N的阶乘二进制表示的最低位1的位置

《编程之美》中的一道题：

#include <iostream>#include <string>using std::endl;using std::string;using std::cout;typedef unsigned long long ULLONG;//给定整数N，求N!的二进制表示中最低位1的位置template<class T>string ToBinary(T n){if (n==0){return string("0");}const int size=8*sizeof(n);string binstr(size,' ');for (int i=0;n;i++){binstr.at(size-i-1)=(n&1)+'0';n>>=1;}if(binstr.at(0)==' ')binstr = binstr.substr(binstr.find_first_not_of(' '));return binstr;}ULLONG Fact(ULLONG n){ULLONG rst=1;while(n){rst*=n--;}return rst;}int FactLowestOne1(int n){int nt=n;int cnt=0;while(n>1){cnt++;n&=n-1;}return nt-cnt;}int FactLowestOne2(int n){int cnt=0;while(n){n>>=1;cnt+=n;}return cnt;}int main(){ULLONG n=12;ULLONG fact=Fact(n);cout<<n<<"!="<<fact<<endl;cout<<"binary form: "<<ToBinary(fact)<<endl;cout<<"Lowest one bit(1): "<<FactLowestOne1(n)<<endl;cout<<"Lowest one bit(2): "<<FactLowestOne2(n);}