分数-完整版
2026-09-12 20:32:45
发布于：吉林
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现在可以看了
run里面自己加自己想加的东西即可
终于写完了啊啊啊啊啊啊啊啊啊啊啊啊
不喜勿喷，代码里需要可以直接用，不用声明是我的。
#include<bits/stdc++.h>
using namespace std;
const unsigned long long ullmax=18446744073709551615ull;
const int mod=998244353;
const int g=3;
int base=10;
unsigned long long ullabs(long long a){
if(a>=0) return (unsigned long long)a;
unsigned long long res=(unsigned long long)a;
res=ullmax-res+1;
return res;
}
int powmod(long long a,long long b){
long long res=1;
while(b){
if(b%2==1) res=res*a%mod;
a=a*a%mod;
b/=2;
}
return (int)res;
}
int toint(char c){
if('0'<=c&&c<='9') return c-'0';
else return c-'A'+10;
}
char tochar(int a){
if(0<=a&&a<=9) return a+'0';
else return a+'A'-10;
}
string forms(const string& s){
int i=s.size();
for(;i>1&&s[i-1]=='0';i--);
return s.substr(0,i);
}
bool ucmp(const string& a,const string& b){
if(a.size()<b.size()) return true;
if(a.size()>b.size()) return false;
for(int i=(int)a.size()-1;i>=0;i--){
if(a[i]>b[i]) return false;
if(a[i]<b[i]) return true;
}
return false;
}
string usub(string a,string b){
bool flag=false;
string ans="";
if(ucmp(a,b)){
flag=true;
swap(a,b);
}
int now=0;
for(int i=0;i<(int)a.size();i++){
int x;
if(i<(int)b.size()) x=toint(b[i]);
else x=0;
if(toint(a[i])-now<x){
ans+=tochar(toint(a[i])+base-now-x);
now=1;
}else{
ans+=tochar(toint(a[i])-now-x);
now=0;
}
}
ans=forms(ans);
if(flag) ans=ans+"-";
return ans;
}
string uadd(const string& a,const string& b){
string ans="";
int nx=0,now=0,len=max(a.size(),b.size());
for(int i=0;i<len;i++){
nx=0;
if(i<(int)a.size()) nx+=toint(a[i]);
if(i<(int)b.size()) nx+=toint(b[i]);
nx+=now;
now=0;
if(nx>=base){
now=1;
nx-=base;
}
ans+=tochar(nx);
}
ans+=tochar(now);
return forms(ans);
}
void ntt(vector<int>& a,bool b){
int n=a.size();
vector<int>to(n,0);
for(int i=0;i<n;i++){
to[i]=to[i>>1]>>1;
if(i&1) to[i]|=(n>>1);
if(i<to[i]) swap(a[i],a[to[i]]);
}
for(int l=2;l<=n;l<<=1){
int wl=powmod(g,(mod-1)/l);
if(b) wl=powmod(wl,mod-2);
for(int i=0;i<n;i+=l){
long long w=1;
int mid=l>>1;
for(int j=0;j<mid;j++){
int x=a[i+j],y=w*a[i+j+mid]%mod;
a[i+j]=(1ll*x+y)%mod;
a[i+j+mid]=(1ll*x-y+mod)%mod;
w=w*wl%mod;
}
}
}
if(b){
int nf=powmod(n,mod-2);
for(int i=0;i<n;i++) a[i]=1ll*a[i]*nf%mod;
}
}
string umul(const string& a,const string& b){
vector<int>va,vb;
for(int i=0;i<(int)a.size();i++) va.push_back(toint(a[i]));
for(int i=0;i<(int)b.size();i++) vb.push_back(toint(b[i]));
int n=1;
while(n<(int)va.size()+(int)vb.size()-1) n<<=1;
va.resize(n);
vb.resize(n);
ntt(va,false);
ntt(vb,false);
for(int i=0;i<(int)va.size();i++) va[i]=1ll*va[i]*vb[i]%mod;
ntt(va,true);
for(int i=0;i<(int)va.size();i++){
if(i<(int)va.size()-1) va[i+1]+=va[i]/base;
else if(va[i]/base>0) va.push_back(va[i]/base);
va[i]%=base;
}
string ans;
for(int i=0;i<(int)va.size();i++) ans+=tochar(va[i]);
return forms(ans);
}
