1 = 0 偶数 
a&1 = 1 奇数

a = a&~(1<<k)

a=a|(1<<k)

a=a<<k|a>>sizeof(unsigned int)*8-k   

a=a>>k|a<<sizeof(unsigned int)*8-k   

int average(int x, int y)   //返回X,Y 的平均值
{   
     return (x&y)+((x^y)>>1);
}

bool power2(int x)
{
    return ((x&(x-1))==0)&&(x!=0)；
}

void swap( int& x , int& y)
{
    x ^= y;
    y ^= x;
    x ^= y;
}

void swap01(int& x , int& y）{
   x += y;
   y = x - y;
   x = x - y;
}

int abs( int x )
{
int y ;
y = x >> 31 ;
return (x^y)-y ;        //or: (x+y)^y
}

int abs01(int a){
	return (a>0)?a:(~a+1);
}

a % (2^n) 等价于 a & (2^n - 1)

a * (2^n) 等价于 a<< n

  a / (2^n) 等价于 a>> n
    例: 12/8 == 12>>3

int add(int a,int b){
	while(b!=0){
		int temp=a^b;
		b=(unsigned int)(a&b)<<1;
		a = temp;
	}
	return a;
}

#include <iostream>
#include <vector>
using namespace std;

class BitMap
{
public:
    BitMap(size_t range)
    {
        //此时多开辟一个空间
        _bits.resize(range / 32 + 1);
    }
    void Set(size_t x)
    {
        int index = x / 32;//确定哪个数据（区间）
        int temp = x % 32;//确定哪个Bit位
        _bits[index] |= (1 << temp);//位操作即可
    }
    void Reset(size_t x)
    {
        int index = x / 32;
        int temp = x % 32;
        _bits[index] &= ~(1 << temp);//取反
    }
    bool Test(size_t x)
    {
        int index = x / 32;
        int temp = x % 32;
        if (_bits[index]&(1<<temp))
            return 1;
        else
            return 0;
    }

private:
    vector<int> _bits;
};

void TestBitMap()
{
    BitMap am(-1);
    BitMap bm(200);
    bm.Set(136);
    bm.Set(1);
    cout << bm.Test(136) << endl;
    bm.Reset(136);
    cout << bm.Test(136) << endl;
}

int main()
{
    TestBitMap();
    return 0;
}