问题标题: 大整数类型（高精度整数）[九次更新]

Question

5

已解决

董安雅

新手光能

代码如下：

#include<bits/stdc++.h>
using namespace std;
namespace BIG_NUM{
	namespace BN{
		int a[50005],b[50005],c[100005];
		string Mul(string x,string y){//乘法 
			memset(a,0,sizeof(a));
			memset(b,0,sizeof(b));
			memset(c,0,sizeof(c));
			a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=a[0]+b[0];//积的位数
			for(int i=1;i<=a[0];i++){
				for(int j=1;j<=b[0];j++){
					c[i+j-1]+=a[i]*b[j];//这里一定要+= 
				}
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=c[i]+jw;
				jw=c[i]/10;
				c[i]%=10;
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
			string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		string Minus(string x,string y){//减法 
		    if(x==y)return "0";
			memset(a,0,sizeof(a));
			memset(b,0,sizeof(b));
			memset(c,0,sizeof(c));
		    a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存差的位数
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				if(a[i]<b[i]){//借位的情况 
					a[i+1]--;
					a[i]+=10;
				}
				c[i]=a[i]-b[i];
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
		    string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		string Plus(string x,string y){//加法 
			memset(a,0,sizeof(a));
			memset(b,0,sizeof(b));
			memset(c,0,sizeof(c));
			a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存和的位数
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=a[i]+b[i]+jw;
				jw=c[i]/10;//先处理进位 
				c[i]%=10;
			}
			if(jw!=0)c[++c[0]]=jw;//判断是否进位，进位，位数+1，这一位为1 
			string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		bool check_size(string x,string y){
			if(x.size()>y.size())return false;
			else if(x.size()<y.size())return true;
			else{
				if(x>y)return false;
				else{
					return true;
				}
			}
		}
		class abnormal:public exception{
			private:
				string message;
			public:
				abnormal(string other){
					message=other;
				}
				const char* what(){
					return message.c_str();
				}
		};
		string Div(string x,string y){
			if(y=="0"){
				abnormal e("Divider cannot be 0.");
				throw e;
				return "NULL";
			}
			else if(!check_size(y,x))return "0";
			string ans="";
			while(1){
				string a=x.substr(0,y.size());
				if(!check_size(y,a))a+=x[y.size()];
				int l=0,r=9;
				string k,k2;
				while(l<r){
					int mid=(l+r+1)/2;
					k=Mul(y,to_string(mid));
					if(check_size(k,a))l=mid;
					else r=mid-1;
				}
				string t=to_string(l);
				ans+=t;
				k=x.substr(a.size(),x.size()-a.size()+1);
				k2=Mul(y,t);
				x=Minus(a,k2);
				if(x=="0")x="";
				int len=x.size();
				x+=k;
				if(k=="")break;
				else if(!check_size(y,x)&&k.size()==1){
					ans+="0";
					break;
				}
				while(len<y.size()-1){
					ans+="0";
					len++;
				}
				while(!check_size(y,x.substr(0,len+1))){
					ans+="0";
					len++;
				}
			}
			return ans;
		}
		string Comple(string x,string y){
			string t=Div(x,y);
			string k=Minus(x,t);
			return k;
		}
	}
	class Big_num{
		friend string to_string(Big_num x);
		friend istream& operator>>(istream& is,const Big_num& num);
		private:
			#define Plus(x,y) BN::Plus(x,y)
			#define Minus(x,y) BN::Minus(x,y)
			#define Mul(x,y) BN::Mul(x,y)
			#define Div(x,y) BN::Div(x,y)
			#define Comple(x,y) BN::Comple(x,y)
			string num;
		public: 
			Big_num(){
				num="0";
			}
			Big_num(string other){
				num=other;
			}
			Big_num(const char* other){
				num=other;
			}
			Big_num(int other){
				num=to_string(other);
			}
			Big_num(short other){
				num=to_string((int)other);
			}
			Big_num(long other){
				num=to_string(other);
			}
			Big_num(long long other){
				num=to_string(other);
			}
			Big_num(const Big_num& other){
				num=other.num;
			}
			Big_num& operator=(Big_num other){
				num=other.num;
				return *this;
			}
			Big_num operator+(Big_num other){
				string x=Plus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator-(Big_num other){
				string x=Minus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator*(Big_num other){
				string x=Mul(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator/(Big_num other){
				string x=Div(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator%(Big_num other){
				string x=Comple(num,other.num);
				Big_num y=x;
				return y;
			}
	};
	string to_string(Big_num x){
		return x.num;
	}
	ostream& operator<<(ostream& os,const Big_num& num){
	    os<<to_string(num);
	    return os;
	}
	istream& operator>>(istream& is,const Big_num& num){
		is>>num.num;
		return is;
	}
}
using namespace BIG_NUM;

举个例子：

Big_num a="6534289857563748923958462",b="3782594234875294";
cout<<a+b<<endl;

然后就能得到结果了。

董安雅在2023-04-09 10:35:17追加了内容

#include<bits/stdc++.h>
using namespace std;
namespace BIG_NUM{
	namespace BN{
		int a[50005],b[50005],c[100005];
		string Mul(string x,string y){//乘法 
			memset(a,0,sizeof(a));
			memset(b,0,sizeof(b));
			memset(c,0,sizeof(c));
			a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=a[0]+b[0];//积的位数
			for(int i=1;i<=a[0];i++){
				for(int j=1;j<=b[0];j++){
					c[i+j-1]+=a[i]*b[j];//这里一定要+= 
				}
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=c[i]+jw;
				jw=c[i]/10;
				c[i]%=10;
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
			string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		string Minus(string x,string y){//减法 
		    if(x==y)return "0";
			memset(a,0,sizeof(a));
			memset(b,0,sizeof(b));
			memset(c,0,sizeof(c));
		    a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存差的位数
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				if(a[i]<b[i]){//借位的情况 
					a[i+1]--;
					a[i]+=10;
				}
				c[i]=a[i]-b[i];
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
		    string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		string Plus(string x,string y){//加法 
			memset(a,0,sizeof(a));
			memset(b,0,sizeof(b));
			memset(c,0,sizeof(c));
			a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存和的位数
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=a[i]+b[i]+jw;
				jw=c[i]/10;//先处理进位 
				c[i]%=10;
			}
			if(jw!=0)c[++c[0]]=jw;//判断是否进位，进位，位数+1，这一位为1 
			string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		bool check_size(string x,string y){
			if(x.size()>y.size())return false;
			else if(x.size()<y.size())return true;
			else{
				if(x>y)return false;
				else{
					return true;
				}
			}
		}
		class abnormal:public exception{
			private:
				string message;
			public:
				abnormal(string other){
					message=other;
				}
				const char* what(){
					return message.c_str();
				}
		};
		string Div(string x,string y){
			if(y=="0"){
				abnormal e("Divider cannot be 0.");
				throw e;
				return "NULL";
			}
			else if(!check_size(y,x))return "0";
			string ans="";
			while(1){
				string a=x.substr(0,y.size());
				if(!check_size(y,a))a+=x[y.size()];
				int l=0,r=9;
				string k,k2;
				while(l<r){
					int mid=(l+r+1)/2;
					k=Mul(y,to_string(mid));
					if(check_size(k,a))l=mid;
					else r=mid-1;
				}
				string t=to_string(l);
				ans+=t;
				k=x.substr(a.size(),x.size()-a.size()+1);
				k2=Mul(y,t);
				x=Minus(a,k2);
				if(x=="0")x="";
				int len=x.size();
				x+=k;
				if(k=="")break;
				else if(!check_size(y,x)&&k.size()==1){
					ans+="0";
					break;
				}
				while(len<y.size()-1){
					ans+="0";
					len++;
				}
				while(!check_size(y,x.substr(0,len+1))){
					ans+="0";
					len++;
				}
			}
			return ans;
		}
		string Comple(string x,string y){
			string t=Div(x,y);
			string k=Minus(x,Mul(t,y));
			return k;
		}
	}
	class Big_num{
		friend string to_string(Big_num x);
		friend istream& operator>>(istream& is,const Big_num& num);
		private:
			#define Plus(x,y) BN::Plus(x,y)
			#define Minus(x,y) BN::Minus(x,y)
			#define Mul(x,y) BN::Mul(x,y)
			#define Div(x,y) BN::Div(x,y)
			#define Comple(x,y) BN::Comple(x,y)
			string num;
		public: 
			Big_num(){
				num="0";
			}
			Big_num(string other){
				num=other;
			}
			Big_num(const char* other){
				num=other;
			}
			Big_num(int other){
				num=to_string(other);
			}
			Big_num(short other){
				num=to_string((int)other);
			}
			Big_num(long other){
				num=to_string(other);
			}
			Big_num(long long other){
				num=to_string(other);
			}
			Big_num(const Big_num& other){
				num=other.num;
			}
			Big_num& operator=(Big_num other){
				num=other.num;
				return *this;
			}
			Big_num operator+(Big_num other){
				string x=Plus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator-(Big_num other){
				string x=Minus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator*(Big_num other){
				string x=Mul(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator/(Big_num other){
				string x=Div(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator%(Big_num other){
				string x=Comple(num,other.num);
				Big_num y=x;
				return y;
			}
	};
	string to_string(Big_num x){
		return x.num;
	}
	ostream& operator<<(ostream& os,const Big_num& num){
	    os<<to_string(num);
	    return os;
	}
	istream& operator>>(istream& is,Big_num& num){
		is>>num.num;
		return is;
	}
}
using namespace BIG_NUM;

修复了某些BUG.

