模板 高精度大整数

//http://www.cnblogs.com/HarryGuo2012/p/4524041.html

#include <bits/stdc++.h>

#define MAX_L 2005 //最大长度，可以修改

using namespace std;
typedef int Integer ;
typedef long long LL;

class bign
{
    public:
    int len, s[MAX_L];//数的长度，记录数组

//构造函数
    bign();
    bign(const char*);
    bign(Integer);
    bool sign;//符号 1正数 0负数

    string toStr() const;//转化为字符串，主要是便于输出
    Integer toInteger() const;

    friend istream& operator>>(istream &,bign &);//重载输入流
    friend ostream& operator<<(ostream &,bign &);//重载输出流
//重载复制
    bign operator=(const char*);
    bign operator=(int);
    bign operator=(const string);
//重载各种比较
    bool operator>(const bign &) const;
    bool operator>=(const bign &) const;
    bool operator<(const bign &) const;
    bool operator<=(const bign &) const;
    bool operator==(const bign &) const;
    bool operator!=(const bign &) const;
//重载四则运算
    bign operator+(const bign &) const;
    bign operator-(const bign &) const;
    bign operator*(const bign &) const;
    bign operator/(const bign &) const;
    bign operator+(const Integer &) const;
    bign operator-(const Integer &) const;
    bign operator*(const Integer &) const;
    bign operator/(const Integer &) const;
//四则运算的衍生运算
    bign operator%(const bign &)const;//取模（余数）
    bign operator%(const Integer &)const;

    bign factorial()const;//阶乘
    bign Sqrt()const;//整数开根（向下取整）
    bign pow(const bign &)const;//次方
    bign pow(const Integer &)const;
//一些乱乱的函数
    void clean();
};
#define max(a,b) a>b ? a : b
#define min(a,b) a<b ? a : b

bign::bign()
{
    memset(s, 0, sizeof(s));
    len = 1;
    sign = 1;
}

bign::bign(const char *num)
{
    *this=num;
}

bign::bign(Integer num)
{
    *this=num;
}

string bign::toStr() const
{
    string res;
    res = "";
    for (int i=0;i<len;i++)
        res=(char)(s[i]+'0')+res;
    if (res=="")
        res="0";
    if (!sign && res!="0")
        res="-"+res;
    return res;
}

Integer bign::toInteger() const
{
    LL res=0;
    for (int i=len-1;i>=0;--i)
    {
        res=(10*res+s[i]);
    }
    return res;
}

istream &operator>>(istream &in, bign &num)
{
    string str;
    in>>str;
    num=str;
    return in;
}

ostream &operator<<(ostream &out, bign &num)
{
    out<<num.toStr();
    return out;
}

bign bign::operator=(const char *num)
{
    memset(s,0,sizeof(s));
    char a[MAX_L]="";
    if (num[0]!='-')
        strcpy(a,num);
    else
        for(int i=1;i<strlen(num);i++)
            a[i - 1]=num[i];
    sign=!(num[0]=='-');
    len=strlen(a);
    for (int i=0;i<strlen(a);i++)
        s[i]=a[len-i-1]-48;
    return *this;
}

bign bign::operator=(Integer num)
{
    char temp[MAX_L];
    sprintf(temp,"%d",num);
    *this=temp;
    return *this;
}

bign bign::operator=(const string num)
{
    const char *tmp;
    tmp=num.c_str();
    *this=tmp;
    return *this;
}

bool bign::operator<(const bign &num) const
{
    if (sign^num.sign)
        return num.sign;
    if (len!=num.len)
        return len<num.len;
    for (int i=len-1;i>=0;i--)
        if (s[i]!=num.s[i])
            return sign ? (s[i] < num.s[i]) : (!(s[i] < num.s[i]));
    return !sign;
}

bool bign::operator>(const bign&num)const
{
    return num<*this;
}

bool bign::operator<=(const bign&num)const
{
    return !(*this>num);
}

bool bign::operator>=(const bign &num)const
{
    return !(*this<num);
}

bool bign::operator!=(const bign &num)const
{
    return *this > num || *this < num;
}

bool bign::operator==(const bign &num)const
{
    return !(num!=*this);
}

bign bign::operator + (const bign &num) const
{
    if (sign^num.sign)
    {
        bign tmp=sign?num:*this;
        tmp.sign=1;
        return sign ? *this-tmp : num-tmp;
    }
    bign result;
    result.len=0;
    int temp=0;
    for (int i=0;temp || i <(max(len,num.len));i++)
    {
        int t=s[i]+num.s[i]+temp;
        result.s[result.len++]=t%10;
        temp=t/10;
    }
    result.sign=sign;
    return result;
}

bign bign::operator + (const Integer &num) const
{
    bign tmp(num);
    return *this+tmp;
}