pair<string,string> udiv(const string& a,const string& b){
if(b=="0") throw runtime_error("除以零");
if(a=="0") return {"0","0"};
string r="0";
string hq="";
string na[44];
na[0]="0";
for(int nq=1;nq<base;nq++) na[nq]=uadd(na[nq-1],b);
for(int i=(int)a.size()-1;i>=0;i--){
r="0"+r;
r=uadd(r,string(1,a[i]));
int nq=base-1;
while(nq>=0){
if(!ucmp(r,na[nq])){
r=usub(r,na[nq]);
break;
}
nq--;
}
hq+=tochar(nq);
}
string q=hq;
reverse(q.begin(),q.end());
return {forms(q),forms(r)};
}
string to_string_ll(long long a){
string s;
if(a==0) return "0";
unsigned long long x=ullabs(a);
while(x){
s+=tochar(x%base);
x/=base;
}
if(a<0) s+="-";
return s;
}
class bnum{
private:
bool pn;
string num;
void form(){
num=forms(num);
if((int)num.size()==1&&num[0]=='0') pn=true;
}
public:
bnum():pn(true),num("0"){}
bnum(bool b,string s):pn(b),num(s){
form();
}
bnum(string s){
if(!s.size()){
num="0";
pn=true;
}else{
if(s[(int)s.size()-1]=='-'){
num=s.substr(0,(int)s.size()-1);
pn=false;
}else if(s[(int)s.size()-1]=='+'){
num=s.substr(0,(int)s.size()-1);
pn=true;
}else{
num=s;
pn=true;
}
}
if((int)num.size()==0) num="0";
form();
}
bnum(long long x):bnum(to_string_ll(x)){}
bnum(int x):bnum((long long)x){}
explicit operator bool() const{
return num!="0";
}
string get_num() const{
string ans=num;
reverse(ans.begin(),ans.end());
return ans;
}
bool get_porn() const{return pn;}
bnum& operator=(const bnum& other)=default;
bnum& operator+=(const bnum& a){
if(pn==a.pn){
num=uadd(a.num,num);
return *this;
}else{
num=usub(num,a.num);
if(num[(int)num.size()-1]=='-'){
pn=!pn;
num=num.substr(0,(int)num.size()-1);
}
form();
return *this;
}
}
bnum& operator-=(const bnum& a){
if(pn!=a.pn){
num=uadd(a.num,num);
return *this;
}else{
num=usub(num,a.num);
if(num[(int)num.size()-1]=='-'){
pn=!pn;
num=num.substr(0,(int)num.size()-1);
}
form();
return *this;
}
}
bnum& operator*=(const bnum& a){
num=umul(num,a.num);
pn=(pn==a.pn);
form();
return *this;
}
bnum& operator/=(const bnum& a){
num=udiv(num,a.num).first;
pn=(pn==a.pn);
form();
return *this;
}
bnum& operator%=(const bnum& a){
num=udiv(num,a.num).second;
form();
return *this;
}
bnum& operator++(){
*this+=bnum(1);
return *this;
}
bnum operator++(int){
bnum old=*this;
++(*this);
return old;
}
bnum& operator--(){
*this-=bnum(1);
return *this;
}
bnum operator--(int){
bnum old=*this;
--(*this);
return old;
}
friend bool operator==(const bnum& a,const bnum& b){
if(a.pn!=b.pn) return false;
if(a.num.size()!=b.num.size()) return false;
for(int i=0;i<(int)a.num.size();i++){
if(a.num[i]!=b.num[i]) return false;
}
return true;
}
friend bool operator<(const bnum& a,const bnum& b){
if(a.pn&&!b.pn) return false;
if(!a.pn&&b.pn) return true;
if(a.pn) return ucmp(a.num,b.num);
else return ucmp(b.num,a.num);
}
friend bool operator>(const bnum& a,const bnum& b){
if(a.pn&&!b.pn) return true;
if(!a.pn&&b.pn) return false;