编译器为。

董安雅在2023-04-09 13:24:26追加了内容

最新代码：

#include<bits/stdc++.h>
using namespace std;
namespace BIG_NUM{
	namespace BN{
		int a[50005],b[50005],c[100005];
		string Mul(string x,string y){//乘法 
			bool flag=false;
			if(x[0]=='-'){
				flag=!flag;
				x.erase(0,1);
			}
			if(y[0]=='-'){
				flag=!flag;
				y.erase(0,1);
			}
			memset(a,0,sizeof(a));
			memset(b,0,sizeof(b));
			memset(c,0,sizeof(c));
			a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=a[0]+b[0];//积的位数
			for(int i=1;i<=a[0];i++){
				for(int j=1;j<=b[0];j++){
					c[i+j-1]+=a[i]*b[j];//这里一定要+= 
				}
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=c[i]+jw;
				jw=c[i]/10;
				c[i]%=10;
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
			string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			z=(flag==true?"-":"")+z;
			return z;
		}
		string Plus(string x,string y);//加法
		string Minus(string x,string y){//减法 
		    if(x==y)return "0";
		    if(x[0]=='-'&&y[0]=='-'){
				return Minus(y.substr(1,y.size()-1),
				             x.substr(1,y.size()-1));
			}
			else if(x[0]=='-'&&y[0]!='-'){
				string t=Plus(x.substr(1,x.size()-1),y);
				t="-"+t;
				return t;
			}
			else if(x[0]!='-'&&y[0]=='-'){
				return Plus(x,y.substr(1,y.size()-1));
			}
			memset(a,0,sizeof(a));
			memset(b,0,sizeof(b));
			memset(c,0,sizeof(c));
		    a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存差的位数
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				if(a[i]<b[i]){//借位的情况 
					a[i+1]--;
					a[i]+=10;
				}
				c[i]=a[i]-b[i];
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
		    string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		string Plus(string x,string y){//加法 
			if(x[0]=='-'&&y[0]=='-'){
				string t=Plus(x.substr(1,x.size()-1),
							  y.substr(1,y.size()-1));
				t="-"+t;
				return t;
			}
			else if(x[0]=='-'&&y[0]!='-'){
				return Minus(y,x.substr(1,x.size()-1));
			}
			else if(x[0]!='-'&&y[0]=='-'){
				return Minus(x,y.substr(1,y.size()-1));
			}
			memset(a,0,sizeof(a));
			memset(b,0,sizeof(b));
			memset(c,0,sizeof(c));
			a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存和的位数
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=a[i]+b[i]+jw;
				jw=c[i]/10;//先处理进位 
				c[i]%=10;
			}
			if(jw!=0)c[++c[0]]=jw;//判断是否进位，进位，位数+1，这一位为1 
			string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		bool check_size(string x,string y){
			if(x.size()>y.size())return false;
			else if(x.size()<y.size())return true;
			else{
				if(x>y)return false;
				else{
					return true;
				}
			}
		}
		class abnormal:public exception{
			private:
				string message;
			public:
				abnormal(string other){
					message=other;
				}
				const char* what(){
					return message.c_str();
				}
		};
		string Div(string x,string y){
			if(y=="0"){
				abnormal e("Divider cannot be 0.");
				throw e;
				return "NULL";
			}
			else if(!check_size(y,x))return "0";
			string ans="";
			while(1){
				string a=x.substr(0,y.size());
				if(!check_size(y,a))a+=x[y.size()];
				int l=0,r=9;
				string k,k2;
				while(l<r){
					int mid=(l+r+1)/2;
					k=Mul(y,to_string(mid));
					if(check_size(k,a))l=mid;
					else r=mid-1;
				}
				string t=to_string(l);
				ans+=t;
				k=x.substr(a.size(),x.size()-a.size()+1);
				k2=Mul(y,t);
				x=Minus(a,k2);
				if(x=="0")x="";
				int len=x.size();
				x+=k;
				if(k=="")break;
				else if(!check_size(y,x)&&k.size()==1){
					ans+="0";
					break;
				}
				while(len<y.size()-1){
					ans+="0";
					len++;
				}
				while(!check_size(y,x.substr(0,len+1))){
					ans+="0";
					len++;
				}
			}
			return ans;
		}
		string Comple(string x,string y){
			string t=Div(x,y);
			string k=Minus(x,Mul(t,y));
			return k;
		}
	}
	class Big_num{
		friend string to_string(Big_num x);
		friend istream& operator>>(istream& is,Big_num& num);
		private:
			#define Plus(x,y) BN::Plus(x,y)
			#define Minus(x,y) BN::Minus(x,y)
			#define Mul(x,y) BN::Mul(x,y)
			#define Div(x,y) BN::Div(x,y)
			#define Comple(x,y) BN::Comple(x,y)
			string num;
		public: 
			Big_num(){
				num="0";
			}
			Big_num(string other){
				num=other;
			}
			Big_num(const char* other){
				num=other;
			}
			Big_num(int other){
				num=to_string(other);
			}
			Big_num(short other){
				num=to_string((int)other);
			}
			Big_num(long other){
				num=to_string(other);
			}
			Big_num(long long other){
				num=to_string(other);
			}
			Big_num(const Big_num& other){
				num=other.num;
			}
			Big_num& operator=(Big_num other){
				num=other.num;
				return *this;
			}
			Big_num operator+(Big_num other){
				string x=Plus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator-(Big_num other){
				string x=Minus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator*(Big_num other){
				string x=Mul(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator/(Big_num other){
				string x=Div(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator%(Big_num other){
				string x=Comple(num,other.num);
				Big_num y=x;
				return y;
			}
	};
	string to_string(Big_num x){
		return x.num;
	}
	ostream& operator<<(ostream& os,const Big_num& num){
	    os<<to_string(num);
	    return os;
	}
	istream& operator>>(istream& is,Big_num& num){
		is>>num.num;
		return is;
	}
}
using namespace BIG_NUM;

修复了一个BUG.

支持大负整数的加减乘法运算了！

编译器不变。

董安雅在2023-04-09 13:25:06追加了内容

改个标题。

下次继续更新！

董安雅在2023-04-14 18:57:16追加了内容

#include<bits/stdc++.h>
using namespace std;
namespace BIG_NUM{
	namespace BN{
		int a[50005],b[50005],c[100005];
		string Mul(string x,string y){//乘法 
			bool flag=false;
			if(x[0]=='-'){
				flag=!flag;
				x.erase(0,1);
			}
			if(y[0]=='-'){
				flag=!flag;
				y.erase(0,1);
			}
			memset(a,0,sizeof(a));
			memset(b,0,sizeof(b));
			memset(c,0,sizeof(c));
			a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=a[0]+b[0];//积的位数
			for(int i=1;i<=a[0];i++){
				for(int j=1;j<=b[0];j++){
					c[i+j-1]+=a[i]*b[j];//这里一定要+= 
				}
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=c[i]+jw;
				jw=c[i]/10;
				c[i]%=10;
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
			string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			z=(flag==true?"-":"")+z;
			return z;
		}
		string Plus(string x,string y);//加法
		string Minus(string x,string y){//减法 
		    if(x==y)return "0";
		    if(x[0]=='-'&&y[0]=='-'){
				return Minus(y.substr(1,y.size()-1),
				             x.substr(1,y.size()-1));
			}
			else if(x[0]=='-'&&y[0]!='-'){
				string t=Plus(x.substr(1,x.size()-1),y);
				t="-"+t;
				return t;
			}
			else if(x[0]!='-'&&y[0]=='-'){
				return Plus(x,y.substr(1,y.size()-1));
			}
			memset(a,0,sizeof(a));
			memset(b,0,sizeof(b));
			memset(c,0,sizeof(c));
		    a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存差的位数
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				if(a[i]<b[i]){//借位的情况 
					a[i+1]--;
					a[i]+=10;
				}
				c[i]=a[i]-b[i];
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
		    string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		string Plus(string x,string y){//加法 
			if(x[0]=='-'&&y[0]=='-'){
				string t=Plus(x.substr(1,x.size()-1),
							  y.substr(1,y.size()-1));
				t="-"+t;
				return t;
			}
			else if(x[0]=='-'&&y[0]!='-'){
				return Minus(y,x.substr(1,x.size()-1));
			}
			else if(x[0]!='-'&&y[0]=='-'){
				return Minus(x,y.substr(1,y.size()-1));
			}
			memset(a,0,sizeof(a));
			memset(b,0,sizeof(b));
			memset(c,0,sizeof(c));
			a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存和的位数
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=a[i]+b[i]+jw;
				jw=c[i]/10;//先处理进位 
				c[i]%=10;
			}
			if(jw!=0)c[++c[0]]=jw;//判断是否进位，进位，位数+1，这一位为1 
			string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		bool check_size(string x,string y){
			if(x.size()>y.size())return false;
			else if(x.size()<y.size())return true;
			else{
				if(x>y)return false;
				else{
					return true;
				}
			}
		}
		class abnormal:public exception{
			private:
				string message;
			public:
				abnormal(string other){
					message=other;
				}
				const char* what(){
					return message.c_str();
				}
		};
		string Div(string x,string y){
			bool flag=false;
			if(x[0]=='-'){
				flag=!flag;
				x.erase(0,1);
			}
			if(y[0]=='-'){
				flag=!flag;
				y.erase(0,1);
			}
			if(y=="0"){
				abnormal e("Divider cannot be 0.");
				throw e;
				return "NULL";
			}
			else if(!check_size(y,x))return "0";
			string ans="";
			while(1){
				string a=x.substr(0,y.size());
				if(!check_size(y,a))a+=x[y.size()];
				int l=0,r=9;
				string k,k2;
				while(l<r){
					int mid=(l+r+1)/2;
					k=Mul(y,to_string(mid));
					if(check_size(k,a))l=mid;
					else r=mid-1;
				}
				string t=to_string(l);
				ans+=t;
				k=x.substr(a.size(),x.size()-a.size()+1);
				k2=Mul(y,t);
				x=Minus(a,k2);
				if(x=="0")x="";
				int len=x.size();
				x+=k;
				if(k=="")break;
				else if(!check_size(y,x)&&k.size()==1){
					ans+="0";
					break;
				}
				while(len<y.size()-1){
					ans+="0";
					len++;
				}
				while(!check_size(y,x.substr(0,len+1))){
					ans+="0";
					len++;
				}
			}
			ans=(flag==true?"-":"")+ans;
			return ans;
		}
		string Comple(string x,string y){
			string t=Div(x,y);
			string k=Minus(x,Mul(t,y));
			return k;
		}
	}
	class Big_num{
		friend string to_string(Big_num x);
		friend istream& operator>>(istream& is,Big_num& num);
		private:
			#define Plus(x,y) BN::Plus(x,y)
			#define Minus(x,y) BN::Minus(x,y)
			#define Mul(x,y) BN::Mul(x,y)
			#define Div(x,y) BN::Div(x,y)
			#define Comple(x,y) BN::Comple(x,y)
			string num;
		public: 
			Big_num(){
				num="0";
			}
			Big_num(string other){
				num=other;
			}
			Big_num(const char* other){
				num=other;
			}
			Big_num(int other){
				num=to_string(other);
			}
			Big_num(short other){
				num=to_string((int)other);
			}
			Big_num(long other){
				num=to_string(other);
			}
			Big_num(long long other){
				num=to_string(other);
			}
			Big_num(const Big_num& other){
				num=other.num;
			}
			Big_num& operator=(Big_num other){
				num=other.num;
				return *this;
			}
			Big_num operator+(Big_num other){
				string x=Plus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator-(Big_num other){
				string x=Minus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator*(Big_num other){
				string x=Mul(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator/(Big_num other){
				string x=Div(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator%(Big_num other){
				string x=Comple(num,other.num);
				Big_num y=x;
				return y;
			}
	};
	string to_string(Big_num x){
		return x.num;
	}
	ostream& operator<<(ostream& os,const Big_num& num){
	    os<<to_string(num);
	    return os;
	}
	istream& operator>>(istream& is,Big_num& num){
		is>>num.num;
		return is;
	}
}
using namespace BIG_NUM;

