BigInteger

首先上模板（不断更新中...）（根据刘汝佳AOAPCII修改）

 #include <iostream>
 #include <sstream>
 #include <cstdio>
 #include <cstring>
 #include <cmath>
 #include <string>
 #include <vector>
 #include <set>
 #include <cctype>
 #include <algorithm>
 #include <cmath>
 #include <deque>
 #include <queue>
 #include <map>
 #include <stack>
 #include <list>
 #include <iomanip>
 using namespace std;
 ///
 #define lc o << 1
 #define rc o << 1 | 1
 #define lson L , M , o << 1
 #define rson M + 1 , R , o << 1 | 1
 #define PI acos(-1.0)
 #define INF 0x7fffffff
 #define esp 1e-6
 #define maxn 2001

 typedef long long ll;
 ///
 struct BigInteger
 {
     //初始化.
     static const int BASE = ;
     static const int WIDTH = ;
     vector<int> s;

     int len;
     BigInteger(ll num = )  {
         *this = num;
     }
     BigInteger operator = (ll num)
     {
         s.clear();
         do
         {
             s.push_back(num%BASE);
             num /= BASE;
         }
         while(num > );
         return *this;
     }
     BigInteger operator = (const string& num)
     {
         s.clear();
         int x, len = (num.length() - ) / WIDTH + ;//这里就是把一个“1221434 125432 52526266”这样的大数转换成3个8位int型存入s中

         for(int i = ; i < len; i++)
         {
             int end = num.length() - i*WIDTH;
             int start = max(, end-WIDTH);
             sscanf(num.substr(start, end-start).c_str(), "%d", &x);
             s.push_back(x);
         }
         return *this;
     }

     //加减乘除
     BigInteger operator + (const BigInteger &b) const
     {
         BigInteger c;
         c.s.clear();
         for(int i = , g = ; ; ++i)
         {
             if(!g && i >= s.size() && i >= b.s.size())  break;
             int x = g;
             if(i < s.size())    x += s[i];
             if(i < b.s.size())  x += b.s[i];

             c.s.push_back(x % BASE);
             g = x / BASE;
         }
         return c;
     }

     BigInteger operator += (const BigInteger &b)
     {
         *this = *this + b;
         return *this;
     }

     //注意前提：两个数都没有前导零
     bool operator < (const BigInteger& b) const
     {
         if(!s.size() != b.s.size())
             return s.size() < b.s.size();
         for(int i = s.size()-; i >= ; i--)
             if(s[i] != b.s[i])
                 return s[i] < b.s[i];
         return false;//相等
     }
     bool operator > (const BigInteger& b) const
     {
         return b < *this;
     }
     bool operator <= (const BigInteger& b) const
     {
         return !(b < *this);
     }
     bool operator >= (const BigInteger& b) const
     {
         return !(*this < b);
     }
     bool operator != (const BigInteger& b) const
     {
         return (b < *this) || (*this < b);
     }
     bool operator == (const BigInteger& b) const
     {
         return !(b < *this) && !(*this < b);
     }
 };

 istream & operator >> (istream &in, BigInteger &x)
 {
     string s;
     in >> s;
     x = s.c_str();
     return in;
 }

 ostream & operator << (ostream &out, const BigInteger &x)
 {
     out << x.s.back();
     for(int i=x.s.size()-;i>=;i--)
     {
         char buf[];
         sprintf(buf,"%08d",x.s[i]);
         for(int j=;j<strlen(buf);j++) out<<buf[j];
     }
     return out;
 }

例题：UVA 11375 Matches(高精度 + 递推)

代码如下

 tupedef maxn 

 BigInteger f[maxn];
 BigInteger ans[maxn];
 const int c[]={,,,,,,,,,};
 int n;

 void init()
 {
     for (int i = ; i <= maxn; i++)
         f[i] = ;
     f[] = ;
     for(int i = ; i <= maxn; i++)
     {
         for(int j = ; j <= ; j++)
         {
             if(i+c[j] < maxn && !(i== && j==))
             {
                 f[i+c[j]] += f[i];
             }
         }
     }
     ans[]=;
     for (int i = ; i <= maxn; i++)
     {
         ans[i] = ans[i-] + f[i];
     }
 }
 int main()
 {
     //freopen("out.txt", "w", stdout);
     init();
     while (cin >> n)
     {
         if (n >= )
             cout << ans[n]+ << endl;
         else
             cout << ans[n] << endl;
     }
     return ;
 }

超强模板（网络转载）

#include <deque>
#include <vector>
#include <iostream>
#include <string>
#include <algorithm>
using namespace std;

class DividedByZeroException {};

class BigInteger
{
    private:
        vector<char> digits;
        bool sign;          //  true for positive, false for negitive
        void trim();        //  remove zeros in tail, but if the value is 0, keep only one:)
    public:
        BigInteger(int);    // construct with a int integer
        BigInteger(string&) ;
        BigInteger();
        BigInteger (const BigInteger&);
        BigInteger operator=(const BigInteger& op2);

        BigInteger    abs() const;
        BigInteger    pow(int a);

        //binary operators

        friend BigInteger operator+=(BigInteger&,const BigInteger&);
        friend BigInteger operator-=(BigInteger&,const BigInteger&);
        friend BigInteger operator*=(BigInteger&,const BigInteger&);
        friend BigInteger operator/=(BigInteger&,const BigInteger&) throw(DividedByZeroException);
        friend BigInteger operator%=(BigInteger&,const BigInteger&) throw(DividedByZeroException);

        friend BigInteger operator+(const BigInteger&,const BigInteger&);
        friend BigInteger operator-(const BigInteger&,const BigInteger&);
        friend BigInteger operator*(const BigInteger&,const BigInteger&);
        friend BigInteger operator/(const BigInteger&,const BigInteger&) throw(DividedByZeroException);
        friend BigInteger operator%(const BigInteger&,const BigInteger&) throw(DividedByZeroException);

        //uniary operators
        friend BigInteger operator-(const BigInteger&);   //negative

        friend BigInteger operator++(BigInteger&);        //++v
        friend BigInteger operator++(BigInteger&,int);    //v++
        friend BigInteger operator--(BigInteger&);        //--v
        friend BigInteger operator--(BigInteger&,int);    //v--

        friend bool operator>(const BigInteger&,const BigInteger&);
        friend bool operator<(const BigInteger&,const BigInteger&);
        friend bool operator==(const BigInteger&,const BigInteger&);
        friend bool operator!=(const BigInteger&,const BigInteger&);
        friend bool operator>=(const BigInteger&,const BigInteger&);
        friend bool operator<=(const BigInteger&,const BigInteger&);

        friend ostream& operator<<(ostream&,const BigInteger&);    //print the BigInteger
        friend istream& operator>>(istream&, BigInteger&);         // input the BigInteger

public:
        static const BigInteger ZERO;
        static const BigInteger ONE;
        static const BigInteger TEN;
};
// BigInteger.cpp

 const BigInteger BigInteger::ZERO=BigInteger();
 const BigInteger BigInteger::ONE =BigInteger();
 const BigInteger BigInteger::TEN =BigInteger();

BigInteger::BigInteger()
{
    sign=true;
}

BigInteger::BigInteger(int val){// construct with a int integer
    if (val >= )
        sign = true;
    else{
        sign = false;
        val *= (-);
    }
    do{
        digits.push_back( (char)(val%) );
        val /= ;
    } while ( val !=  );
}

BigInteger::BigInteger(string& def){
    sign=true;
    for ( string::reverse_iterator iter = def.rbegin() ; iter < def.rend();  iter++){
        char ch = (*iter);
        if (iter == def.rend()-){
            if ( ch == '+' )
                break;
            if(ch == '-' ){
                sign = false;
                break;
            }
        }
        digits.push_back( (char)((*iter) - '' ) );
    }
    trim();
}

void BigInteger::trim(){
    vector<char>::reverse_iterator iter = digits.rbegin();
    while(!digits.empty() && (*iter) == ){
        digits.pop_back();
        iter=digits.rbegin();
    }
    if( digits.size()== ){
        sign = true;
        digits.push_back();
    }
}

BigInteger::BigInteger(const BigInteger& op2){
    sign = op2.sign;
    digits=op2.digits;
}

BigInteger BigInteger::operator=(const BigInteger& op2){
            digits = op2.digits;
            sign = op2.sign;
            return (*this);
 }

BigInteger BigInteger::abs() const {
    if(sign)  return *this;
    else      return -(*this);
}

BigInteger BigInteger::pow(int a)
{
    BigInteger res();
    for(int i=; i<a; i++)
        res*=(*this);
    return res;
}

//binary operators
BigInteger operator+=(BigInteger& op1,const BigInteger& op2){
    if( op1.sign == op2.sign ){     //只处理相同的符号的情况，异号的情况给-处理
        vector<char>::iterator iter1;
        vector<char>::const_iterator iter2;
        iter1 = op1.digits.begin();
        iter2 = op2.digits.begin();
        char to_add = ;        //进位
        while ( iter1 != op1.digits.end() && iter2 != op2.digits.end()){
            (*iter1) = (*iter1) + (*iter2) + to_add;
            to_add = ((*iter1) > );    // 大于9进一位
            (*iter1) = (*iter1) % ;
            iter1++; iter2++;
        }
        while ( iter1 != op1.digits.end() ){   //
            (*iter1) = (*iter1) + to_add;
            to_add = ( (*iter1) >  );
            (*iter1) %= ;
            iter1++;
        }
        while ( iter2 != op2.digits.end() ){
            char val = (*iter2) + to_add;
            to_add = (val > ) ;
            val %= ;
            op1.digits.push_back(val);
            iter2++;
        }
        if( to_add !=  )
            op1.digits.push_back(to_add);
        return op1;
    }
    else{
        if (op1.sign)
            return op1 -= (-op2);
        else
            return op1= op2 - (-op1);
    }

}

BigInteger operator-=(BigInteger& op1,const BigInteger& op2){
    if( op1.sign == op2.sign ){     //只处理相同的符号的情况，异号的情况给+处理
        if(op1.sign) {
            if(op1 < op2)  // 2 - 3
                return  op1=-(op2 - op1);
        }
        else {
            if(-op1 > -op2)  // (-3)-(-2) = -(3 - 2)
                return op1=-((-op1)-(-op2));
            else             // (-2)-(-3) = 3 - 2
                return op1= (-op2) - (-op1);
        }
        vector<char>::iterator iter1;
        vector<char>::const_iterator iter2;
        iter1 = op1.digits.begin();
        iter2 = op2.digits.begin();

        char to_substract = ;  //借位

        while ( iter1 != op1.digits.end() && iter2 != op2.digits.end()){
            (*iter1) = (*iter1) - (*iter2) - to_substract;
            to_substract = ;
            if( (*iter1) <  ){
                to_substract=;
                (*iter1) += ;
            }
            iter1++;
            iter2++;
        }
        while ( iter1 != op1.digits.end() ){
            (*iter1) = (*iter1) - to_substract;
            to_substract = ;
            if( (*iter1) <  ){
                to_substract=;
                (*iter1) += ;
            }
            else break;
            iter1++;
        }
        op1.trim();
        return op1;
    }
    else{
        if (op1 > BigInteger::ZERO)
            return op1 += (-op2);
        else
            return op1 = -(op2 + (-op1));
    }
}
BigInteger operator*=(BigInteger& op1,const BigInteger& op2){
    BigInteger result();
    if (op1 == BigInteger::ZERO || op2==BigInteger::ZERO)
        result = BigInteger::ZERO;
    else{
        vector<char>::const_iterator iter2 = op2.digits.begin();
        while( iter2 != op2.digits.end() ){
            if(*iter2 != ){
                deque<char> temp(op1.digits.begin() , op1.digits.end());
                char to_add = ;
                deque<char>::iterator iter1 = temp.begin();
                while( iter1 != temp.end() ){
                    (*iter1) *= (*iter2);
                    (*iter1) += to_add;
                    to_add = (*iter1) / ;
                    (*iter1) %= ;
                    iter1++;
                }
                if( to_add != )
                    temp.push_back( to_add );
                int num_of_zeros = iter2 - op2.digits.begin();
                while(  num_of_zeros--)
                    temp.push_front();
                BigInteger temp2;
                temp2.digits.insert( temp2.digits.end() , temp.begin() , temp.end() );
                temp2.trim();
                result = result + temp2;
            }
            iter2++;
        }
        result.sign = ( (op1.sign && op2.sign) || (!op1.sign && !op2.sign) );
    }
    op1 = result;
    return op1;
}

BigInteger operator/=(BigInteger& op1 , const BigInteger& op2 ) throw(DividedByZeroException) {
    if( op2 == BigInteger::ZERO )
        throw DividedByZeroException();
    BigInteger t1 = op1.abs(), t2 = op2.abs();
    if ( t1 < t2 ){
        op1 = BigInteger::ZERO;
        return op1;
    }
    //现在 t1 > t2 > 0
    //只需将 t1/t2的结果交给result就可以了
    deque<char> temp;
    vector<char>::reverse_iterator iter = t1.digits.rbegin();

    BigInteger temp2();
    while( iter != t1.digits.rend() ){
        temp2 = temp2 * BigInteger::TEN + BigInteger( (int)(*iter) );
        char s = ;
        while( temp2 >= t2 ){
            temp2 = temp2 - t2;
            s = s + ;
        }
        temp.push_front( s );
        iter++;
    }
    op1.digits.clear();
    op1.digits.insert( op1.digits.end() , temp.begin() , temp.end() );
    op1.trim();
    op1.sign = ( (op1.sign && op2.sign) || (!op1.sign && !op2.sign) );
    return op1;
}

BigInteger operator%=(BigInteger& op1,const BigInteger& op2) throw(DividedByZeroException) {
    return op1 -= ((op1 / op2)*op2);
}

BigInteger operator+(const BigInteger& op1,const BigInteger& op2){
    BigInteger temp(op1);
    temp += op2;
    return temp;
}
BigInteger operator-(const BigInteger& op1,const BigInteger& op2){
    BigInteger temp(op1);
    temp -= op2;
    return temp;
}

BigInteger operator*(const BigInteger& op1,const BigInteger& op2){
    BigInteger temp(op1);
    temp *= op2;
    return temp;

}

BigInteger operator/(const BigInteger& op1,const BigInteger& op2) throw(DividedByZeroException) {
    BigInteger temp(op1);
    temp /= op2;
    return temp;
}

BigInteger operator%(const BigInteger& op1,const BigInteger& op2) throw(DividedByZeroException) {
    BigInteger temp(op1);
    temp %= op2;
    return temp;
}

//uniary operators
BigInteger operator-(const BigInteger& op){   //negative
    BigInteger temp = BigInteger(op);
    temp.sign = !temp.sign;
    return temp;
}

BigInteger operator++(BigInteger& op){    //++v
    op += BigInteger::ONE;
    return op;
}

BigInteger operator++(BigInteger& op,int x){  //v++
    BigInteger temp(op);
    ++op;
    return temp;
}

BigInteger operator--(BigInteger& op){    //--v
    op -=  BigInteger::ONE;
    return op;
}

BigInteger operator--(BigInteger& op,int x){  //v--
    BigInteger temp(op);
    --op;
    return temp;
}

bool operator<(const BigInteger& op1,const BigInteger& op2){
    if( op1.sign != op2.sign )
        return !op1.sign;
    else{
        if(op1.digits.size() != op2.digits.size())
            return (op1.sign && op1.digits.size()<op2.digits.size())
                       || (!op1.sign && op1.digits.size()>op2.digits.size());
        vector<char>::const_reverse_iterator iter1,iter2;
        iter1 = op1.digits.rbegin();iter2 = op2.digits.rbegin();
        while( iter1 != op1.digits.rend() ){
            if(  op1.sign &&  *iter1 < *iter2 ) return true;
            if(  op1.sign &&  *iter1 > *iter2 ) return false;
            if( !op1.sign &&  *iter1 > *iter2 ) return true;
            if( !op1.sign &&  *iter1 < *iter2 ) return false;
            iter1++;
            iter2++;
        }
        return false;
    }
}
bool operator==(const BigInteger& op1,const BigInteger& op2){
    if( op1.sign != op2.sign  || op1.digits.size() != op2.digits.size() )
        return false;
    vector<char>::const_iterator iter1,iter2;
    iter1 = op1.digits.begin();
    iter2 = op2.digits.begin();
    while( iter1!= op1.digits.end() ){
        if( *iter1 != *iter2 )  return false;
        iter1++;
        iter2++;
    }
    return true;
}

bool operator!=(const BigInteger& op1,const BigInteger& op2){
    return !(op1==op2);
}

bool operator>=(const BigInteger& op1,const BigInteger& op2){
    return (op1>op2) || (op1==op2);
}

bool operator<=(const BigInteger& op1,const BigInteger& op2){
    return (op1<op2) || (op1==op2);
}

bool operator>(const BigInteger& op1,const BigInteger& op2){
    return !(op1<=op2);
}

ostream& operator<<(ostream& stream,const BigInteger& val){    //print the BigInteger
    if (!val.sign)
        stream << "-";
    for ( vector<char>::const_reverse_iterator iter = val.digits.rbegin(); iter != val.digits.rend() ; iter++)
        stream << (char)((*iter) + '');
    return stream;
}

istream& operator>>(istream& stream, BigInteger& val){    //Input the BigInteger
    string str;
    stream >> str;
    val=BigInteger(str);
    return stream;
}

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