C++實現分數類
阿新 • • 發佈：2018-12-08
在幾乎所有的語言中（至少我知道的語言都是這樣），浮點數都是有精度丟失的。
怎麼解決呢？
分數類就是解決辦法之一。
分數類採用分數的形式，儲存了兩個整數之比，確保了精度。
分數類，肯定是要有約分、通分等函式和加、減、乘、除運算子的。（當然，要先實現求最大公因數和最小公倍數函式）這些都是基本數學知識。
程式碼如下：
#ifndef FRACTION_H #define FRACTION_H #include<iostream> #include<cstdio> using std::istream; using std::ostream; using std::getchar; namespace math{ template<typename T> T gcd(T x,T y){ if(x<y){ int temp=x; x=y,y=temp; } int z; while(y!=0){ z=x%y,x=y,y=z; } return x; } template<typename T> T lcm(T x,T y){ return x/gcd(x,y)*y; } } template<typename T,typename Tvalue=double> //T==int,long long,your big_int class ...... class fraction{ private: T _up,_down; bool input_with_reduction,output_with_reduction,multi_optimize; //optimize指上界優化，即：以犧牲時間為代價換取不溢位 public: // constructors fraction(){ _up=1,_down=1,input_with_reduction=output_with_reduction=1,multi_optimize=0; } fraction(T up,T down){ _up=up,_down=down,input_with_reduction=output_with_reduction=1,multi_optimize=0; if(input_with_reduction) reduction(); } fraction(bool optimize){ _up=1,_down=1,input_with_reduction=output_with_reduction=1,multi_optimize=optimize; } fraction(T up,T down,bool optimize){ _up=up,_down=down,input_with_reduction=output_with_reduction=1,multi_optimize=optimize; if(input_with_reduction) reduction(); } fraction(bool input_reduct,bool output_reduct){ _up=1,_down=1,input_with_reduction=input_reduct,output_with_reduction=output_reduct, multi_optimize=0; } fraction(T up,T down,bool input_reduct,bool output_reduct){ _up=up,_down=down,input_with_reduction=input_reduct,output_with_reduction=output_reduct, multi_optimize=0; if(input_with_reduction) reduction(); } fraction(bool input_reduct,bool output_reduct,bool optimize){ _up=1,_down=1,input_with_reduction=input_reduct,output_with_reduction=output_reduct, multi_optimize=optimize; } fraction(T up,T down,bool input_reduct,bool output_reduct,bool optimize){ _up=up,_down=down,input_with_reduction=input_reduct,output_with_reduction=output_reduct, multi_optimize=optimize; if(input_with_reduction) reduction(); } // inputs friend istream& operator >> (istream& input,fraction<T>& the_frac){ if(the_frac.input_with_reduction) the_frac.reduction(); input>>the_frac._up; getchar(); input>>the_frac._down; return input; } fraction<T> input_cin(bool with_reduction=1){ if(with_reduction) reduction(); using std::cin; cin>>_up; getchar(); cin>>_down; return *this; } // outputs friend ostream& operator << (ostream& output,fraction<T> the_frac){ if(the_frac.output_with_reduction) the_frac.reduction(); output<<the_frac._up<<'/'<<the_frac._down; return output; } fraction<T> output_cout(bool with_reduction=1){ if(with_reduction) reduction(); using std::cout; cout<<_up<<'/'<<_down; return *this; } // basic_functions T up(){ return _up; } T down(){ return _down; } // (bool change) bool input_reduction(bool change_to){ input_with_reduction=change_to; return change_to; } bool output_reduction(bool change_to){ output_with_reduction=change_to; return change_to; } bool multi_optimize_change(bool change_to){ multi_optimize=change_to; return change_to; } bool all_reduction(bool input_change_to,bool output_change_to){ input_with_reduction=input_change_to,output_with_reduction=output_change_to; return input_change_to&&output_change_to; } bool all_bool_change(bool input_change_to,bool output_change_to,bool optimize_change_to){ input_with_reduction=input_change_to,output_with_reduction=output_change_to, multi_optimize=optimize_change_to; return (input_change_to&&output_change_to)^optimize_change_to; } // (end of bool change) template<typename Tans=Tvalue> Tans value()const{ return Tans(_up)/Tans(_down); } fraction<T> reduction(){ //約分 T gcd_result=math::gcd(_up,_down); _up/=gcd_result,_down/=gcd_result; return *this; } fraction<T> reciprocal(bool with_reduction=1)const{ return fraction<T>(_down,_up,with_reduction,1); } template<typename