编译器不变。

已支持负高精度整数的除法.

董安雅在2023-04-14 22:16:06追加了内容

#include<bits/stdc++.h>
using namespace std;
namespace BIG_NUM{
	namespace BN{
		int a[50005],b[50005],c[100005];
		string Plus(string x,string y);//加法
		string Minus(string x,string y){//减法 
		    if(x==y)return "0";
		    if(x[0]=='-'&&y[0]=='-'){
				return Minus(y.substr(1,y.size()-1),
				             x.substr(1,y.size()-1));
			}
			else if(x[0]=='-'&&y[0]!='-'){
				string t=Plus(x.substr(1,x.size()-1),y);
				t="-"+t;
				return t;
			}
			else if(x[0]!='-'&&y[0]=='-'){
				return Plus(x,y.substr(1,y.size()-1));
			}
			memset(a,0,sizeof(a));
			memset(b,0,sizeof(b));
			memset(c,0,sizeof(c));
		    a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存差的位数
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				if(a[i]<b[i]){//借位的情况 
					a[i+1]--;
					a[i]+=10;
				}
				c[i]=a[i]-b[i];
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
		    string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		string Plus(string x,string y){//加法 
			if(x[0]=='-'&&y[0]=='-'){
				string t=Plus(x.substr(1,x.size()-1),
							  y.substr(1,y.size()-1));
				t="-"+t;
				return t;
			}
			else if(x[0]=='-'&&y[0]!='-'){
				return Minus(y,x.substr(1,x.size()-1));
			}
			else if(x[0]!='-'&&y[0]=='-'){
				return Minus(x,y.substr(1,y.size()-1));
			}
			memset(a,0,sizeof(a));
			memset(b,0,sizeof(b));
			memset(c,0,sizeof(c));
			a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存和的位数
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=a[i]+b[i]+jw;
				jw=c[i]/10;//先处理进位 
				c[i]%=10;
			}
			if(jw!=0)c[++c[0]]=jw;//判断是否进位，进位，位数+1，这一位为1 
			string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		string mobm(string x,char y){
			vector<int> ans;
			string t="";
			int k=(int)y-48,len=x.size();
			for(int i=len-1;i>=0;i--){
				int num=((int)x[i]-48)*k;
				if(ans.size()<len-i)ans.push_back(0);
				ans[len-i-1]+=num%10;
				ans.push_back(0);
				ans[len-i]+=num/10;
			}
			while(ans.size()>1&&ans[ans.size()-1]==0){
				ans.pop_back();
			}
			while(!ans.empty()){
				t+=(char)(ans.back()+48);
				ans.pop_back();
			}
			return t;
		}
		string azate(int len){
			string ans="";
			for(int i=1;i<=len;i++){
				ans+="0";
			}
			return ans;
		}
		string Mul(string x,string y){
			bool flag=false;
			if(x[0]=='-'){
				flag=!flag;
				x.erase(0,1);
			}
			if(y[0]=='-'){
				flag=!flag;
				y.erase(0,1);
			}
			string f[10],k[50005];
			for(int i=0;i<10;i++){
				f[i]="+_-INF";
			}
			f[0]="0",f[1]=y;
			int len=x.size();
			for(int i=len-1;i>=0;i--){
				if(f[(int)x[i]-48]!="+_-INF"){
					k[i]=f[(int)x[i]-48];
					continue;
				}
				k[i]=mobm(y,x[i]);
				k[i]+=azate(len-i-1);
			}
			string ans=k[len-1];
			for(int i=len-2;i>=0;i--){
				ans=Plus(ans,k[i]);
			}
			ans=(flag==true?"-":"")+ans;
			return ans;
		}
		bool check_size(string x,string y){
			if(x.size()>y.size())return false;
			else if(x.size()<y.size())return true;
			else{
				if(x>y)return false;
				else{
					return true;
				}
			}
		}
		class abnormal:public exception{
			private:
				string message;
			public:
				abnormal(string other){
					message=other;
				}
				const char* what(){
					return message.c_str();
				}
		};
		string Div(string x,string y){
			bool flag=false;
			if(x[0]=='-'){
				flag=!flag;
				x.erase(0,1);
			}
			if(y[0]=='-'){
				flag=!flag;
				y.erase(0,1);
			}
			if(y=="0"){
				abnormal e("Divider cannot be 0.");
				throw e;
				return "NULL";
			}
			else if(!check_size(y,x))return "0";
			string ans="";
			while(1){
				string a=x.substr(0,y.size());
				if(!check_size(y,a))a+=x[y.size()];
				int l=0,r=9;
				string k,k2;
				while(l<r){
					int mid=(l+r+1)/2;
					k=Mul(y,to_string(mid));
					if(check_size(k,a))l=mid;
					else r=mid-1;
				}
				string t=to_string(l);
				ans+=t;
				k=x.substr(a.size(),x.size()-a.size()+1);
				k2=Mul(y,t);
				x=Minus(a,k2);
				if(x=="0")x="";
				int len=x.size();
				x+=k;
				if(k=="")break;
				else if(!check_size(y,x)&&k.size()==1){
					ans+="0";
					break;
				}
				while(len<y.size()-1){
					ans+="0";
					len++;
				}
				while(!check_size(y,x.substr(0,len+1))){
					ans+="0";
					len++;
				}
			}
			ans=(flag==true?"-":"")+ans;
			return ans;
		}
		string Comple(string x,string y){
			string t=Div(x,y);
			string k=Minus(x,Mul(t,y));
			return k;
		}
	}
	class Big_num{
		friend string to_string(Big_num x);
		friend istream& operator>>(istream& is,Big_num& num);
		private:
			#define Plus(x,y) BN::Plus(x,y)
			#define Minus(x,y) BN::Minus(x,y)
			#define Mul(x,y) BN::Mul(x,y)
			#define Div(x,y) BN::Div(x,y)
			#define Comple(x,y) BN::Comple(x,y)
			string num;
		public: 
			Big_num(){
				num="0";
			}
			Big_num(string other){
				num=other;
			}
			Big_num(const char* other){
				num=other;
			}
			Big_num(int other){
				num=to_string(other);
			}
			Big_num(short other){
				num=to_string((int)other);
			}
			Big_num(long other){
				num=to_string(other);
			}
			Big_num(long long other){
				num=to_string(other);
			}
			Big_num(const Big_num& other){
				num=other.num;
			}
			Big_num& operator=(Big_num other){
				num=other.num;
				return *this;
			}
			Big_num operator+(Big_num other){
				string x=Plus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator-(Big_num other){
				string x=Minus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator*(Big_num other){
				string x=Mul(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator/(Big_num other){
				string x=Div(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator%(Big_num other){
				string x=Comple(num,other.num);
				Big_num y=x;
				return y;
			}
	};
	string to_string(Big_num x){
		return x.num;
	}
	ostream& operator<<(ostream& os,const Big_num& num){
	    os<<to_string(num);
	    return os;
	}
	istream& operator>>(istream& is,Big_num& num){
		is>>num.num;
		return is;
	}
}
using namespace BIG_NUM;