bign bign::operator - (const bign &num) const
{
    bign b=num,a=*this;
    if (!num.sign && !sign)
    {
        b.sign=1;
        a.sign=1;
        return b-a;
    }
    if (!b.sign)
    {
        b.sign=1;
        return a+b;
    }
    if (!a.sign)
    {
        a.sign=1;
        b=bign(0)-(a+b);
        return b;
    }
    if (a<b)
    {
        bign c=(b-a);
        c.sign=false;
        return c;
    }
    bign result;
    result.len=0;
    for (int i=0,g=0;i<a.len;i++)
    {
        int x=a.s[i]-g;
        if (i<b.len) x-=b.s[i];
        if (x>=0) g=0;
        else
        {
            g=1;
            x+=10;
        }
        result.s[result.len++]=x;
    }
    result.clean();
    return result;
}

bign bign::operator - (const Integer &num) const
{
    bign tmp(num);
    return *this-tmp;
}

bign bign::operator * (const bign &num)const
{
    bign result;
    result.len=len+num.len;

    for (int i=0;i<len;i++)
        for (int j=0;j<num.len;j++)
            result.s[i+j]+=s[i]*num.s[j];

    for (int i=0;i<result.len;i++)
    {
        result.s[i+1]+=result.s[i]/10;
        result.s[i]%=10;
    }
    result.clean();
    result.sign =!(sign^num.sign);
    return result;
}

bign bign::operator * (const Integer &num) const
{
    bign tmp(num);
    return *this*tmp;
}

bign bign::operator / (const bign& num)const
{
    bign ans;
    ans.len=len-num.len+1;
    if (ans.len<0)
    {
        ans.len=1;
        return ans;
    }

    bign divisor=*this,divid=num;
    divisor.sign=divid.sign=1;
    int k=ans.len-1;
    int j=len-1;
    while (k>=0)
    {
        while (divisor.s[j]==0) j--;
        if (k>j) k=j;
        char z[MAX_L];
        memset(z,0,sizeof(z));
        for (int i=j;i>=k;i--)
            z[j-i]=divisor.s[i]+'0';
        bign dividend=z;
        if (dividend<divid) {k--; continue; }
        int key=0;
        while (divid*key<=dividend) key++;
        key--;
        ans.s[k]=key;
        bign temp=divid*key;
        for (int i=0;i<k;i++)
            temp=temp*10;
        divisor=divisor-temp;
        k--;
    }
    ans.clean();
    ans.sign=!(sign^num.sign);
    return ans;
}

bign bign::operator / (const Integer &num) const
{
    bign tmp(num);
    return *this/tmp;
}

bign bign::operator % (const bign& num)const
{
    bign a=*this, b=num;
    a.sign=b.sign=1;
    bign result,temp =a / b*b;
    result=a-temp;
    result.sign=sign;
    return result;
}

bign bign::operator % (const Integer &num) const
{
    bign tmp(num);
    return *this%tmp;
}

bign bign::pow(const bign& num) const
{
    bign result=1;
    for (bign i=0;i < num;i=i+1)
        result=result*(*this);
    return result;
}

bign bign::pow(const Integer &num) const
{
    bign result=1;
    for (Integer i=0;i<num; i=i+1)
        result=result*(*this);
    return result;
}

bign bign::factorial() const
{
    bign result=1;
    for (bign i=1;i<=*this;i=i+1)
        result=result*i;
    return result;
}

void bign::clean()
{
    if (len==0) len++;
    while (len>1 && s[len - 1]=='')
        len--;
}

bign bign::Sqrt() const
{
    if(*this<0)return -1;
    if(*this<=1)return *this;
    bign l=0,r=*this,mid;
    while(r-l>1)
    {
        mid=(l+r)/2;
        if(mid*mid>*this)
            r=mid;
        else
            l=mid;
    }
    return l;
}

bign Sqrt(bign x)
{
    bign remain=0;
    bign odd=0;
    bign ans=0;

    int group=0,k=0;

    string s=x.toStr();
    int len=s.length();

    if (len%2==1)
    {
        group=s[0]-'0';
        k=-1;
    }
    else
    {
        group=(s[0]-'0')*10+s[1]-'0';
        k=0;
    }

    for (int j=0;j<(len+1)/2;++j)
    {
        if (j!=0) group=((s[2*j+k]-'0')*10+(s[2*j+k+1]-'0'));

        odd=ans*20+1;
        remain=remain*100+group;

        int cnt=0;
        while (remain>=odd)
        {
            ++cnt;
            remain=remain-odd;
            odd=odd+2;
        }
        ans=ans*10+cnt;

    }

    return ans;
}


int main()
{

}

从卿学姐那里转来的转自郭爷的模板，原来的做减法会有迷之错误