POJ2389 Bull Math【大数】

Bull Math

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 15040		Accepted: 7737

Description

Bulls are so much better at math than the cows. They can multiply huge integers together and get perfectly precise answers ... or so they say. Farmer John wonders if their answers are correct. Help him check the bulls' answers. Read in two positive integers (no more than 40 digits each) and compute their product. Output it as a normal number (with no extra leading zeros).

FJ asks that you do this yourself; don't use a special library function for the multiplication.

Input

* Lines 1..2: Each line contains a single decimal number.

Output

* Line 1: The exact product of the two input lines

Sample Input

11111111111111
1111111111

Sample Output

12345679011110987654321

Source

USACO 2004 November

USACO 2004 November

问题链接：POJ2389 Bull Math。

问题简述：输入两个正整数，它们不超过40位，计算它们的乘积。

问题分析：这是一个大整数计算问题，可以用一个大整数类来实现。

程序说明：编译的时候需要使用G++编译器。求整数绝对值的函数abs()需要用C语言库stdlib.h中的函数，否则会出问题。该问题只用到了乘法运算，为了代码的简洁，可以将不需要的代码删除。这里使用了一个完整的大整数运算类，也可以用于其他地方。

参考链接：B00008 C++实现的大整数计算（一）。

AC的C++语言程序如下：

/* POJ2389 Bull Math */

#include <iostream>
#include <string>
#include <sstream>
#include <cstdlib>

#define MAX 100 // 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 a, b;
    BigInteger bia, bib, bic;

    while(cin >> a >> b) {
        bia.setNumber(a);
        bib.setNumber(b);

        bic = bia * bib;

        cout << bic.getNumber() << endl;
    }


    return 0;
}