优化了乘法的时间复杂度（即将使用FFT优化）

董安雅在2023-04-16 12:49:03追加了内容

#include<bits/stdc++.h>
using namespace std;
namespace BIG_NUM{
	namespace BN{
		int a[50005],b[50005],c[100005];
		string k[50005];
		string f[10];
		/*
		const double PI = acos(-1.0);
		struct Complex {
			double x, y;
			Complex(double _x = 0.0, double _y = 0.0) {
				x = _x;
				y = _y;
			}
			Complex operator-(const Complex &b) const {
				return Complex(x - b.x, y - b.y);
			}
			Complex operator+(const Complex &b) const {
				return Complex(x + b.x, y + b.y);
			}
			Complex operator*(const Complex &b) const {
				return Complex(x * b.x - y * b.y, x * b.y + y * b.x);
			}
		};
		void change(Complex y[], int len) {
			int i, j, k;
			for (int i = 1, j = len / 2; i < len - 1; i++) {
				if (i < j) std::swap(y[i], y[j]);
				k = len / 2;
				while (j >= k) {
					j = j - k;
					k = k / 2;
				}
				if (j < k) j += k;
			}
		}
		void fft(Complex y[], int len, int on) {
			change(y, len);
			for (int h = 2; h <= len; h <<= 1) {
				Complex wn(cos(2 * PI / h), sin(on * 2 * PI / h));
				for (int j = 0; j < len; j += h) {
					Complex w(1, 0);
					for (int k = j; k < j + h / 2; k++) {
						Complex u = y[k];
						Complex t = w * y[k + h / 2];
						y[k] = u + t;
						y[k + h / 2] = u - t;
						w = w * wn;
					}
				}
			}
			if (on == -1) {
				for (int i = 0; i < len; i++) {
					y[i].x /= len;
				}
			}
		}
		string Mul(string x,string y){//乘法 
			bool flag=false;
			if(x[0]=='-'){
				flag=!flag;
				x.erase(0,1);
			}
			if(y[0]=='-'){
				flag=!flag;
				y.erase(0,1);
			}
			memset(a,0,sizeof(a));
			memset(b,0,sizeof(b));
			memset(c,0,sizeof(c));
			a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=a[0]+b[0];//积的位数
			for(int i=1;i<=a[0];i++){
				for(int j=1;j<=b[0];j++){
					c[i+j-1]+=a[i]*b[j];//这里一定要+= 
				}
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=c[i]+jw;
				jw=c[i]/10;
				c[i]%=10;
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
			string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			z=(flag==true?"-":"")+z;
			return z;
		}
		*/
		string Plus(string x,string y);//加法
		string Minus(string x,string y){//减法 
		    if(x==y)return "0";
		    if(x[0]=='-'&&y[0]=='-'){
				return Minus(y.substr(1,y.size()-1),
				             x.substr(1,y.size()-1));
			}
			else if(x[0]=='-'&&y[0]!='-'){
				string t=Plus(x.substr(1,x.size()-1),y);
				t="-"+t;
				return t;
			}
			else if(x[0]!='-'&&y[0]=='-'){
				return Plus(x,y.substr(1,y.size()-1));
			}
		    a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存差的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				if(a[i]<b[i]){//借位的情况 
					a[i+1]--;
					a[i]+=10;
				}
				c[i]=a[i]-b[i];
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
		    string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		string Plus(string x,string y){//加法 
			if(x[0]=='-'&&y[0]=='-'){
				string t=Plus(x.substr(1,x.size()-1),
							  y.substr(1,y.size()-1));
				t="-"+t;
				return t;
			}
			else if(x[0]=='-'&&y[0]!='-'){
				return Minus(y,x.substr(1,x.size()-1));
			}
			else if(x[0]!='-'&&y[0]=='-'){
				return Minus(x,y.substr(1,y.size()-1));
			}
			a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存和的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=a[i]+b[i]+jw;
				jw=c[i]/10;//先处理进位 
				c[i]%=10;
			}
			if(jw!=0)c[++c[0]]=jw;//判断是否进位，进位，位数+1，这一位为1 
			string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		void Plus(){//加法 
			c[0]=max(a[0],b[0]);//c[0]存和的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=a[i]+b[i]+jw;
				jw=c[i]/10;//先处理进位 
				c[i]%=10;
			}
			if(jw!=0)c[++c[0]]=jw;//判断是否进位，进位，位数+1，这一位为1 
		}
		void Minus(){//减法 
			c[0]=max(a[0],b[0]);//c[0]存差的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				if(a[i]<b[i]){//借位的情况 
					a[i+1]--;
					a[i]+=10;
				}
				c[i]=a[i]-b[i];
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
		}
		string mobm(string x,char y){
			vector<int> ans;
			string t="";
			int k=(int)y-48,len=x.size();
			for(int i=len-1;i>=0;i--){
				int num=((int)x[i]-48)*k;
				if(ans.size()<len-i)ans.push_back(0);
				ans[len-i-1]+=num%10;
				ans.push_back(0);
				ans[len-i]+=num/10;
			}
			while(ans.size()>1&&ans[ans.size()-1]==0){
				ans.pop_back();
			}
			while(!ans.empty()){
				t+=(char)(ans.back()+48);
				ans.pop_back();
			}
			return t;
		}
		string azate(int len){
			string ans="";
			for(int i=1;i<=len;i++){
				ans+="0";
			}
			return ans;
		}
		string Mul(string x,string y){
			bool flag=false;
			if(x[0]=='-'){
				flag=!flag;
				x.erase(0,1);
			}
			if(y[0]=='-'){
				flag=!flag;
				y.erase(0,1);
			}
			for(int i=0;i<10;i++){
				f[i]="+_-INF";
			}
			f[0]="0",f[1]=y;
			int len=x.size();
			for(int i=len-1;i>=0;i--){
				if(f[(int)x[i]-48]!="+_-INF"){
					k[i]=f[(int)x[i]-48];
					continue;
				}
				k[i]=mobm(y,x[i]);
				k[i]+=azate(len-i-1);
			}
			string ans="";
			c[0]=k[len-1].size();
			for(int i=1;i<=c[0];i++){
				c[i]=k[len-1][c[0]-i]-'0';
			}
			for(int i=len-2;i>=0;i--){
				a[0]=c[0];
				for(int j=1;j<=c[0];j++){
					a[j]=c[j];
				}
				b[0]=k[i].size();
				for(int j=1;j<=b[0];j++){
					b[j]=k[i][b[0]-j]-'0';
				}
				Plus();
			}
			for(int i=c[0];i>=1;i--)ans=ans+(char)(c[i]+48);
			ans=(flag==true?"-":"")+ans;
			return ans;
		}
		bool check_size(string x,string y){
			if(x.size()>y.size())return false;
			else if(x.size()<y.size())return true;
			else{
				if(x>y)return false;
				else{
					return true;
				}
			}
		}
		class abnormal:public exception{
			private:
				string message;
			public:
				abnormal(string other){
					message=other;
				}
				const char* what(){
					return message.c_str();
				}
		};
		string Div(string x,string y){
			bool flag=false;
			if(x[0]=='-'){
				flag=!flag;
				x.erase(0,1);
			}
			if(y[0]=='-'){
				flag=!flag;
				y.erase(0,1);
			}
			if(y=="0"){
				abnormal e("Divider cannot be 0.");
				throw e;
				return "NULL";
			}
			else if(!check_size(y,x))return "0";
			string ans="";
			while(1){
				string a=x.substr(0,y.size());
				if(!check_size(y,a))a+=x[y.size()];
				int l=0,r=9;
				string k,k2;
				while(l<r){
					int mid=(l+r+1)/2;
					k=Mul(y,to_string(mid));
					if(check_size(k,a))l=mid;
					else r=mid-1;
				}
				string t=to_string(l);
				ans+=t;
				k=x.substr(a.size(),x.size()-a.size()+1);
				k2=Mul(y,t);
				x=Minus(a,k2);
				if(x=="0")x="";
				int len=x.size();
				x+=k;
				if(k=="")break;
				else if(!check_size(y,x)&&k.size()==1){
					ans+="0";
					break;
				}
				while(len<y.size()-1){
					ans+="0";
					len++;
				}
				while(!check_size(y,x.substr(0,len+1))){
					ans+="0";
					len++;
				}
			}
			ans=(flag==true?"-":"")+ans;
			return ans;
		}
		string Comple(string x,string y){
			string t=Div(x,y);
			string k=Minus(x,Mul(t,y));
			return k;
		}
	}
	class Big_num{
		friend string to_string(Big_num x);
		friend istream& operator>>(istream& is,Big_num& num);
		private:
			#define Plus(x,y) BN::Plus(x,y)
			#define Minus(x,y) BN::Minus(x,y)
			#define Mul(x,y) BN::Mul(x,y)
			#define Div(x,y) BN::Div(x,y)
			#define Comple(x,y) BN::Comple(x,y)
			string num;
		public: 
			Big_num(){
				num="0";
			}
			Big_num(string other){
				num=other;
			}
			Big_num(const char* other){
				num=other;
			}
			Big_num(int other){
				num=to_string(other);
			}
			Big_num(short other){
				num=to_string((int)other);
			}
			Big_num(long other){
				num=to_string(other);
			}
			Big_num(long long other){
				num=to_string(other);
			}
			Big_num(const Big_num& other){
				num=other.num;
			}
			Big_num& operator=(Big_num other){
				num=other.num;
				return *this;
			}
			Big_num operator+(Big_num other){
				string x=Plus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator-(Big_num other){
				string x=Minus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator*(Big_num other){
				string x=Mul(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator/(Big_num other){
				string x=Div(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator%(Big_num other){
				string x=Comple(num,other.num);
				Big_num y=x;
				return y;
			}
	};
	string to_string(Big_num x){
		return x.num;
	}
	ostream& operator<<(ostream& os,const Big_num& num){
	    os<<to_string(num);
	    return os;
	}
	istream& operator>>(istream& is,Big_num& num){
		is>>num.num;
		return is;
	}
}
using namespace BIG_NUM;