T1,typename T2=T1> static void common(fraction<T1> &frac_x,fraction<T2> &frac_y){ //通分 T gcd_num=math::gcd(frac_x._down,frac_y._down); T1 x_multi_num=frac_y._down/gcd_num,y_multi_num=frac_x._down/gcd_num; frac_x._down*=x_multi_num,frac_x._up*=x_multi_num; frac_y._down*=y_multi_num,frac_y._up*=y_multi_num; } operator Tvalue()const{ return Tvalue(_up)/Tvalue(_down); } // operator + , - , * , / // operator + fraction<T> operator + (T another_adder)const{ fraction<T> frac_adder(another_adder*_down,_down,0,0); return fraction<T>(_up+frac_adder._up,_down,1,1); } fraction<T> operator + (fraction<T> another_adder)const{ two_fracs<T> commoned=common_value(*this,another_adder); return fraction<T>(commoned.first._up+commoned.second._up,commoned.first._down,true,true); } friend fraction<T> operator + (T adder,fraction<T> frac_adder){ fraction<T> frac_adder_eq1(adder*frac_adder._down,frac_adder._down,false,false); return fraction<T>(frac_adder._up+frac_adder_eq1._up,frac_adder._down,true,true); } //operator - fraction<T> operator - (fraction<T> another_adder)const{ two_fracs<T> commoned=common_value(*this,another_adder); return fraction<T>(commoned.first._up-commoned.second._up,commoned.first._down,true,true); } friend fraction<T> operator - (T adder,fraction<T> frac_adder){ fraction<T> frac_adder_eq1(adder*frac_adder._down,frac_adder._down,false,false); return fraction<T>(frac_adder_eq1._up-frac_adder._up,frac_adder._down,true,true); } //operator * fraction<T> operator * (T another_adder){ T gcd_num; if((gcd_num=math::gcd(_down,another_adder))!=1) _down/=gcd_num,another_adder/=gcd_num; return fraction<T>(_up*another_adder,_down,false,false); } fraction<T> operator * (fraction<T> another_adder){ if(multi_optimize){ T gcd_num; if(math::gcd(_up,_down)!=1) reduction(); if(math::gcd(another_adder._up,another_adder._down)!=1) another_adder.reduction(); if((gcd_num=math::gcd(_up,another_adder._down))!=1) _up/=gcd_num,another_adder._down/=gcd_num; if((gcd_num=math::gcd(_down,another_adder._up)!=1)) _down/=gcd_num,another_adder._up/=gcd_num; return fraction<T>(_up*another_adder._up,_down*another_adder._down,false,false); } else{ return fraction<T>(_up*another_adder._up,_down*another_adder._down,true,true); } } friend fraction<T> operator * (T adder,fraction<T> frac_adder){ T gcd_num; if((gcd_num=math::gcd(frac_adder._down,adder))!=1) frac_adder._down/=gcd_num,adder/=gcd_num; return fraction<T>(frac_adder._up*adder,frac_adder._down,false,false); } //operator / fraction<T> operator / (T divider){ return operator * (fraction<T>(divider,1,multi_optimize)); } fraction<T> operator / (fraction<T> divider){ return operator * (divider.reciprocal(!multi_optimize)); } friend fraction<T> operator / (T dividend,fraction<T> divider){ return operator * (dividend,divider.reciprocal(false)); } // operator < , == , != , > , <= , >= // operator < bool operator < (fraction<T> frac_arg)const{ two_fracs<T> commoned=common_value(*this,frac_arg); return commoned.first._up<commoned.second._up; } bool operator < (T integer_arg)const{ fraction<T> frac_arg_eqint(integer_arg*_down,_down,false,false); return _up<frac_arg_eqint._up; } friend bool operator < (T integer_arg,fraction<T> frac_arg){ fraction<T> frac_arg_eqint(integer_arg*frac_arg._down,frac_arg._down,false,false); return frac_arg._up<frac_arg_eqint._up; } // operator == bool operator == (fraction<T> frac_arg)const{ two_fracs<T> commoned=common_value(*this,frac_arg); return commoned.first._up==commoned.second._up; } bool operator == (T integer_arg)const{ fraction<T> frac_arg_eqint(integer_arg*_down,_down,false,false); return _up==frac_arg_eqint._up; } friend bool operator == (T integer_arg,fraction<T> frac_arg){ fraction<T> frac_arg_eqint(integer_arg*frac_arg._down,frac_arg._down,false,false); return frac_arg._up==frac_arg_eqint._up; } // operator != bool operator != (fraction<T> frac_arg)const{ two_fracs<T> commoned=common_value(*this,frac_arg); return commoned.first._up!