大整数类

#include <iostream>
#include <string>
#include <iomanip>
#include <algorithm>
#include <cstring>
using namespace std;
#define MAXN 9999 // 大数类里面的数组中每个单元的最大正整数
#define MAXSIZE 10
#define DLEN 4 // 对应于MAXN的大小
#define MAX_LEN 500
class BigNum{
public:
    int a[MAX_LEN];    //可以控制大数的位数
    int len;       //大数长度
public:
    BigNum(){len = 1; memset(a,0,sizeof(a));} //构造函数
    BigNum(const int);   //将一个int类型的变量转化为大数
    BigNum(const char*); //将一个字符串类型的变量转化为大数
    BigNum(const BigNum&);  //拷贝构造函数
    BigNum &operator =(const BigNum&);//重载赋值运算符，大数之间进行赋值运算

    friend istream& operator >>(istream&,BigNum&);//重载输入运算符
    friend ostream& operator <<(ostream&,BigNum&);//重载输出运算符

    BigNum operator +(const BigNum&) const;//重载加法运算符，两个大数之间的相加运算
    BigNum operator -(const BigNum&) const;//重载减法运算符，两个大数之间的相减运算
    BigNum operator *(const BigNum&) const;//重载乘法运算符，两个大数之间的相乘运算
    BigNum operator /(const int&) const;//重载除法运算符，大数对一个整数进行相除运算

    BigNum operator ^(const int&) const;//大数的n次方运算
    int    operator %(const int&) const;//大数对一个int类型的变量进行取模运算
    bool   operator >(const BigNum& T)const;//大数和另一个大数的大小比较
    bool   operator >(const int& t)const; //大数和一个int类型的变量的大小比较