继续优化了时间复杂度。

董安雅在2023-04-16 13:20:56追加了内容

#include<bits/stdc++.h>
using namespace std;
namespace BIG_NUM{
	namespace BN{
		int a[50005],b[50005],c[100005];
		string k[50005];
		string f[10];
		string Plus(string x,string y);//加法
		string Minus(string x,string y){//减法 
		    if(x==y)return "0";
		    if(x[0]=='-'&&y[0]=='-'){
				return Minus(y.substr(1,y.size()-1),
				             x.substr(1,y.size()-1));
			}
			else if(x[0]=='-'&&y[0]!='-'){
				string t=Plus(x.substr(1,x.size()-1),y);
				t="-"+t;
				return t;
			}
			else if(x[0]!='-'&&y[0]=='-'){
				return Plus(x,y.substr(1,y.size()-1));
			}
		    a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存差的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				if(a[i]<b[i]){//借位的情况 
					a[i+1]--;
					a[i]+=10;
				}
				c[i]=a[i]-b[i];
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
		    string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		string Plus(string x,string y){//加法 
			if(x[0]=='-'&&y[0]=='-'){
				string t=Plus(x.substr(1,x.size()-1),
							  y.substr(1,y.size()-1));
				t="-"+t;
				return t;
			}
			else if(x[0]=='-'&&y[0]!='-'){
				return Minus(y,x.substr(1,x.size()-1));
			}
			else if(x[0]!='-'&&y[0]=='-'){
				return Minus(x,y.substr(1,y.size()-1));
			}
			a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存和的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=a[i]+b[i]+jw;
				jw=c[i]/10;//先处理进位 
				c[i]%=10;
			}
			if(jw!=0)c[++c[0]]=jw;//判断是否进位，进位，位数+1，这一位为1 
			string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		void Plus(){//加法 
			c[0]=max(a[0],b[0]);//c[0]存和的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=a[i]+b[i]+jw;
				jw=c[i]/10;//先处理进位 
				c[i]%=10;
			}
			if(jw!=0)c[++c[0]]=jw;//判断是否进位，进位，位数+1，这一位为1 
		}
		void Minus(){//减法 
			c[0]=max(a[0],b[0]);//c[0]存差的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				if(a[i]<b[i]){//借位的情况 
					a[i+1]--;
					a[i]+=10;
				}
				c[i]=a[i]-b[i];
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
		}
		string mobm(string x,char y){
			vector<int> ans;
			string t="";
			int k=(int)y-48,len=x.size();
			for(int i=len-1;i>=0;i--){
				int num=((int)x[i]-48)*k;
				if(ans.size()<len-i)ans.push_back(0);
				ans[len-i-1]+=num%10;
				ans.push_back(0);
				ans[len-i]+=num/10;
			}
			while(ans.size()>1&&ans[ans.size()-1]==0){
				ans.pop_back();
			}
			while(!ans.empty()){
				t+=(char)(ans.back()+48);
				ans.pop_back();
			}
			return t;
		}
		string azate(int len){
			string ans="";
			for(int i=1;i<=len;i++){
				ans+="0";
			}
			return ans;
		}
		string Mul(string x,string y){
			bool flag=false;
			if(x[0]=='-'){
				flag=!flag;
				x.erase(0,1);
			}
			if(y[0]=='-'){
				flag=!flag;
				y.erase(0,1);
			}
			for(int i=0;i<10;i++){
				f[i]="+_-INF";
			}
			f[0]="0",f[1]=y;
			int len=x.size();
			for(int i=len-1;i>=0;i--){
				if(f[(int)x[i]-48]!="+_-INF"){
					k[i]=f[(int)x[i]-48];
					k[i]+=azate(len-i-1);
					continue;
				}
				k[i]=mobm(y,x[i]);
				k[i]+=azate(len-i-1);
			}
			string ans="";
			c[0]=k[len-1].size();
			for(int i=1;i<=c[0];i++){
				c[i]=k[len-1][c[0]-i]-'0';
			}
			for(int i=len-2;i>=0;i--){
				a[0]=c[0];
				for(int j=1;j<=c[0];j++){
					a[j]=c[j];
				}
				b[0]=k[i].size();
				for(int j=1;j<=b[0];j++){
					b[j]=k[i][b[0]-j]-'0';
				}
				Plus();
			}
			for(int i=c[0];i>=1;i--)ans=ans+(char)(c[i]+48);
			ans=(flag==true?"-":"")+ans;
			return ans;
		}
		bool check_size(string x,string y){
			if(x.size()>y.size())return false;
			else if(x.size()<y.size())return true;
			else{
				if(x>y)return false;
				else{
					return true;
				}
			}
		}
		class abnormal:public exception{
			private:
				string message;
			public:
				abnormal(string other){
					message=other;
				}
				const char* what(){
					return message.c_str();
				}
		};
		string Div(string x,string y){
			bool flag=false;
			if(x[0]=='-'){
				flag=!flag;
				x.erase(0,1);
			}
			if(y[0]=='-'){
				flag=!flag;
				y.erase(0,1);
			}
			if(y=="0"){
				abnormal e("Divider cannot be 0.");
				throw e;
				return "NULL";
			}
			else if(!check_size(y,x))return "0";
			string ans="";
			while(1){
				string a=x.substr(0,y.size());
				if(!check_size(y,a))a+=x[y.size()];
				int l=0,r=9;
				string k,k2;
				while(l<r){
					int mid=(l+r+1)/2;
					k=Mul(y,to_string(mid));
					if(check_size(k,a))l=mid;
					else r=mid-1;
				}
				string t=to_string(l);
				ans+=t;
				k=x.substr(a.size(),x.size()-a.size()+1);
				k2=Mul(y,t);
				x=Minus(a,k2);
				if(x=="0")x="";
				int len=x.size();
				x+=k;
				if(k=="")break;
				else if(!check_size(y,x)&&k.size()==1){
					ans+="0";
					break;
				}
				while(len<y.size()-1){
					ans+="0";
					len++;
				}
				while(!check_size(y,x.substr(0,len+1))){
					ans+="0";
					len++;
				}
			}
			ans=(flag==true?"-":"")+ans;
			return ans;
		}
		string Comple(string x,string y){
			string t=Div(x,y);
			string k=Minus(x,Mul(t,y));
			return k;
		}
	}
	class Big_num{
		friend string to_string(Big_num x);
		friend istream& operator>>(istream& is,Big_num& num);
		private:
			#define Plus(x,y) BN::Plus(x,y)
			#define Minus(x,y) BN::Minus(x,y)
			#define Mul(x,y) BN::Mul(x,y)
			#define Div(x,y) BN::Div(x,y)
			#define Comple(x,y) BN::Comple(x,y)
			string num;
		public: 
			Big_num(){
				num="0";
			}
			Big_num(string other){
				num=other;
			}
			Big_num(const char* other){
				num=other;
			}
			Big_num(int other){
				num=to_string(other);
			}
			Big_num(short other){
				num=to_string((int)other);
			}
			Big_num(long other){
				num=to_string(other);
			}
			Big_num(long long other){
				num=to_string(other);
			}
			Big_num(const Big_num& other){
				num=other.num;
			}
			Big_num& operator=(Big_num other){
				num=other.num;
				return *this;
			}
			Big_num operator+(Big_num other){
				string x=Plus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator-(Big_num other){
				string x=Minus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator*(Big_num other){
				string x=Mul(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator/(Big_num other){
				string x=Div(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num operator%(Big_num other){
				string x=Comple(num,other.num);
				Big_num y=x;
				return y;
			}
	};
	string to_string(Big_num x){
		return x.num;
	}
	ostream& operator<<(ostream& os,const Big_num& num){
	    os<<to_string(num);
	    return os;
	}
	istream& operator>>(istream& is,Big_num& num){
		is>>num.num;
		return is;
	}
}
using namespace BIG_NUM;

修复了一个BUG.