=commoned.second._up; } bool operator != (T integer_arg)const{ fraction<T> frac_arg_eqint(integer_arg*_down,_down,false,false); return _up!=frac_arg_eqint._up; } friend bool operator != (T integer_arg,fraction<T> frac_arg){ fraction<T> frac_arg_eqint(integer_arg*frac_arg._down,frac_arg._down,false,false); return frac_arg._up!=frac_arg_eqint._up; } // operator > bool operator > (fraction<T> frac_arg)const{ two_fracs<T> commoned=common_value(*this,frac_arg); return commoned.first._up>commoned.second._up; } bool operator > (T integer_arg)const{ fraction<T> frac_arg_eqint(integer_arg*_down,_down,false,false); return _up>frac_arg_eqint._up; } friend bool operator > (T integer_arg,fraction<T> frac_arg){ fraction<T> frac_arg_eqint(integer_arg*frac_arg._down,frac_arg._down,false,false); return frac_arg._up>frac_arg_eqint._up; } // operator <= bool operator <= (fraction<T> frac_arg)const{ two_fracs<T> commoned=common_value(*this,frac_arg); return commoned.first._up<=commoned.second._up; } bool operator <= (T integer_arg)const{ fraction<T> frac_arg_eqint(integer_arg*_down,_down,false,false); return _up<=frac_arg_eqint._up; } friend bool operator <= (T integer_arg,fraction<T> frac_arg){ fraction<T> frac_arg_eqint(integer_arg*frac_arg._down,frac_arg._down,false,false); return frac_arg._up<=frac_arg_eqint._up; } // operator >= bool operator >= (fraction<T> frac_arg)const{ two_fracs<T> commoned=common_value(*this,frac_arg); return commoned.first._up>=commoned.second._up; } bool operator >= (T integer_arg)const{ fraction<T> frac_arg_eqint(integer_arg*_down,_down,false,false); return _up>=frac_arg_eqint._up; } friend bool operator >= (T integer_arg,fraction<T> frac_arg){ fraction<T> frac_arg_eqint(integer_arg*frac_arg._down,frac_arg._down,false,false); return frac_arg._up>=frac_arg_eqint._up; } // operator += , -= , *= , /= // operator += fraction<T> operator += (fraction<T> add_num){ return *this=*this+add_num; } fraction<T> operator += (T add_num){ return *this=*this+add_num; } friend fraction<T> operator += (T add_num,fraction<T> add_frac){ return add_frac=add_frac+add_num; } // operator -= fraction<T> operator -= (fraction<T> add_num){ return *this=*this-add_num; } fraction<T> operator -= (T add_num){ return *this=*this-add_num; } friend fraction<T> operator -= (T add_num,fraction<T> add_frac){ return add_frac=add_frac-add_num; } // operator *= fraction<T> operator *= (fraction<T> add_num){ return *this=*this*add_num; } fraction<T> operator *= (T add_num){ return *this=*this*add_num; } friend fraction<T> operator *= (T add_num,fraction<T> add_frac){ return add_frac=add_frac*add_num; } // operator /= fraction<T> operator /= (fraction<T> add_num){ return *this=*this/add_num; } fraction<T> operator /= (T add_num){ return *this=*this/add_num; } friend fraction<T> operator /= (T add_num,fraction<T> add_frac){ return add_frac=add_frac/add_num; } private: template<typename T1,typename T2=T1> struct two_fracs{ fraction<T1> first; fraction<T2> second; two_fracs(){} two_fracs(fraction<T1> new_1,fraction<T2> new_2){ first=new_1,second=new_2; } }; template<typename T1,typename T2=T1> static two_fracs<T1,T2> common_value(fraction<T1> frac_x,fraction<T2> frac_y){ T1 gcd_num=math::gcd(frac_x._down,frac_y._down); T1 x_multi_num=frac_y._down/gcd_num,y_multi_num=frac_x._down/gcd_num; frac_x._down*=x_multi_num,frac_x._up*=x_multi_num; frac_y._down*=y_multi_num,frac_y._up*=y_multi_num; return two_fracs<T1,T2>(frac_x,frac_y); } }; namespace math{ template<typename T> fraction<T> reduction(fraction<T> the_frac){ return the_frac.reduction(); } } #endif
注意：分數與浮點數之間的運算要用這樣的形式：
fraction<int> frac(1,2);
double doub=0.3;
cout<<frac.value()+doub; // 或 cout<<double(frac)+doub;歡迎轉載，但請在文章中附加上本文連結： https://blog.csdn.net/weixin_41461277/article/details/84890580 。