if(a.pn) return ucmp(b.num,a.num);
else return ucmp(a.num,b.num);
}
friend bool operator<=(const bnum& a,const bnum& b){
return !(a>b);
}
friend bool operator>=(const bnum& a,const bnum& b){
return !(a<b);
}
friend bnum operator+(const bnum& a,const bnum& b){
string ans;
bool s=a.pn;
if(a.pn==b.pn) ans=uadd(a.num,b.num);
else{
ans=usub(a.num,b.num);
if(ans[(int)ans.size()-1]=='-'){
s=!s;
ans=ans.substr(0,(int)ans.size()-1);
}
}
return bnum(s,ans);
}
friend bnum operator-(const bnum& a,const bnum& b){
string ans;
bool s=a.pn;
if(a.pn!=b.pn) ans=uadd(a.num,b.num);
else{
ans=usub(a.num,b.num);
if(ans[(int)ans.size()-1]=='-'){
s=!s;
ans=ans.substr(0,(int)ans.size()-1);
}
}
return bnum(s,ans);
}
friend bnum operator*(const bnum& a,const bnum& b){
string ans=umul(a.num,b.num);
bool s=(a.pn==b.pn);
return bnum(s,ans);
}
friend bnum operator/(const bnum& a,const bnum& b){
string ans=udiv(a.num,b.num).first;
bool s=(a.pn==b.pn);
return bnum(s,ans);
}
friend bnum operator%(const bnum& a,const bnum& b){
string ans=udiv(a.num,b.num).second;
bool s=a.pn;
return bnum(s,ans);
}
friend bnum operator-(const bnum& a){
return bnum(!a.pn,a.num);
}
friend ostream& operator<<(ostream& o,const bnum& x){
if(!x.pn) o<<'-';
for(int i=(int)x.num.size()-1;i>=0;i--) o<<x.num[i];
return o;
}
friend istream& operator>>(istream& i,bnum& x){
string s;
i>>s;
if(i.fail()) return i;
for(int j=0;j<(int)s.size();j++){
if(!(j==0&&(s[j]=='+'||s[j]=='-'))&&!(('0'<=s[j]&&s[j]<='0'+min(base-1,9))||('A'<=s[j]&&s[j]<='A'+base-11))){
i.setstate(ios::failbit);
return i;
}
}
reverse(s.begin(),s.end());
x=bnum(s);
return i;
}
};
bnum abs(bnum a){
if(a<0) a=-a;
return a;
}
bnum gcd(bnum a,bnum b){
if(a<b) swap(a,b);
return (b==0)?a:gcd(b,a%b);
}
class frac{
private:
bnum num;
bnum den;
void form(){
if(den==0) throw runtime_error("分母为零 或 除以零");
if(den<0){
num=-num;
den=-den;
}
bnum g=gcd(abs(num),den);
num/=g;
den/=g;
}
public:
frac(bnum n=0,bnum d=1):num(n),den(d){
form();
}
bnum get_num() const{return num;}
bnum get_den() const{return den;}
frac& operator=(const frac& other)=default;
frac& operator+=(const frac& f){
num=num*f.den+f.num*den;
den=den*f.den;
form();
return *this;
}
frac& operator-=(const frac& f){
num=num*f.den-f.num*den;
den=den*f.den;
form();
return *this;
}
frac& operator*=(const frac& f){
num*=f.num;
den*=f.den;
form();
return *this;
}
frac& operator/=(const frac& f){
num*=f.den;
den*=f.num;
form();
return *this;
}
friend frac operator+(const frac& a,const frac& b){
return frac(a.num*b.den+b.num*a.den,a.den*b.den);
}
friend frac operator-(const frac& a,const frac& b){
return frac(a.num*b.den-b.num*a.den,a.den*b.den);
}
friend frac operator*(const frac& a,const frac& b){
return frac(a.num*b.num,a.den*b.den);
}
friend frac operator/(const frac& a,const frac& b){
return frac(a.num*b.den,a.den*b.num);
}
friend frac operator-(const frac& a){
return frac(-a.num,a.den);