董安雅在2023-04-16 14:45:37追加了内容

#include<bits/stdc++.h>
using namespace std;
namespace BIG_NUM{
	namespace BN{
		int a[50005],b[50005],c[100005];
		string k[50005];
		string f[10];
		string Plus(string x,string y);//加法
		string Minus(string x,string y){//减法 
		    if(x==y)return "0";
		    if(x[0]=='-'&&y[0]=='-'){
				return Minus(y.substr(1,y.size()-1),
				             x.substr(1,y.size()-1));
			}
			else if(x[0]=='-'&&y[0]!='-'){
				string t=Plus(x.substr(1,x.size()-1),y);
				t="-"+t;
				return t;
			}
			else if(x[0]!='-'&&y[0]=='-'){
				return Plus(x,y.substr(1,y.size()-1));
			}
		    a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存差的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				if(a[i]<b[i]){//借位的情况 
					a[i+1]--;
					a[i]+=10;
				}
				c[i]=a[i]-b[i];
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
		    string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		string Plus(string x,string y){//加法 
			if(x[0]=='-'&&y[0]=='-'){
				string t=Plus(x.substr(1,x.size()-1),
							  y.substr(1,y.size()-1));
				t="-"+t;
				return t;
			}
			else if(x[0]=='-'&&y[0]!='-'){
				return Minus(y,x.substr(1,x.size()-1));
			}
			else if(x[0]!='-'&&y[0]=='-'){
				return Minus(x,y.substr(1,y.size()-1));
			}
			a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存和的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=a[i]+b[i]+jw;
				jw=c[i]/10;//先处理进位 
				c[i]%=10;
			}
			if(jw!=0)c[++c[0]]=jw;//判断是否进位，进位，位数+1，这一位为1 
			string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		void Plus(){//加法 
			c[0]=max(a[0],b[0]);//c[0]存和的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=a[i]+b[i]+jw;
				jw=c[i]/10;//先处理进位 
				c[i]%=10;
			}
			if(jw!=0)c[++c[0]]=jw;//判断是否进位，进位，位数+1，这一位为1 
		}
		void Minus(){//减法 
			c[0]=max(a[0],b[0]);//c[0]存差的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				if(a[i]<b[i]){//借位的情况 
					a[i+1]--;
					a[i]+=10;
				}
				c[i]=a[i]-b[i];
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
		}
		string mobm(string x,char y){
			vector<int> ans;
			string t="";
			int k=(int)y-48,len=x.size();
			for(int i=len-1;i>=0;i--){
				int num=((int)x[i]-48)*k;
				if(ans.size()<len-i)ans.push_back(0);
				ans[len-i-1]+=num%10;
				ans.push_back(0);
				ans[len-i]+=num/10;
			}
			while(ans.size()>1&&ans[ans.size()-1]==0){
				ans.pop_back();
			}
			while(!ans.empty()){
				t+=(char)(ans.back()+48);
				ans.pop_back();
			}
			return t;
		}
		string azate(int len){
			string ans="";
			for(int i=1;i<=len;i++){
				ans+="0";
			}
			return ans;
		}
		string Mul(string x,string y){
			bool flag=false;
			if(x[0]=='-'){
				flag=!flag;
				x.erase(0,1);
			}
			if(y[0]=='-'){
				flag=!flag;
				y.erase(0,1);
			}
			for(int i=0;i<10;i++){
				f[i]="+_-INF";
			}
			f[0]="0",f[1]=y;
			int len=x.size();
			for(int i=len-1;i>=0;i--){
				if(f[(int)x[i]-48]!="+_-INF"){
					k[i]=f[(int)x[i]-48];
					k[i]+=azate(len-i-1);
					continue;
				}
				k[i]=mobm(y,x[i]);
				k[i]+=azate(len-i-1);
			}
			string ans="";
			c[0]=k[len-1].size();
			for(int i=1;i<=c[0];i++){
				c[i]=k[len-1][c[0]-i]-'0';
			}
			for(int i=len-2;i>=0;i--){
				a[0]=c[0];
				for(int j=1;j<=c[0];j++){
					a[j]=c[j];
				}
				b[0]=k[i].size();
				for(int j=1;j<=b[0];j++){
					b[j]=k[i][b[0]-j]-'0';
				}
				Plus();
			}
			for(int i=c[0];i>=1;i--)ans=ans+(char)(c[i]+48);
			ans=(flag==true?"-":"")+ans;
			return ans;
		}
		bool check_size(string x,string y){
			if(x.size()>y.size())return false;
			else if(x.size()<y.size())return true;
			else{
				if(x>y)return false;
				else{
					return true;
				}
			}
		}
		class abnormal:public exception{
			private:
				string message;
			public:
				abnormal(string other){
					message=other;
				}
				const char* what(){
					return message.c_str();
				}
		};
		string Div(string x,string y){
			bool flag=false;
			if(x[0]=='-'){
				flag=!flag;
				x.erase(0,1);
			}
			if(y[0]=='-'){
				flag=!flag;
				y.erase(0,1);
			}
			if(y=="0"){
				abnormal e("Divider cannot be 0.");
				throw e;
				return "NULL";
			}
			else if(!check_size(y,x))return "0";
			string ans="";
			while(1){
				string a=x.substr(0,y.size());
				if(!check_size(y,a))a+=x[y.size()];
				int l=0,r=9;
				string k,k2;
				while(l<r){
					int mid=(l+r+1)/2;
					k=Mul(y,to_string(mid));
					if(check_size(k,a))l=mid;
					else r=mid-1;
				}
				string t=to_string(l);
				ans+=t;
				k=x.substr(a.size(),x.size()-a.size()+1);
				k2=Mul(y,t);
				x=Minus(a,k2);
				if(x=="0")x="";
				int len=x.size();
				x+=k;
				if(k=="")break;
				else if(!check_size(y,x)&&k.size()==1){
					ans+="0";
					break;
				}
				while(len<y.size()-1){
					ans+="0";
					len++;
				}
				while(!check_size(y,x.substr(0,len+1))){
					ans+="0";
					len++;
				}
			}
			ans=(flag==true?"-":"")+ans;
			return ans;
		}
		string Comple(string x,string y){
			string t=Div(x,y);
			string k=Minus(x,Mul(t,y));
			return k;
		}
	}
	class Big_num{
		friend string to_string(Big_num x);
		friend istream& operator>>(istream& is,Big_num& num);
		private:
			#define Plus(x,y) BN::Plus(x,y)
			#define Minus(x,y) BN::Minus(x,y)
			#define Mul(x,y) BN::Mul(x,y)
			#define Div(x,y) BN::Div(x,y)
			#define Comple(x,y) BN::Comple(x,y)
			string num;
		public: 
			Big_num(){
				num="0";
			}
			Big_num(string other){
				num=other;
			}
			Big_num(const char* other){
				num=other;
			}
			Big_num(int other){
				num=to_string(other);
			}
			Big_num(short other){
				num=to_string((int)other);
			}
			Big_num(long other){
				num=to_string(other);
			}
			Big_num(long long other){
				num=to_string(other);
			}
			Big_num(const Big_num& other){
				num=other.num;
			}
			Big_num& operator=(Big_num other){
				num=other.num;
				return *this;
			}
			Big_num operator+(Big_num other){
				string x=Plus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num& operator+=(Big_num other){
				string x=Plus(num,other.num);
				num=x;
				return *this;
			}
			Big_num operator-(Big_num other){
				string x=Minus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num& operator-=(Big_num other){
				string x=Minus(num,other.num);
				num=x;
				return *this;
			}
			Big_num operator*(Big_num other){
				string x=Mul(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num& operator*=(Big_num other){
				string x=Mul(num,other.num);
				num=x;
				return *this;
			}
			Big_num operator/(Big_num other){
				string x=Div(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num& operator/=(Big_num other){
				string x=Div(num,other.num);
				num=x;
				return *this;
			}
			Big_num operator%(Big_num other){
				string x=Comple(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num& operator%=(Big_num other){
				string x=Comple(num,other.num);
				num=x;
				return *this;
			}
	};
	string to_string(Big_num x){
		return x.num;
	}
	ostream& operator<<(ostream& os,const Big_num& num){
	    os<<to_string(num);
	    return os;
	}
	istream& operator>>(istream& is,Big_num& num){
		is>>num.num;
		return is;
	}
}
using namespace BIG_NUM;

