• CCF NOI1140 高精度乘法


    问题链接CCF NOI1140 高精度乘法


    时间限制: 1000 ms  空间限制: 262144 KB

    题目描述 

      给两个正整数a和b,计算它们的积。

    输入

      两行,每行一个数分别表示a和b(位数达1000位)。

    输出

      输出它们的积。

    样例输入

    2

    1

    样例输出

    2

    数据范围限制

      2




    问题分析

      有了一个大数计算类(借用来的),大数计算就不是问题了。

    程序说明

      有了大数计算类,实际需要编写的代码就很少了。

    要点详解

    • 类可以封装很多东西,比如大数类



    参考链接

    B00008 C++实现的大整数计算(一)

    100分通过的C++程序:

    #include <iostream>
    #include <string>
    #include <sstream>
    #include <cmath>
    
    using namespace std;
    
    /*
     * @author panks
     * Big Integer library in C++, single file implementation.
     */
    
    #define MAX 10000 // for strings
    
    using namespace std;
    class BigInteger {
    private:
        string number;
        bool sign;
    public:
        BigInteger(); // empty constructor initializes zero
        BigInteger(string s); // "string" constructor
        BigInteger(string s, bool sin); // "string" constructor
        BigInteger(int n); // "int" constructor
        void setNumber(string s);
        const string& getNumber(); // retrieves the number
        void setSign(bool s);
        const bool& getSign();
        BigInteger absolute(); // returns the absolute value
        void operator = (BigInteger b);
        bool operator == (BigInteger b);
        bool operator != (BigInteger b);
        bool operator > (BigInteger b);
        bool operator < (BigInteger b);
        bool operator >= (BigInteger b);
        bool operator <= (BigInteger b);
        BigInteger& operator ++(); // prefix
        BigInteger  operator ++(int); // postfix
        BigInteger& operator --(); // prefix
        BigInteger  operator --(int); // postfix
        BigInteger operator + (BigInteger b);
        BigInteger operator - (BigInteger b);
        BigInteger operator * (BigInteger b);
        BigInteger operator / (BigInteger b);
        BigInteger operator % (BigInteger b);
        BigInteger& operator += (BigInteger b);
        BigInteger& operator -= (BigInteger b);
        BigInteger& operator *= (BigInteger b);
        BigInteger& operator /= (BigInteger b);
        BigInteger& operator %= (BigInteger b);
        BigInteger& operator [] (int n);
        BigInteger operator -(); // unary minus sign
        operator string(); // for conversion from BigInteger to string
    private:
        bool equals(BigInteger n1, BigInteger n2);
        bool less(BigInteger n1, BigInteger n2);
        bool greater(BigInteger n1, BigInteger n2);
        string add(string number1, string number2);
        string subtract(string number1, string number2);
        string multiply(string n1, string n2);
        pair<string, long long> divide(string n, long long den);
        string toString(long long n);
        long long toInt(string s);
    };
    
    //------------------------------------------------------------------------------
    
    BigInteger::BigInteger() { // empty constructor initializes zero
        number = "0";
        sign = false;
    }
    
    BigInteger::BigInteger(string s) { // "string" constructor
        if( isdigit(s[0]) ) { // if not signed
            setNumber(s);
            sign = false; // +ve
        } else {
            setNumber( s.substr(1) );
            sign = (s[0] == '-');
        }
    }
    
    BigInteger::BigInteger(string s, bool sin) { // "string" constructor
        setNumber( s );
        setSign( sin );
    }
    
    BigInteger::BigInteger(int n) { // "int" constructor
        stringstream ss;
        string s;
        ss << n;
        ss >> s;
    
    
        if( isdigit(s[0]) ) { // if not signed
            setNumber( s );
            setSign( false ); // +ve
        } else {
            setNumber( s.substr(1) );
            setSign( s[0] == '-' );
        }
    }
    
    void BigInteger::setNumber(string s) {
        number = s;
    }
    
    const string& BigInteger::getNumber() { // retrieves the number
        return number;
    }
    
    void BigInteger::setSign(bool s) {
        sign = s;
    }
    
    const bool& BigInteger::getSign() {
        return sign;
    }
    
    BigInteger BigInteger::absolute() {
        return BigInteger( getNumber() ); // +ve by default
    }
    
    void BigInteger::operator = (BigInteger b) {
        setNumber( b.getNumber() );
        setSign( b.getSign() );
    }
    
    bool BigInteger::operator == (BigInteger b) {
        return equals((*this) , b);
    }
    
    bool BigInteger::operator != (BigInteger b) {
        return ! equals((*this) , b);
    }
    
    bool BigInteger::operator > (BigInteger b) {
        return greater((*this) , b);
    }
    
    bool BigInteger::operator < (BigInteger b) {
        return less((*this) , b);
    }
    
    bool BigInteger::operator >= (BigInteger b) {
        return equals((*this) , b)
               || greater((*this), b);
    }
    
    bool BigInteger::operator <= (BigInteger b) {
        return equals((*this) , b)
               || less((*this) , b);
    }
    
    BigInteger& BigInteger::operator ++() { // prefix
        (*this) = (*this) + 1;
        return (*this);
    }
    
    BigInteger BigInteger::operator ++(int) { // postfix
        BigInteger before = (*this);
    
        (*this) = (*this) + 1;
    
        return before;
    }
    
    BigInteger& BigInteger::operator --() { // prefix
        (*this) = (*this) - 1;
        return (*this);
    
    }
    
    BigInteger BigInteger::operator --(int) { // postfix
        BigInteger before = (*this);
    
        (*this) = (*this) - 1;
    
        return before;
    }
    
    BigInteger BigInteger::operator + (BigInteger b) {
        BigInteger addition;
        if( getSign() == b.getSign() ) { // both +ve or -ve
            addition.setNumber( add(getNumber(), b.getNumber() ) );
            addition.setSign( getSign() );
        } else { // sign different
            if( absolute() > b.absolute() ) {
                addition.setNumber( subtract(getNumber(), b.getNumber() ) );
                addition.setSign( getSign() );
            } else {
                addition.setNumber( subtract(b.getNumber(), getNumber() ) );
                addition.setSign( b.getSign() );
            }
        }
        if(addition.getNumber() == "0") // avoid (-0) problem
            addition.setSign(false);
    
        return addition;
    }
    
    BigInteger BigInteger::operator - (BigInteger b) {
        b.setSign( ! b.getSign() ); // x - y = x + (-y)
        return (*this) + b;
    }
    
    BigInteger BigInteger::operator * (BigInteger b) {
        BigInteger mul;
    
        mul.setNumber( multiply(getNumber(), b.getNumber() ) );
        mul.setSign( getSign() != b.getSign() );
    
        if(mul.getNumber() == "0") // avoid (-0) problem
            mul.setSign(false);
    
        return mul;
    }
    
    // Warning: Denomerator must be within "long long" size not "BigInteger"
    BigInteger BigInteger::operator / (BigInteger b) {
        long long den = toInt( b.getNumber() );
        BigInteger div;
    
        div.setNumber( divide(getNumber(), den).first );
        div.setSign( getSign() != b.getSign() );
    
        if(div.getNumber() == "0") // avoid (-0) problem
            div.setSign(false);
    
        return div;
    }
    
    // Warning: Denomerator must be within "long long" size not "BigInteger"
    BigInteger BigInteger::operator % (BigInteger b) {
        long long den = toInt( b.getNumber() );
    
        BigInteger rem;
        long long rem_int = divide(number, den).second;
        rem.setNumber( toString(rem_int) );
        rem.setSign( getSign() != b.getSign() );
    
        if(rem.getNumber() == "0") // avoid (-0) problem
            rem.setSign(false);
    
        return rem;
    }
    
    BigInteger& BigInteger::operator += (BigInteger b) {
        (*this) = (*this) + b;
        return (*this);
    }
    
    BigInteger& BigInteger::operator -= (BigInteger b) {
        (*this) = (*this) - b;
        return (*this);
    }
    
    BigInteger& BigInteger::operator *= (BigInteger b) {
        (*this) = (*this) * b;
        return (*this);
    }
    
    BigInteger& BigInteger::operator /= (BigInteger b) {
        (*this) = (*this) / b;
        return (*this);
    }
    
    BigInteger& BigInteger::operator %= (BigInteger b) {
        (*this) = (*this) % b;
        return (*this);
    }
    
    BigInteger& BigInteger::operator [] (int n) {
        return *(this + (n*sizeof(BigInteger)));
    }
    
    BigInteger BigInteger::operator -() { // unary minus sign
        return (*this) * -1;
    }
    
    BigInteger::operator string() { // for conversion from BigInteger to string
        string signedString = ( getSign() ) ? "-" : ""; // if +ve, don't print + sign
        signedString += number;
        return signedString;
    }
    
    bool BigInteger::equals(BigInteger n1, BigInteger n2) {
        return n1.getNumber() == n2.getNumber()
               && n1.getSign() == n2.getSign();
    }
    
    bool BigInteger::less(BigInteger n1, BigInteger n2) {
        bool sign1 = n1.getSign();
        bool sign2 = n2.getSign();
    
        if(sign1 && ! sign2) // if n1 is -ve and n2 is +ve
            return true;
    
        else if(! sign1 && sign2)
            return false;
    
        else if(! sign1) { // both +ve
            if(n1.getNumber().length() < n2.getNumber().length() )
                return true;
            if(n1.getNumber().length() > n2.getNumber().length() )
                return false;
            return n1.getNumber() < n2.getNumber();
        } else { // both -ve
            if(n1.getNumber().length() > n2.getNumber().length())
                return true;
            if(n1.getNumber().length() < n2.getNumber().length())
                return false;
            return n1.getNumber().compare( n2.getNumber() ) > 0; // greater with -ve sign is LESS
        }
    }
    
    bool BigInteger::greater(BigInteger n1, BigInteger n2) {
        return ! equals(n1, n2) && ! less(n1, n2);
    }
    
    string BigInteger::add(string number1, string number2) {
        string add = (number1.length() > number2.length()) ?  number1 : number2;
        char carry = '0';
        int differenceInLength = abs( (int) (number1.size() - number2.size()) );
    
        if(number1.size() > number2.size())
            number2.insert(0, differenceInLength, '0'); // put zeros from left
    
        else// if(number1.size() < number2.size())
            number1.insert(0, differenceInLength, '0');
    
        for(int i=number1.size()-1; i>=0; --i) {
            add[i] = ((carry-'0')+(number1[i]-'0')+(number2[i]-'0')) + '0';
    
            if(i != 0) {
                if(add[i] > '9') {
                    add[i] -= 10;
                    carry = '1';
                } else
                    carry = '0';
            }
        }
        if(add[0] > '9') {
            add[0]-= 10;
            add.insert(0,1,'1');
        }
        return add;
    }
    
    string BigInteger::subtract(string number1, string number2) {
        string sub = (number1.length()>number2.length())? number1 : number2;
        int differenceInLength = abs( (int)(number1.size() - number2.size()) );
    
        if(number1.size() > number2.size())
            number2.insert(0, differenceInLength, '0');
    
        else
            number1.insert(0, differenceInLength, '0');
    
        for(int i=number1.length()-1; i>=0; --i) {
            if(number1[i] < number2[i]) {
                number1[i] += 10;
                number1[i-1]--;
            }
            sub[i] = ((number1[i]-'0')-(number2[i]-'0')) + '0';
        }
    
        while(sub[0]=='0' && sub.length()!=1) // erase leading zeros
            sub.erase(0,1);
    
        return sub;
    }
    
    string BigInteger::multiply(string n1, string n2) {
        if(n1.length() > n2.length())
            n1.swap(n2);
    
        string res = "0";
        for(int i=n1.length()-1; i>=0; --i) {
            string temp = n2;
            int currentDigit = n1[i]-'0';
            int carry = 0;
    
            for(int j=temp.length()-1; j>=0; --j) {
                temp[j] = ((temp[j]-'0') * currentDigit) + carry;
    
                if(temp[j] > 9) {
                    carry = (temp[j]/10);
                    temp[j] -= (carry*10);
                } else
                    carry = 0;
    
                temp[j] += '0'; // back to string mood
            }
    
            if(carry > 0)
                temp.insert(0, 1, (carry+'0'));
    
            temp.append((n1.length()-i-1), '0'); // as like mult by 10, 100, 1000, 10000 and so on
    
            res = add(res, temp); // O(n)
        }
    
        while(res[0] == '0' && res.length()!=1) // erase leading zeros
            res.erase(0,1);
    
        return res;
    }
    
    pair<string, long long> BigInteger::divide(string n, long long den) {
        long long rem = 0;
        string result;
        result.resize(MAX);
    
        for(int indx=0, len = n.length(); indx<len; ++indx) {
            rem = (rem * 10) + (n[indx] - '0');
            result[indx] = rem / den + '0';
            rem %= den;
        }
        result.resize( n.length() );
    
        while( result[0] == '0' && result.length() != 1)
            result.erase(0,1);
    
        if(result.length() == 0)
            result = "0";
    
        return make_pair(result, rem);
    }
    
    string BigInteger::toString(long long n) {
        stringstream ss;
        string temp;
    
        ss << n;
        ss >> temp;
    
        return temp;
    }
    
    long long BigInteger::toInt(string s) {
        long long sum = 0;
    
        for(int i=0; i<(int)s.length(); i++)
            sum = (sum*10) + (s[i] - '0');
    
        return sum;
    }
    
    int main()
    {
        string sa, sb;
    
        cin >> sa >> sb;
    
        BigInteger a(sa), b(sb), c;
        c = a * b;
    
        cout << c.getNumber() << endl;
    
        return 0;
    }


     

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  • 原文地址:https://www.cnblogs.com/tigerisland/p/7563797.html
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