}
friend bool operator==(const frac& a,const frac& b){
if(a.num==b.num&&a.den==b.den) return true;
return false;
}
friend bool operator<(const frac& a,const frac& b){
if(a.num*b.den<b.num*a.den) return true;
return false;
}
friend bool operator>(const frac& a,const frac& b){
if(a.num*b.den>b.num*a.den) return true;
return false;
}
friend bool operator<=(const frac& a,const frac& b){
return (a<b)||(a==b);
}
friend bool operator>=(const frac& a,const frac& b){
return (a>b)||(a==b);
}
friend ostream& operator<<(ostream& o,const frac& f){
if(f.den==1) o<<f.num;
else o<<f.num<<'/'<<f.den;
return o;
}
friend istream& operator>>(istream& i,frac& f){
bnum n,d=1;
char s=0;
if(!(i>>n)) return i;
if(i.peek()=='/'){
i>>s;
if(!(i>>d)) return i;
}
if(d==0){
i.setstate(ios::failbit);
return i;
}
f=frac(n,d);
return i;
}
};
bool check_in(bool b){
if(b){
cout<<"请重新输入\n";
cin.clear();
cin.ignore(numeric_limits<streamsize>::max(),'\n');
}
return b;
}
void run(){
frac f1,f2;
do{
cout<<"f1=";
cin>>f1;
}while(check_in(cin.fail()));
do{
cout<<"f2=";
cin>>f2;
}while(check_in(cin.fail()));
cout<<"f1+f2="<<f1+f2<<endl;
cout<<"f1-f2="<<f1-f2<<endl;
cout<<"f1*f2="<<f1*f2<<endl;
cout<<"f1/f2="<<f1/f2<<endl;
if(f1>f2) cout<<"f1>f2"<<endl;
if(f1<f2) cout<<"f1<f2"<<endl;
if(f1==f2) cout<<"f1=f2"<<endl;
if(f1>=f2) cout<<"f1>=f2"<<endl;
if(f1<=f2) cout<<"f1<=f2"<<endl;
}
int main(){
// freopen("data.in","r",stdin);
// freopen("user.out","w",stdout);
try{
run();
}catch(const runtime_error& e){
cerr<<"错误："<<e.what()<<endl;
}
return 0;
}
然后这个是头文件版：
#ifndef _more_nums_h
#define _more_nums_h
#include<string>
#include<vector>
#include<iostream>
#include<sstream>
#include<algorithm>
#include<stdexcept>
#include<utility>
#include<cctype>
namespace mnums{
const unsigned long long ullmax=18446744073709551615ull;
const int mod=998244353;
const int g=3;
extern int base;
inline unsigned long long ullabs(long long a){
if(a>=0) return (unsigned long long)a;
unsigned long long res=(unsigned long long)a;
res=ullmax-res+1;
return res;
}
inline int powmod(long long a,long long b){
long long res=1;
while(b){
if(b%2==1) res=res*a%mod;
a=a*a%mod;
b/=2;
}
return (int)res;
}
inline int toint(char c){
if('0'<=c&&c<='9') return c-'0';
else return c-'A'+10;
}
inline char tochar(int a){
if(0<=a&&a<=9) return a+'0';
else return a+'A'-10;
}
inline std::string forms(const std::string& s){
int i=s.size();
for(;i>1&&s[i-1]=='0';i--);
return s.substr(0,i);
}
inline bool ucmp(const std::string& a,const std::string& b){
if(a.size()<b.size()) return true;
if(a.size()>b.size()) return false;
for(int i=(int)a.size()-1;i>=0;i--){
if(a[i]>b[i]) return false;
if(a[i]<b[i]) return true;
}
return false;
}
inline std::string usub(std::string a,std::string b){
bool flag=false;
std::string ans="";
if(ucmp(a,b)){
flag=true;
std::swap(a,b);
}
int now=0;
for(int i=0;i<(int)a.size();i++){
int x;
if(i<(int)b.size()) x=toint(b[i]);
else x=0;
if(toint(a[i])-now<x){
ans+=tochar(toint(a[i])+base-now-x);
now=1;
}else{
ans+=tochar(toint(a[i])-now-x);
now=0;
}
}
ans=forms(ans);
if(flag) ans=ans+"-";
return ans;
}
inline std::string uadd(const std::string& a,const std::string& b){
std::string ans="";
int nx=0,now=0,len=std::max(a.size(),b.size());
for(int i=0;i<len;i++){
nx=0;
if(i<(int)a.size()) nx+=toint(a[i]);
if(i<(int)b.size()) nx+=toint(b[i]);
nx+=now;
now=0;
if(nx>=base){
now=1;
nx-=base;
}
ans+=tochar(nx);
}
ans+=tochar(now);
return forms(ans);
}
inline void ntt(std::vector<int>& a,bool b){
int n=a.size();
std::vector<int>to(n,0);
for(int i=0;i<n;i++){
to[i]=to[i>>1]>>1;
if(i&1) to[i]|=(n>>1);
if(i<to[i]) std::swap(a[i],a[to[i]]);
}
for(int l=2;l<=n;l<<=1){
int wl=powmod(g,(mod-1)/l);
if(b) wl=powmod(wl,mod-2);
for(int i=0;i<n;i+=l){
long long w=1;
int mid=l>>1;
for(int j=0;j<mid;j++){
int x=a[i+j],y=w*a[i+j+mid]%mod;
a[i+j]=(1ll*x+y)%mod;
a[i+j+mid]=(1ll*x-y+mod)%mod;
w=w*wl%mod;
}
}
}
if(b){
int nf=powmod(n,mod-2);
for(int i=0;i<n;i++) a[i]=1ll*a[i]*nf%mod;
}
}
inline std::string umul(const std::string& a,const std::string& b){
std::vector<int>va,vb;
for(int i=0;i<(int)a.size();i++) va.push_back(toint(a[i]));
for(int i=0;i<(int)b.size();i++) vb.push_back(toint(b[i]));
int n=1;
while(n<(int)va.size()+(int)vb.size()-1) n<<=1;
va.resize(n);
vb.resize(n);
ntt(va,false);
ntt(vb,false);
for(int i=0;i<(int)va.size();i++) va[i]=1ll*va[i]*vb[i]%mod;
ntt(va,true);
for(int i=0;i<(int)va.size();i++){
if(i<(int)va.size()-1) va[i+1]+=va[i]/base;
else if(va[i]/base>0) va.push_back(va[i]/base);
va[i]%=base;
}
std::string ans;
for(int i=0;i<(int)va.size();i++) ans+=tochar(va[i]);
return forms(ans);
}
inline std::pair<std::string,std::string> udiv(const std::string& a,const std::string& b){
if(b=="0") throw std::runtime_error("除以零");
if(a=="0") return {"0","0"};
std::string r="0";
std::string hq="";
std::string na[44];
na[0]="0";
for(int nq=1;nq<base;nq++) na[nq]=uadd(na[nq-1],b);
for(int i=(int)a.size()-1;i>=0;i--){
r="0"+r;
r=uadd(r,std::string(1,a[i]));
int nq=base-1;
while(nq>=0){
if(!ucmp(r,na[nq])){
r=usub(r,na[nq]);
break;
}
nq--;
}
hq+=tochar(nq);
}
std::string q=hq;
std::reverse(q.begin(),q.end());
return {forms(q),forms(r)};
}
inline std::string lltostr(long long a){
std::string s;
if(a==0) return "0";
unsigned long long x=ullabs(a);
while(x){
s+=tochar(x%base);
x/=base;
}
if(a<0) s+="-";
return s;
}
class bnum{
private:
bool sign;
std::string num;
void form(){
num=forms(num);
if((int)num.size()==1&&num[0]=='0') sign=true;
}
public:
bnum():sign(true),num("0"){}
bnum(bool b,std::string s):sign(b),num(s){
form();
}
bnum(std::string s){
if(!s.size()){
num="0";
sign=true;
}else{
if(s[(int)s.size()-1]=='-'){
num=s.substr(0,(int)s.size()-1);
sign=false;
}else if(s[(int)s.size()-1]=='+'){
num=s.substr(0,(int)s.size()-1);
