实现大整数类BigInt

#include <string>
#include <iostream>
#include <iosfwd>
#include <cmath>
#include <cstring>
#include <stdlib.h>
#include <stdio.h>
#include <cstring>
#define MAX_L 2005
using namespace std;

#define max(a,b) a>b ? a:b
#define min(a,b) a<b ? a:b

class bign
{
public:
	int len, s[MAX_L];//数的长度，记录数组
	bool sign; // 符号 1正数 0负数
	bign();
	bign(const char*);
	bign(int);
	string toStr() const; //转化为字符串，主要是便于输出
	friend istream& operator>>(istream &, bign &)
	friend ostream& operator<<(ostream &, bign &);
	//重载=
	bign operator=(const char*)
	bign operator=(int);
	bign operator=(const string);
	//重载比较
	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++();
	bign operator++(int);
	bign operator+=(const bign &);

	bign operator-(const bign &) const;
	bign operator--();
	bign operator--(int);
	bign operator-=(const bign &);

	bign operator*(const bign &) const;
	bign operator*(const int num) const;
	bign operator*=(const bign &);

	bign operator/(const bign &) const;
	bign operator/=(const bign &);
	//四则运算衍生运算
	bign operator%(const bign &) const;
	bign factorial()const;
	bign Sqrt()const;
	bign pow(const bign &)const;

	void clean();
	~bign();
}

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

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

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

stirng 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;
}

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=(int num)
{
    if (num < 0)
        sign = 0, num = -num;
    else
        sign = 1;
    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++()
{
    *this = *this + 1;
    return *this;
}

bign bign::operator++(int)
{
    bign old = *this;
    ++(*this);
    return old;
}

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


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 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 int num)const
{
    bign x = num;
    bign z = *this;
    return x*z;
}
bign bign::operator*=(const bign&num)
{
    *this = *this * num;
    return *this;
}

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 bign&num)
{
    *this = *this / num;
    return *this;
}
 
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::pow(const bign& num)const
{
    bign result = 1;
    for (bign i = 0; i < num; i++)
        result = result*(*this);
    return result;
}
 
bign bign::factorial()const
{
    bign result = 1;
    for (bign i = 1; i <= *this; i++)
        result *= i;
    return result;
}
 
void bign::clean()
{
    if (len == 0) len++;
    while (len > 1 && s[len - 1] == '\0')
        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::~bign()
{
}

bign num0,num1,res;
 
int main()
{
    cin>>num0>>num1;
    res=num0+num1;
    cout<<res<<endl;
 
    num0=5;
    num1="71";
    res=num0-num1;
    cout<<res<<endl;
 
    res=num0.Sqrt();
    cout<<res<<endl;
 
    res=num0.pow(5);
    cout<<res<<endl;
    return 0;
}