董安雅在2023-04-16 14:55:59追加了内容

#include<bits/stdc++.h>
using namespace std;
namespace BIG_NUM{
	namespace BN{
		int a[50005],b[50005],c[100005];
		string k[50005];
		string f[10];
		string Plus(string x,string y);//加法
		string Minus(string x,string y){//减法 
		    if(x==y)return "0";
		    if(x[0]=='-'&&y[0]=='-'){
				return Minus(y.substr(1,y.size()-1),
				             x.substr(1,y.size()-1));
			}
			else if(x[0]=='-'&&y[0]!='-'){
				string t=Plus(x.substr(1,x.size()-1),y);
				t="-"+t;
				return t;
			}
			else if(x[0]!='-'&&y[0]=='-'){
				return Plus(x,y.substr(1,y.size()-1));
			}
		    a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存差的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				if(a[i]<b[i]){//借位的情况 
					a[i+1]--;
					a[i]+=10;
				}
				c[i]=a[i]-b[i];
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
		    string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		string Plus(string x,string y){//加法 
			if(x[0]=='-'&&y[0]=='-'){
				string t=Plus(x.substr(1,x.size()-1),
							  y.substr(1,y.size()-1));
				t="-"+t;
				return t;
			}
			else if(x[0]=='-'&&y[0]!='-'){
				return Minus(y,x.substr(1,x.size()-1));
			}
			else if(x[0]!='-'&&y[0]=='-'){
				return Minus(x,y.substr(1,y.size()-1));
			}
			a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存和的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=a[i]+b[i]+jw;
				jw=c[i]/10;//先处理进位 
				c[i]%=10;
			}
			if(jw!=0)c[++c[0]]=jw;//判断是否进位，进位，位数+1，这一位为1 
			string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		void Plus(){//加法 
			c[0]=max(a[0],b[0]);//c[0]存和的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=a[i]+b[i]+jw;
				jw=c[i]/10;//先处理进位 
				c[i]%=10;
			}
			if(jw!=0)c[++c[0]]=jw;//判断是否进位，进位，位数+1，这一位为1 
		}
		void Minus(){//减法 
			c[0]=max(a[0],b[0]);//c[0]存差的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				if(a[i]<b[i]){//借位的情况 
					a[i+1]--;
					a[i]+=10;
				}
				c[i]=a[i]-b[i];
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
		}
		string mobm(string x,char y){
			vector<int> ans;
			string t="";
			int k=(int)y-48,len=x.size();
			for(int i=len-1;i>=0;i--){
				int num=((int)x[i]-48)*k;
				if(ans.size()<len-i)ans.push_back(0);
				ans[len-i-1]+=num%10;
				ans.push_back(0);
				ans[len-i]+=num/10;
			}
			while(ans.size()>1&&ans[ans.size()-1]==0){
				ans.pop_back();
			}
			while(!ans.empty()){
				t+=(char)(ans.back()+48);
				ans.pop_back();
			}
			return t;
		}
		string azate(int len){
			string ans="";
			for(int i=1;i<=len;i++){
				ans+="0";
			}
			return ans;
		}
		string Mul(string x,string y){
			bool flag=false;
			if(x[0]=='-'){
				flag=!flag;
				x.erase(0,1);
			}
			if(y[0]=='-'){
				flag=!flag;
				y.erase(0,1);
			}
			for(int i=0;i<10;i++){
				f[i]="+_-INF";
			}
			f[0]="0",f[1]=y;
			int len=x.size();
			for(int i=len-1;i>=0;i--){
				if(f[(int)x[i]-48]!="+_-INF"){
					k[i]=f[(int)x[i]-48];
					k[i]+=azate(len-i-1);
					continue;
				}
				k[i]=mobm(y,x[i]);
				k[i]+=azate(len-i-1);
			}
			string ans="";
			c[0]=k[len-1].size();
			for(int i=1;i<=c[0];i++){
				c[i]=k[len-1][c[0]-i]-'0';
			}
			for(int i=len-2;i>=0;i--){
				a[0]=c[0];
				for(int j=1;j<=c[0];j++){
					a[j]=c[j];
				}
				b[0]=k[i].size();
				for(int j=1;j<=b[0];j++){
					b[j]=k[i][b[0]-j]-'0';
				}
				Plus();
			}
			for(int i=c[0];i>=1;i--)ans=ans+(char)(c[i]+48);
			ans=(flag==true?"-":"")+ans;
			return ans;
		}
		bool check_size(string x,string y){
			if(x.size()>y.size())return false;
			else if(x.size()<y.size())return true;
			else{
				if(x>y)return false;
				else{
					return true;
				}
			}
		}
		class abnormal:public exception{
			private:
				string message;
			public:
				abnormal(string other){
					message=other;
				}
				const char* what(){
					return message.c_str();
				}
		};
		string Div(string x,string y){
			bool flag=false;
			if(x[0]=='-'){
				flag=!flag;
				x.erase(0,1);
			}
			if(y[0]=='-'){
				flag=!flag;
				y.erase(0,1);
			}
			if(y=="0"){
				abnormal e("Divider cannot be 0.");
				throw e;
				return "NULL";
			}
			else if(!check_size(y,x))return "0";
			string ans="";
			while(1){
				string a=x.substr(0,y.size());
				if(!check_size(y,a))a+=x[y.size()];
				int l=0,r=9;
				string k,k2;
				while(l<r){
					int mid=(l+r+1)/2;
					k=Mul(y,to_string(mid));
					if(check_size(k,a))l=mid;
					else r=mid-1;
				}
				string t=to_string(l);
				ans+=t;
				k=x.substr(a.size(),x.size()-a.size()+1);
				k2=Mul(y,t);
				x=Minus(a,k2);
				if(x=="0")x="";
				int len=x.size();
				x+=k;
				if(k=="")break;
				else if(!check_size(y,x)&&k.size()==1){
					ans+="0";
					break;
				}
				while(len<y.size()-1){
					ans+="0";
					len++;
				}
				while(!check_size(y,x.substr(0,len+1))){
					ans+="0";
					len++;
				}
			}
			ans=(flag==true?"-":"")+ans;
			return ans;
		}
		string Comple(string x,string y){
			string t=Div(x,y);
			string k=Minus(x,Mul(t,y));
			return k;
		}
	}
	class Big_num{
		friend string to_string(Big_num x);
		friend istream& operator>>(istream& is,Big_num& num);
		private:
			#define Plus(x,y) BN::Plus(x,y)
			#define Minus(x,y) BN::Minus(x,y)
			#define Mul(x,y) BN::Mul(x,y)
			#define Div(x,y) BN::Div(x,y)
			#define Comple(x,y) BN::Comple(x,y)
			string num;
		public: 
			Big_num(){
				num="0";
			}
			Big_num(string other){
				num=other;
			}
			Big_num(const char* other){
				num=other;
			}
			Big_num(int other){
				num=to_string(other);
			}
			Big_num(short other){
				num=to_string((int)other);
			}
			Big_num(long other){
				num=to_string(other);
			}
			Big_num(long long other){
				num=to_string(other);
			}
			Big_num(const Big_num& other){
				num=other.num;
			}
			Big_num& operator=(Big_num other){
				num=other.num;
				return *this;
			}
			Big_num operator+(Big_num other){
				string x=Plus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num& operator+=(Big_num other){
				string x=Plus(num,other.num);
				num=x;
				return *this;
			}
			Big_num operator-(Big_num other){
				string x=Minus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num& operator-=(Big_num other){
				string x=Minus(num,other.num);
				num=x;
				return *this;
			}
			Big_num operator*(Big_num other){
				string x=Mul(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num& operator*=(Big_num other){
				string x=Mul(num,other.num);
				num=x;
				return *this;
			}
			Big_num operator/(Big_num other){
				string x=Div(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num& operator/=(Big_num other){
				string x=Div(num,other.num);
				num=x;
				return *this;
			}
			Big_num operator%(Big_num other){
				string x=Comple(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num& operator%=(Big_num other){
				string x=Comple(num,other.num);
				num=x;
				return *this;
			}
			Big_num& operator++(){
				num=Plus(num,"1");
				return *this;
			}
			Big_num operator++(int){
				Big_num old=num;
				num=Plus(num,"1");
				return old;
			}
	};
	string to_string(Big_num x){
		return x.num;
	}
	Big_num abs(Big_num x){
		string y=to_string(x);
		if(y[0]=='-')y.erase(0,1);
		Big_num z=y;
		return z;
	}
	Big_num fabs(Big_num x){
		return abs(x);
	}
	ostream& operator<<(ostream& os,const Big_num& num){
	    os<<to_string(num);
	    return os;
	}
	istream& operator>>(istream& is,Big_num& num){
		is>>num.num;
		return is;
	}
}
using namespace BIG_NUM;