sign=true;
}else{
num=s;
sign=true;
}
}
if((int)num.size()==0) num="0";
form();
}
bnum(long long x):bnum(lltostr(x)){}
bnum(int x):bnum((long long)x){}
explicit operator bool() const{
return num!="0";
}
std::string get_num() const{
std::string ans=num;
reverse(ans.begin(),ans.end());
return ans;
}
bool get_sign() const{return sign;}
bnum& operator=(const bnum& other)=default;
bnum& operator+=(const bnum& a){
if(sign==a.sign){
num=uadd(a.num,num);
return *this;
}else{
num=usub(num,a.num);
if(num[(int)num.size()-1]=='-'){
sign=!sign;
num=num.substr(0,(int)num.size()-1);
}
form();
return *this;
}
}
bnum& operator-=(const bnum& a){
if(sign!=a.sign){
num=uadd(a.num,num);
return *this;
}else{
num=usub(num,a.num);
if(num[(int)num.size()-1]=='-'){
sign=!sign;
num=num.substr(0,(int)num.size()-1);
}
form();
return *this;
}
}
bnum& operator*=(const bnum& a){
num=umul(num,a.num);
sign=(sign==a.sign);
form();
return *this;
}
bnum& operator/=(const bnum& a){
num=udiv(num,a.num).first;
sign=(sign==a.sign);
form();
return *this;
}
bnum& operator%=(const bnum& a){
num=udiv(num,a.num).second;
form();
return *this;
}
bnum& operator++(){
*this+=bnum(1);
return *this;
}
bnum operator++(int){
bnum old=*this;
++(*this);
return old;
}
bnum& operator--(){
*this-=bnum(1);
return *this;
}
bnum operator--(int){
bnum old=*this;
--(*this);
return old;
}
friend bool operator==(const bnum& a,const bnum& b){
if(a.sign!=b.sign) return false;
if(a.num.size()!=b.num.size()) return false;
for(int i=0;i<(int)a.num.size();i++){
if(a.num[i]!=b.num[i]) return false;
}
return true;
}
friend bool operator<(const bnum& a,const bnum& b){
if(a.sign&&!b.sign) return false;
if(!a.sign&&b.sign) return true;
if(a.sign) return ucmp(a.num,b.num);
else return ucmp(b.num,a.num);
}
friend bool operator>(const bnum& a,const bnum& b){
if(a.sign&&!b.sign) return true;
if(!a.sign&&b.sign) return false;
if(a.sign) return ucmp(b.num,a.num);
else return ucmp(a.num,b.num);
}
friend bool operator<=(const bnum& a,const bnum& b){
return !(a>b);
}
friend bool operator>=(const bnum& a,const bnum& b){
return !(a<b);
}
friend bnum operator+(const bnum& a,const bnum& b){
std::string ans;
bool s=a.sign;
if(a.sign==b.sign) ans=uadd(a.num,b.num);
else{
ans=usub(a.num,b.num);
if(ans[(int)ans.size()-1]=='-'){
s=!s;
ans=ans.substr(0,(int)ans.size()-1);
}
}
return bnum(s,ans);
}
friend bnum operator-(const bnum& a,const bnum& b){
std::string ans;
bool s=a.sign;
if(a.sign!=b.sign) ans=uadd(a.num,b.num);
else{
ans=usub(a.num,b.num);
if(ans[(int)ans.size()-1]=='-'){
s=!s;
ans=ans.substr(0,(int)ans.size()-1);
}
}
return bnum(s,ans);
}
friend bnum operator*(const bnum& a,const bnum& b){
std::string ans=umul(a.num,b.num);
bool s=(a.sign==b.sign);
return bnum(s,ans);
}
friend bnum operator/(const bnum& a,const bnum& b){
std::string ans=udiv(a.num,b.num).first;
bool s=(a.sign==b.sign);
