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 = 100000000;
    static const int WIDTH = 8;
    vector<int> s;

    int len;
    BigInteger(ll num = 0)  {
        *this = num;
    }
    BigInteger operator = (ll num)
    {
        s.clear();
        do
        {
            s.push_back(num%BASE);
            num /= BASE;
        }
        while(num > 0);
        return *this;
    }
    BigInteger operator = (const string& num)
    {
        s.clear();
        int x, len = (num.length() - 1) / WIDTH + 1;//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 = 0; i < len; i++)
        {
            int end = num.length() - i*WIDTH;
            int start = max(0, 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 = 0, g = 0; ; ++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()-1; i >= 0; 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()-2;i>=0;i--)
    {
        char buf[20];
        sprintf(buf,"%08d",x.s[i]);
        for(int j=0;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 2001

BigInteger f[maxn];
BigInteger ans[maxn];
const int c[]={6,2,5,5,4,5,6,3,7,6};
int n;

void init()
{
    for (int i = 0; i <= maxn; i++)
        f[i] = 0;
    f[0] = 1;
    for(int i = 0; i <= maxn; i++)
    {
        for(int j = 0; j <= 9; j++)
        {
            if(i+c[j] < maxn && !(i==0 && j==0))
            {
                f[i+c[j]] += f[i];
            }
        }
    }
    ans[0]=0;
    for (int i = 1; i <= maxn; i++)
    {
        ans[i] = ans[i-1] + f[i];
    }
}
int main()
{
    //freopen("out.txt", "w", stdout);
    init();
    while (cin >> n)
    {
        if (n >= 6)
            cout << ans[n]+1 << endl;
        else
            cout << ans[n] << endl;
    }
    return 0;
}

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(0);
 const BigInteger BigInteger::ONE =BigInteger(1);
 const BigInteger BigInteger::TEN =BigInteger(10);


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


BigInteger::BigInteger(int val){// construct with a int integer
    if (val >= 0)
        sign = true;
    else{
        sign = false;
        val *= (-1);
    }
    do{
        digits.push_back( (char)(val%10) );
        val /= 10;
    } while ( val != 0 );
}


BigInteger::BigInteger(string& def){
    sign=true;
    for ( string::reverse_iterator iter = def.rbegin() ; iter < def.rend();  iter++){
        char ch = (*iter);
        if (iter == def.rend()-1){
            if ( ch == '+' )
                break;
            if(ch == '-' ){
                sign = false;
                break;
            }
        }
        digits.push_back( (char)((*iter) - '0' ) );
    }
    trim();
}

void BigInteger::trim(){
    vector<char>::reverse_iterator iter = digits.rbegin();
    while(!digits.empty() && (*iter) == 0){
        digits.pop_back();
        iter=digits.rbegin();
    }
    if( digits.size()==0 ){
        sign = true;
        digits.push_back(0);
    }
}


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(1);
    for(int i=0; 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 = 0;        //进位
        while ( iter1 != op1.digits.end() && iter2 != op2.digits.end()){
            (*iter1) = (*iter1) + (*iter2) + to_add;
            to_add = ((*iter1) > 9);    // 大于9进一位
            (*iter1) = (*iter1) % 10;
            iter1++; iter2++;
        }
        while ( iter1 != op1.digits.end() ){   //
            (*iter1) = (*iter1) + to_add;
            to_add = ( (*iter1) > 9 );
            (*iter1) %= 10;
            iter1++;
        }
        while ( iter2 != op2.digits.end() ){
            char val = (*iter2) + to_add;
            to_add = (val > 9) ;
            val %= 10;
            op1.digits.push_back(val);
            iter2++;
        }
        if( to_add != 0 )
            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 = 0;  //借位

        while ( iter1 != op1.digits.end() && iter2 != op2.digits.end()){
            (*iter1) = (*iter1) - (*iter2) - to_substract;
            to_substract = 0;
            if( (*iter1) < 0 ){
                to_substract=1;
                (*iter1) += 10;
            }
            iter1++;
            iter2++;
        }
        while ( iter1 != op1.digits.end() ){
            (*iter1) = (*iter1) - to_substract;
            to_substract = 0;
            if( (*iter1) < 0 ){
                to_substract=1;
                (*iter1) += 10;
            }
            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(0);
    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 != 0){
                deque<char> temp(op1.digits.begin() , op1.digits.end());
                char to_add = 0;
                deque<char>::iterator iter1 = temp.begin();
                while( iter1 != temp.end() ){
                    (*iter1) *= (*iter2);
                    (*iter1) += to_add;
                    to_add = (*iter1) / 10;
                    (*iter1) %= 10;
                    iter1++;
                }
                if( to_add != 0)
                    temp.push_back( to_add );
                int num_of_zeros = iter2 - op2.digits.begin();
                while(  num_of_zeros--)
                    temp.push_front(0);
                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(0);
    while( iter != t1.digits.rend() ){
        temp2 = temp2 * BigInteger::TEN + BigInteger( (int)(*iter) );
        char s = 0;
        while( temp2 >= t2 ){
            temp2 = temp2 - t2;
            s = s + 1;
        }
        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) + '0');
    return stream;
}

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

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