    void print(); //输出大数
};
BigNum::BigNum(const int b){//将一个int类型的变量转化为大数
    int c,d = b;
    len = 0;
    memset(a,0,sizeof(a));
    while(d > MAXN){
        c = d - (d / (MAXN + 1)) * (MAXN + 1);
        d = d / (MAXN + 1);
        a[len++] = c;
    }
    a[len++] = d;
}
BigNum::BigNum(const char*s){//将一个字符串类型的变量转化为大数
    int t,k,index,l,i;
    memset(a,0,sizeof(a));
    l = strlen(s);
    len = l / DLEN;
    if(l % DLEN) len++;
    index = 0;
    for(i = l - 1 ; i >= 0 ; i -= DLEN){
        t = 0;
        k = i - DLEN + 1;
        if(k < 0) k = 0;
        for(int j = k ; j <= i ; j++)
            t = t * 10 + s[j] - '0';
        a[index++] = t;
    }
}
BigNum::BigNum(const BigNum& T) : len(T.len){//拷贝构造函数
    int i;
    memset(a,0,sizeof(a));
    for(i = 0 ; i < len ; i++)
        a[i] = T.a[i];
}
BigNum& BigNum::operator =(const BigNum& n){//重载赋值运算符，大数之间进行赋值运算
    int i;
    len = n.len;
    memset(a,0,sizeof(a));
    for(i = 0 ; i < len ; i++)
        a[i] = n.a[i];
    return *this;
}
istream& operator >>(istream& in,BigNum& b){//重载输入运算符
    char ch[MAXSIZE * 4];
    int i = -1;
    in >> ch;
    int l = strlen(ch);
    int cnt = 0,sum = 0;
    for(i = l - 1 ; i >= 0 ; ){
        sum = 0;
        int t = 1;
        for(int j = 0 ; j < 4 && i >= 0 ; j++,i--,t *= 10)
            sum += (ch[i] - '0') * t;
        b.a[cnt] = sum;
        cnt++;
    }
    b.len = cnt++;
    return in;
}
ostream& operator <<(ostream& out,BigNum& b){//重载输出运算符
    int i;
    cout << b.a[b.len - 1];
    for(i = b.len - 2 ; i >= 0 ; i--){
        cout.width(DLEN);
        cout.fill('0');
        cout << b.a[i];
    }
    return out;
}
BigNum BigNum::operator +(const BigNum& T) const{//两个大数之间的相加运算
    BigNum t(*this);
    int i,big;      //位数
    big = T.len > len ? T.len : len;
    for(i = 0 ; i < big ; i++){
        t.a[i] += T.a[i];
        if(t.a[i] > MAXN){
            t.a[i + 1]++;
            t.a[i] -= MAXN+1;
        }
    }
    if(t.a[big] != 0) t.len = big + 1;
    else t.len = big;
    return t;
}
BigNum BigNum::operator -(const BigNum& T) const{  //两个大数之间的相减运算
    int i,j,big;
    bool flag;
    BigNum t1,t2;
    if(*this > T){
        t1 = *this;
        t2 = T;
        flag = 0;
    }
    else{
        t1 = T;
        t2 = *this;
        flag = 1;
    }
    big = t1.len;
    for(i = 0 ; i < big ; i++)
        if(t1.a[i] < t2.a[i]){
            j = i + 1;
            while(t1.a[j] == 0) j++;
            t1.a[j--]--;
            while(j > i) t1.a[j--] += MAXN;
            t1.a[i] += MAXN + 1 - t2.a[i];
        }
        else t1.a[i] -= t2.a[i];
    t1.len = big;
    while(t1.a[len - 1] == 0 && t1.len > 1){
        t1.len--;
        big--;
    }
    if(flag) t1.a[big - 1] = 0 - t1.a[big - 1];
    return t1;
}
BigNum BigNum::operator *(const BigNum& T) const{//两个大数之间的相乘运算
    BigNum ret;
    int i,j,up;
    int temp,temp1;
    for(i = 0 ; i < len ; i++){
        up = 0;
        for(j = 0 ; j < T.len ; j++){
            temp = a[i] * T.a[j] + ret.a[i + j] + up;
            if(temp > MAXN){
                temp1 = temp - temp / (MAXN + 1) * (MAXN + 1);
                up = temp / (MAXN + 1);
                ret.a[i + j] = temp1;
            }
            else{
                up = 0;
                ret.a[i + j] = temp;
            }
        }
        if(up != 0) ret.a[i + j] = up;
    }
    ret.len = i + j;
    while(ret.a[ret.len - 1] == 0 && ret.len > 1) ret.len--;
    return ret;
}
BigNum BigNum::operator /(const int& b) const{//大数对一个整数进行相除运算
    BigNum ret;
    int i,down = 0;
    for(i = len - 1 ; i >= 0 ; i--){
        ret.a[i] = (a[i] + down * (MAXN + 1)) / b;
        down = a[i] + down * (MAXN + 1) - ret.a[i] * b;
    }
    ret.len = len;
    while(ret.a[ret.len - 1] == 0 && ret.len > 1)
        ret.len--;
    return ret;
}
int BigNum::operator %(const int& b) const{//大数对一个int类型的变量进行取模运算
    int i,d = 0;
    for (i = len - 1 ; i >= 0 ; i--)
        d = ((d * (MAXN + 1)) % b + a[i]) % b;
    return d;
}
BigNum BigNum::operator ^(const int& n) const{    //大数的n次方运算
    BigNum t,ret(1);
    int i;
    if(n < 0) exit(-1);
    if(n == 0) return 1;
    if(n == 1) return *this;
    int m = n;
    while(m > 1){
        t = *this;
        for(i = 1 ; i << 1 <= m ; i <<= 1) t = t * t;
        m -= i;
        ret = ret * t;
        if(m == 1) ret = ret * (*this);
    }
    return ret;
}
bool BigNum::operator >(const BigNum& T) const{   //大数和另一个大数的大小比较
    int ln;
    if(len > T.len) return true;
    else if(len == T.len){
        ln = len - 1;
        while(a[ln] == T.a[ln] && ln >= 0) ln--;
        if(ln >= 0 && a[ln] > T.a[ln]) return true;
        else return false;
    }
    else return false;
}
bool BigNum::operator >(const int& t) const{//大数和一个int类型的变量的大小比较
    BigNum b(t);
    return *this > b;
}
void BigNum::print(){    //输出大数
    int i;
    cout << a[len - 1];
    for(i = len - 2 ; i >= 0 ; i--){
        cout.width(DLEN);
        cout.fill('0');
        cout << a[i];
    }
    cout << endl;
}
int main(void){
    BigNum val;
    val = "123456789101112131415161718192021222324252627282930";
    val.print();
    val = "10"; BigNum val1 = "1234";
    BigNum val2 = "11";
    BigNum tmp = val + val1;
    tmp.print();
    tmp = val * val1;
    tmp.print();
    tmp = val1 / 10;
    tmp.print();
    tmp = val2 ^ 2;
    tmp.print();
    return 0;
}