return bnum(s,ans);
}
friend bnum operator%(const bnum& a,const bnum& b){
std::string ans=udiv(a.num,b.num).second;
bool s=a.sign;
return bnum(s,ans);
}
friend bnum operator-(const bnum& a){
return bnum(!a.sign,a.num);
}
friend std::ostream& operator<<(std::ostream& o,const bnum& x){
if(!x.sign) o<<'-';
for(int i=(int)x.num.size()-1;i>=0;i--) o<<x.num[i];
return o;
}
friend std::istream& operator>>(std::istream& i,bnum& x){
std::string s;
i>>s;
if(i.fail()) return i;
for(int j=0;j<(int)s.size();j++){
if(!(j==0&&(s[j]=='+'||s[j]=='-'))&&!(('0'<=s[j]&&s[j]<='0'+std::min(base-1,9))||('A'<=s[j]&&s[j]<='A'+base-11))){
i.setstate(std::ios::failbit);
return i;
}
}
std::reverse(s.begin(),s.end());
x=bnum(s);
return i;
}
};
inline bnum abs(bnum a){
if(a<0) a=-a;
return a;
}
inline bnum gcd(bnum a,bnum b){
if(a<b) std::swap(a,b);
return (b==0)?a:gcd(b,a%b);
}
class frac{
private:
bnum num;
bnum den;
void form(){
if(den==0) throw std::runtime_error("分母为零 或 除以零");
if(den<0){
num=-num;
den=-den;
}
bnum g=gcd(abs(num),den);
num/=g;
den/=g;
}
public:
frac(bnum n=0,bnum d=1):num(n),den(d){
form();
}
bnum get_num() const{return num;}
bnum get_den() const{return den;}
frac& operator=(const frac& other)=default;
frac& operator+=(const frac& f){
num=num*f.den+f.num*den;
den=den*f.den;
form();
return *this;
}
frac& operator-=(const frac& f){
num=num*f.den-f.num*den;
den=den*f.den;
form();
return *this;
}
frac& operator*=(const frac& f){
num*=f.num;
den*=f.den;
form();
return *this;
}
frac& operator/=(const frac& f){
num*=f.den;
den*=f.num;
form();
return *this;
}
friend frac operator+(const frac& a,const frac& b){
return frac(a.num*b.den+b.num*a.den,a.den*b.den);
}
friend frac operator-(const frac& a,const frac& b){
return frac(a.num*b.den-b.num*a.den,a.den*b.den);
}
friend frac operator*(const frac& a,const frac& b){
return frac(a.num*b.num,a.den*b.den);
}
friend frac operator/(const frac& a,const frac& b){
return frac(a.num*b.den,a.den*b.num);
}
friend frac operator-(const frac& a){
return frac(-a.num,a.den);
}
friend bool operator==(const frac& a,const frac& b){
if(a.num==b.num&&a.den==b.den) return true;
return false;
}
friend bool operator<(const frac& a,const frac& b){
if(a.num*b.den<b.num*a.den) return true;
return false;
}
friend bool operator>(const frac& a,const frac& b){
if(a.num*b.den>b.num*a.den) return true;
return false;
}
friend bool operator<=(const frac& a,const frac& b){
return !(a>b);
}
friend bool operator>=(const frac& a,const frac& b){
return !(a<b);
}
friend std::ostream& operator<<(std::ostream& o,const frac& f){
if(f.den==1) o<<f.num;
else o<<f.num<<'/'<<f.den;
return o;
}
friend std::istream& operator>>(std::istream& i,frac& f){
bnum n,d=1;
char s=0;
if(!(i>>n)) return i;
if(i.peek()=='/'){
i>>s;
if(!(i>>d)) return i;
}
if(d==0){
i.setstate(std::ios::failbit);
return i;
}
f=frac(n,d);
return i;
}
};
}
#endif
扩展-解析几何：
#ifndef _EX_GEO_H
#define _EX_GEO_H
#include<bits/stdc++.h>
namespace ana_geo{
inline std::pair<double,double>StToSi(double a,double b,double c){
if(b==0) throw std::invalid_argument("无法转为斜截式");
//ax+by+c=0 to y=kx+b
return {-a/b,-c/b};
}
inline std::pair<double,std::pair<double,double>>SiToSt(double k,double b){
//y=kx+b to ax+by+c=0
return {-k,{1,-b}};
}
inline double dis_ptp(double x,double y,double xx,double yy){
//point to point
return std::hypot(x-xx,y-yy);
}
inline double dis_ptl(double x,double y,double a,double b,double c){
if(a==0&&b==0) throw std::invalid_argument("直线不合法");
// return dis_ptp(x,y,(b*b*x-a*b*y-a*c)/(a*a+b*b),(a*a*y-a*b*x-b*c)/(a*a+b*b));
return fabs(a*x+b*y+c)/std::hypot(a,b);//sqrt(a*a+b*b)
}
inline double dis_ltl_prl(double a1,double b1,double c1,double a2,double b2,double c2){
if(b1!=0) return dis_ptl(0,-c1/b1,a2,b2,c2);
else return dis_ptl(-c1/a1,0,a2,b2,c2);
}
inline bool is_prl(double a1,double b1,double c1,double a2,double b2,double c2){
if(fabs(a1*b2-a2*b1)>1e-9*std::hypot(a1,b1)*std::hypot(a2,b2)) return false;
return true;
}
inline std::pair<bool,double>dis_ltl(double a1,double b1,double c1,double a2,double b2,double c2){
if(a1==0&&b1==0) throw std::invalid_argument("直线不合法");
if(a2==0&&b2==0) throw std::invalid_argument("直线不合法");
if(is_prl(a1,b1,c1,a2,b2,c2)) return {true,dis_ltl_prl(a1,b1,c1,a2,b2,c2)};
else return {false,0.0};
}
inline int LandC(double a,double b,double c,double d,double e,double f,bool k){
if(a==0&&b==0) throw std::invalid_argument("直线不合法");
if(k){
//ax+by+c=0 & x^2+y^2+dx+ey+f=0
if(d*d+e*e-4*f<=0) throw std::invalid_argument("圆不合法");
double x=-d/2,y=-e/2,r=sqrt(d*d+e*e-4*f)/2;
double dk=dis_ptl(x,y,a,b,c);
if(dk>r+1e-9) return -1;
if(fabs(dk-r)<=1e-9) return 0;
return 1;
}else{
//ax+by+c=0 & (x-d)^2+(y-e)^2=f^2
if(f<=0) throw std::invalid_argument("圆不合法");
double dk=dis_ptl(d,e,a,b,c);
if(dk>f+1e-9) return -1;
if(fabs(dk-f)<=1e-9) return 0;
return 1;
}
}
inline int CandC(double a,double b,double c,bool k1,double d,double e,double f,bool k2){
//x^2+y^2+ax+by+c=0/(x-a)^2+(y-b)^2=c^2 & x^2+y^2+dx+ey+f=0/(x-d)^2+(y-e)^2=f^2
if(k1&&a*a+b*b-4*c<=0) throw std::invalid_argument("圆不合法");
if(k2&&d*d+e*e-4*f<=0) throw std::invalid_argument("圆不合法");
if(!k1&&c<=0) throw std::invalid_argument("圆不合法");
if(!k2&&f<=0) throw std::invalid_argument("圆不合法");
double x,y,r,xx,yy,rr;
if(k1) x=-a/2,y=-b/2,r=sqrt(a*a+b*b-4*c)/2;
else x=a,y=b,r=c;
if(k2) xx=-d/2,yy=-e/2,rr=sqrt(d*d+e*e-4*f)/2;
else xx=d,yy=e,rr=f;
double dk=dis_ptp(x,y,xx,yy);
if(dk>r+rr+1e-9) return -2;
if(fabs(dk-r-rr)<=1e-9) return -1;
if(std::max(r,rr)-std::min(r,rr)+1e-9<dk&&dk<r+rr-1e-9) return 0;
if(fabs(dk-std::max(r,rr)+std::min(r,rr))<=1e-9) return 1;
if(dk<=1e-9&&fabs(r-rr)<=1e-9) return 3;
return 2;
}
}
#endif
部分内容使用了AI帮忙挑错，但绝对没有一行代码是AI写的。
这里空空如也
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