大整数类BIGN的设计与实现 C++高精度模板

首先感谢刘汝佳所著的《算法竞赛入门经典》。

众所周知,C++中储存能力最大的unsigned long long 也是有着一个上限,如果我们想计算非常大的整数时,就不知所措了,所以,我写了一个高精度类,允许大整数的四则运算

这个类利用字符串进行输入输出,并利用数组进行储存与处理,通过模拟四则运算,可以计算很大的整数的加减乘除比大小。

支持负数,前导零,支持字符串、整型赋值,支持流输入输出

贴上我的代码:

#include<string>
#include<iostream>
#include<iosfwd>
#include<cmath>
#include<cstring>
#include<stdlib.h>
#include<stdio.h>
#include<cstring>
#define MAX_L 2005 //最大长度,可以修改
using namespace std; 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(int);
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
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++();
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&);
//四则运算的衍生运算
bign operator%(const bign&)const;//取模(余数)
bign factorial()const;//阶乘
bign Sqrt()const;//整数开根(向下取整)
bign pow(const bign&)const;//次方
//一些乱乱的函数
void clean();
~bign();
};
#define max(a,b) a>b ? a : b
#define min(a,b) a<b ? a : b bign::bign()
{
memset(s, , sizeof(s));
len = ;
sign = ;
} bign::bign(const char *num)
{
*this = num;
} bign::bign(int num)
{
*this = num;
} string bign::toStr() const
{
string res;
res = "";
for (int i = ; i < len; i++)
res = (char)(s[i] + '') + res;
if (res == "")
res = "";
if (!sign&&res != "")
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, , sizeof(s));
char a[MAX_L] = "";
if (num[] != '-')
strcpy(a, num);
else
for (int i = ; i < strlen(num); i++)
a[i - ] = num[i];
sign = !(num[] == '-');
len = strlen(a);
for (int i = ; i < strlen(a); i++)
s[i] = a[len - i - ] - ;
return *this;
} bign bign::operator=(int 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 - ; i >= ; 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 = ;
return sign ? *this - tmp : num - tmp;
}
bign result;
result.len = ;
int temp = ;
for (int i = ; temp || i < (max(len, num.len)); i++)
{
int t = s[i] + num.s[i] + temp;
result.s[result.len++] = t % ;
temp = t / ;
}
result.sign = sign;
return result;
} bign bign::operator++()
{
*this = *this + ;
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=;
a.sign=;
return b-a;
}
if (!b.sign)
{
b.sign=;
return a+b;
}
if (!a.sign)
{
a.sign=;
b=bign()-(a+b);
return b;
}
if (a<b)
{
bign c=(b-a);
c.sign=false;
return c;
}
bign result;
result.len = ;
for (int i = , g = ; i < a.len; i++)
{
int x = a.s[i] - g;
if (i < b.len) x -= b.s[i];
if (x >= ) g = ;
else
{
g = ;
x += ;
}
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 = ; i < len; i++)
for (int j = ; j < num.len; j++)
result.s[i + j] += s[i] * num.s[j]; for (int i = ; i < result.len; i++)
{
result.s[i + ] += result.s[i] / ;
result.s[i] %= ;
}
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 + ;
if (ans.len < )
{
ans.len = ;
return ans;
} bign divisor = *this, divid = num;
divisor.sign = divid.sign = ;
int k = ans.len - ;
int j = len - ;
while (k >= )
{
while (divisor.s[j] == ) j--;
if (k > j) k = j;
char z[MAX_L];
memset(z, , sizeof(z));
for (int i = j; i >= k; i--)
z[j - i] = divisor.s[i] + '';
bign dividend = z;
if (dividend < divid) { k--; continue; }
int key = ;
while (divid*key <= dividend) key++;
key--;
ans.s[k] = key;
bign temp = divid*key;
for (int i = ; i < k; i++)
temp = temp * ;
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 = ;
bign result, temp = a / b*b;
result = a - temp;
result.sign = sign;
return result;
} bign bign::pow(const bign& num)const
{
bign result = ;
for (bign i = ; i < num; i++)
result = result*(*this);
return result;
} bign bign::factorial()const
{
bign result = ;
for (bign i = ; i <= *this; i++)
result *= i;
return result;
} void bign::clean()
{
if (len == ) len++;
while (len > && s[len - ] == '\0')
len--;
} bign bign::Sqrt()const
{
if(*this<)return -;
if(*this<=)return *this;
bign l=,r=*this,mid;
while(r-l>)
{
mid=(l+r)/;
if(mid*mid>*this)
r=mid;
else
l=mid;
}
return l;
} bign::~bign()
{
} bign num0,num1,res; int main() {
num0 = , num1 = ;
res=num0-num1;
cout << res << endl;
return ;
}
 
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