首页 > 数学相关 > 大数计算-C++模板
2014
02-23

大数计算-C++模板

 分别使用C++中的运算符重载的方法来实现大数之间的数学运算,包括加法、减法、乘法、除法、n次方、取模、大小比较、赋值以及输入流、输出流的重载。。

         并且使用这个大数模板,顺利AC了HDOJ上的1134这个题目的Catalan数计数问题。。http://acm.hdu.edu.cn/showproblem.php?pid=1134

大数模板的代码如下:

#include<iostream> 
#include<string> 
#include<iomanip> 
#include<algorithm> 
using namespace std; 

#define MAXN 9999
#define MAXSIZE 10
#define DLEN 4

class BigNum
{ 
private: 
	int a[500];    //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 count=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[count]=sum;
		count++;
	}
	b.len =count++;
	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)
{
	int i,n;
	BigNum x[101];      //定义大数的对象数组
	x[0]=1;
	for(i=1;i<101;i++)
		x[i]=x[i-1]*(4*i-2)/(i+1);
	while(scanf("%d",&n)==1 && n!=-1)
	{
		x[n].print();
	}
}

 


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