加入了一些新函数、运算符

董安雅在2023-05-07 10:20:02追加了内容

#include<bits/stdc++.h>
using namespace std;
namespace BIG_NUM{
	namespace BN{
		int a[50005],b[50005],c[100005];
		string k[50005];
		string f[10];
		/*
		const double PI = acos(-1.0);
		struct Complex {
			double x, y;
			Complex(double _x = 0.0, double _y = 0.0) {
				x = _x;
				y = _y;
			}
			Complex operator-(const Complex &b) const {
				return Complex(x - b.x, y - b.y);
			}
			Complex operator+(const Complex &b) const {
				return Complex(x + b.x, y + b.y);
			}
			Complex operator*(const Complex &b) const {
				return Complex(x * b.x - y * b.y, x * b.y + y * b.x);
			}
		};
		void change(Complex y[], int len) {
			int i, j, k;
			for (int i = 1, j = len / 2; i < len - 1; i++) {
				if (i < j) std::swap(y[i], y[j]);
				k = len / 2;
				while (j >= k) {
					j = j - k;
					k = k / 2;
				}
				if (j < k) j += k;
			}
		}
		void fft(Complex y[], int len, int on) {
			change(y, len);
			for (int h = 2; h <= len; h <<= 1) {
				Complex wn(cos(2 * PI / h), sin(on * 2 * PI / h));
				for (int j = 0; j < len; j += h) {
					Complex w(1, 0);
					for (int k = j; k < j + h / 2; k++) {
						Complex u = y[k];
						Complex t = w * y[k + h / 2];
						y[k] = u + t;
						y[k + h / 2] = u - t;
						w = w * wn;
					}
				}
			}
			if (on == -1) {
				for (int i = 0; i < len; i++) {
					y[i].x /= len;
				}
			}
		}
		string Mul(string x,string y){//乘法 
			bool flag=false;
			if(x[0]=='-'){
				flag=!flag;
				x.erase(0,1);
			}
			if(y[0]=='-'){
				flag=!flag;
				y.erase(0,1);
			}
			memset(a,0,sizeof(a));
			memset(b,0,sizeof(b));
			memset(c,0,sizeof(c));
			a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=a[0]+b[0];//积的位数
			for(int i=1;i<=a[0];i++){
				for(int j=1;j<=b[0];j++){
					c[i+j-1]+=a[i]*b[j];//这里一定要+= 
				}
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=c[i]+jw;
				jw=c[i]/10;
				c[i]%=10;
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
			string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			z=(flag==true?"-":"")+z;
			return z;
		}
		*/
		string Plus(string x,string y);//加法
		string Minus(string x,string y){//减法 
		    if(x==y)return "0";
		    if(x[0]=='-'&&y[0]=='-'){
				return Minus(y.substr(1,y.size()-1),
				             x.substr(1,y.size()-1));
			}
			else if(x[0]=='-'&&y[0]!='-'){
				string t=Plus(x.substr(1,x.size()-1),y);
				t="-"+t;
				return t;
			}
			else if(x[0]!='-'&&y[0]=='-'){
				return Plus(x,y.substr(1,y.size()-1));
			}
		    a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存差的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				if(a[i]<b[i]){//借位的情况 
					a[i+1]--;
					a[i]+=10;
				}
				c[i]=a[i]-b[i];
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
		    string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		string Plus(string x,string y){//加法 
			if(x[0]=='-'&&y[0]=='-'){
				string t=Plus(x.substr(1,x.size()-1),
							  y.substr(1,y.size()-1));
				t="-"+t;
				return t;
			}
			else if(x[0]=='-'&&y[0]!='-'){
				return Minus(y,x.substr(1,x.size()-1));
			}
			else if(x[0]!='-'&&y[0]=='-'){
				return Minus(x,y.substr(1,y.size()-1));
			}
			a[0]=x.size(),b[0]=y.size();//a[0] b[0]存位数
			for(int i=1;i<=a[0];i++){//倒着存入数组 
				a[i]=x[a[0]-i]-'0';
			}
			for(int i=1;i<=b[0];i++){//倒着存入数组 
				b[i]=y[b[0]-i]-'0';
			}
			c[0]=max(a[0],b[0]);//c[0]存和的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=a[i]+b[i]+jw;
				jw=c[i]/10;//先处理进位 
				c[i]%=10;
			}
			if(jw!=0)c[++c[0]]=jw;//判断是否进位，进位，位数+1，这一位为1 
			string z="";
			for(int i=c[0];i>=1;i--)z=z+(char)(c[i]+48);//倒着放进字符串 
			return z;
		}
		void Plus(){//加法 
			c[0]=max(a[0],b[0]);//c[0]存和的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				c[i]=a[i]+b[i]+jw;
				jw=c[i]/10;//先处理进位 
				c[i]%=10;
			}
			if(jw!=0)c[++c[0]]=jw;//判断是否进位，进位，位数+1，这一位为1 
		}
		void Minus(){//减法 
			c[0]=max(a[0],b[0]);//c[0]存差的位数
			for(int i=a[0]+1;i<=c[0];i++){
				a[i]=0;
			}
			for(int i=b[0]+1;i<=c[0];i++){
				b[i]=0;
			}
			int jw=0;//jw初值0
			for(int i=1;i<=c[0];i++){
				if(a[i]<b[i]){//借位的情况 
					a[i+1]--;
					a[i]+=10;
				}
				c[i]=a[i]-b[i];
			}
			while(c[c[0]]==0)c[0]--;//高位连续0的情况 
		}
		string mobm(string x,char y){
			vector<int> ans;
			string t="";
			int k=(int)y-48,len=x.size();
			for(int i=len-1;i>=0;i--){
				int num=((int)x[i]-48)*k;
				if(ans.size()<len-i)ans.push_back(0);
				ans[len-i-1]+=num%10;
				ans.push_back(0);
				ans[len-i]+=num/10;
			}
			while(ans.size()>1&&ans[ans.size()-1]==0){
				ans.pop_back();
			}
			while(!ans.empty()){
				t+=(char)(ans.back()+48);
				ans.pop_back();
			}
			return t;
		}
		string azate(int len){
			string ans="";
			for(int i=1;i<=len;i++){
				ans+="0";
			}
			return ans;
		}
		string Mul(string x,string y){
			bool flag=false;
			if(x[0]=='-'){
				flag=!flag;
				x.erase(0,1);
			}
			if(y[0]=='-'){
				flag=!flag;
				y.erase(0,1);
			}
			for(int i=0;i<10;i++){
				f[i]="+_-INF";
			}
			f[0]="0",f[1]=y;
			int len=x.size();
			for(int i=len-1;i>=0;i--){
				if(f[(int)x[i]-48]!="+_-INF"){
					k[i]=f[(int)x[i]-48];
					k[i]+=azate(len-i-1);
					continue;
				}
				k[i]=mobm(y,x[i]);
				k[i]+=azate(len-i-1);
			}
			string ans="";
			c[0]=k[len-1].size();
			for(int i=1;i<=c[0];i++){
				c[i]=k[len-1][c[0]-i]-'0';
			}
			for(int i=len-2;i>=0;i--){
				a[0]=c[0];
				for(int j=1;j<=c[0];j++){
					a[j]=c[j];
				}
				b[0]=k[i].size();
				for(int j=1;j<=b[0];j++){
					b[j]=k[i][b[0]-j]-'0';
				}
				Plus();
			}
			for(int i=c[0];i>=1;i--)ans=ans+(char)(c[i]+48);
			ans=(flag==true?"-":"")+ans;
			return ans;
		}
		bool check_size(string x,string y){
			if(x.size()>y.size())return false;
			else if(x.size()<y.size())return true;
			else{
				if(x>y)return false;
				else{
					return true;
				}
			}
		}
		class abnormal:public exception{
			private:
				string message;
			public:
				abnormal(string other){
					message=other;
				}
				const char* what(){
					return message.c_str();
				}
		};
		string Div(string x,string y){
			bool flag=false;
			if(x[0]=='-'){
				flag=!flag;
				x.erase(0,1);
			}
			if(y[0]=='-'){
				flag=!flag;
				y.erase(0,1);
			}
			if(y=="0"){
				abnormal e("Divider cannot be 0.");
				throw e;
				return "NULL";
			}
			else if(!check_size(y,x))return "0";
			string ans="";
			while(1){
				string a=x.substr(0,y.size());
				if(!check_size(y,a))a+=x[y.size()];
				int l=0,r=9;
				string k,k2;
				while(l<r){
					int mid=(l+r+1)/2;
					k=Mul(y,to_string(mid));
					if(check_size(k,a))l=mid;
					else r=mid-1;
				}
				string t=to_string(l);
				ans+=t;
				k=x.substr(a.size(),x.size()-a.size()+1);
				k2=Mul(y,t);
				x=Minus(a,k2);
				if(x=="0")x="";
				int len=x.size();
				x+=k;
				if(k=="")break;
				else if(!check_size(y,x)&&k.size()==1){
					ans+="0";
					break;
				}
				while(len<y.size()-1){
					ans+="0";
					len++;
				}
				while(!check_size(y,x.substr(0,len+1))){
					ans+="0";
					len++;
				}
			}
			ans=(flag==true?"-":"")+ans;
			return ans;
		}
		string Comple(string x,string y){
			string t=Div(x,y);
			string k=Minus(x,Mul(t,y));
			return k;
		}
	}
	class Big_num{
		friend string to_string(Big_num x);
		friend istream& operator>>(istream& is,Big_num& num);
		private:
			string num;
		public: 
			Big_num(){
				num="0";
			}
			Big_num(string other){
				num=other;
			}
			Big_num(const char* other){
				num=other;
			}
			Big_num(int other){
				num=to_string(other);
			}
			Big_num(short other){
				num=to_string((int)other);
			}
			Big_num(long other){
				num=to_string(other);
			}
			Big_num(long long other){
				num=to_string(other);
			}
			Big_num(const Big_num& other){
				num=other.num;
			}
			Big_num& operator=(Big_num other){
				num=other.num;
				return *this;
			}
			Big_num operator+(Big_num other){
				string x=BN::Plus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num& operator+=(Big_num other){
				string x=BN::Plus(num,other.num);
				num=x;
				return *this;
			}
			Big_num operator-(Big_num other){
				string x=BN::Minus(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num& operator-=(Big_num other){
				string x=BN::Minus(num,other.num);
				num=x;
				return *this;
			}
			Big_num operator*(Big_num other){
				string x=BN::Mul(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num& operator*=(Big_num other){
				string x=BN::Mul(num,other.num);
				num=x;
				return *this;
			}
			Big_num operator/(Big_num other){
				string x=BN::Div(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num& operator/=(Big_num other){
				string x=BN::Div(num,other.num);
				num=x;
				return *this;
			}
			Big_num operator%(Big_num other){
				string x=BN::Comple(num,other.num);
				Big_num y=x;
				return y;
			}
			Big_num& operator%=(Big_num other){
				string x=BN::Comple(num,other.num);
				num=x;
				return *this;
			}
			Big_num& operator++(){
				num=BN::Plus(num,"1");
				return *this;
			}
			Big_num operator++(int){
				Big_num old=num;
				num=BN::Plus(num,"1");
				return old;
			}
			bool operator==(Big_num other){
				return num==other.num;
			}
			bool operator!=(Big_num other){
				return num!=other.num;
			}
			bool operator<(Big_num other){
				return !BN::check_size(other.num,num);
			}
			bool operator>(Big_num other){
				return !BN::check_size(num,other.num);
			}
			bool operator<=(Big_num other){
				return BN::check_size(num,other.num);
			}
			bool operator>=(Big_num other){
				return BN::check_size(other.num,num);
			}
	};
	string to_string(Big_num x){
		return x.num;
	}
	Big_num abs(Big_num x){
		string y=to_string(x);
		if(y[0]=='-')y.erase(0,1);
		Big_num z=y;
		return z;
	}
	Big_num fabs(Big_num x){
		return abs(x);
	}
	ostream& operator<<(ostream& os,const Big_num& num){
	    os<<to_string(num);
	    return os;
	}
	istream& operator>>(istream& is,Big_num& num){
		is>>num.num;
		return is;
	}
}
using namespace BIG_NUM;

此为最新代码，第九次更新！

董安雅在2023-05-07 11:23:04追加了内容

因没人关注，停止更新。

Answer 1

已采纳

包思远

资深天翼

1

Answer 2

董安雅

新手光能

1

Answer 3

李奕歌

初级天翼

6

Answer 4

熊智晖

高级天翼

666

Answer 5

董安雅

新手光能

1

Answer 6

王梓轩

资深光能

抄的一手好文章

Answer 7

余彦成

中级守护

怎么回事???

Answer 8

陈泽睿

高级光能

nb

Answer 9

丁炳瑜

高级光能

6

Answer 10

董安雅

新手光能

DING

问题标题: 大整数类型（高精度整数）[九次更新]

10 个回答: