大數模板

Sample Input

2

1 2

112233445566778899 998877665544332211

Sample Output

Case 1:

1 + 2 = 3

 

Case 2:

112233445566778899 + 998877665544332211 = 1111111111111111110

 

#include<stdio.h>
#include<string.h>
#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[1500];    //可以控制大數的位數
	int len;       //大數長度
public:
	BigNum(){ len = 1;memset(a,0,sizeof(a)); }   //構造函數
	BigNum(const int);       //將一個int類型的變量轉化爲大數
	BigNum(const char*);     //將一個字符串類型的變量轉化爲大數
	BigNum(const BigNum &);  //拷貝構造函數
	BigNum &operator=(const BigNum &);   //重載賦值運算符，大數之間進行賦值運算
	friend istream& operator>>(istream&,  BigNum&);   //重載輸入運算符
	friend ostream& operator<<(ostream&,  BigNum&);   //重載輸出運算符
	BigNum operator+(const BigNum &) const;   //重載加法運算符，兩個大數之間的相加運算
	BigNum operator-(const BigNum &) const;   //重載減法運算符，兩個大數之間的相減運算
	BigNum operator*(const BigNum &) const;   //重載乘法運算符，兩個大數之間的相乘運算
	BigNum operator/(const int   &) const;    //重載除法運算符，大數對一個整數進行相除運算
	BigNum operator^(const int  &) const;    //大數的n次方運算
	int    operator%(const int  &) const;    //大數對一個int類型的變量進行取模運算
	bool   operator>(const BigNum & T)const;   //大數和另一個大數的大小比較
	bool   operator>(const int & t)const;      //大數和一個int類型的變量的大小比較
	void print();       //輸出大數
};
BigNum::BigNum(const int b)     //將一個int類型的變量轉化爲大數
{
	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)     //將一個字符串類型的變量轉化爲大數
{
	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)  //拷貝構造函數
{
	int i;
	memset(a,0,sizeof(a));
	for(i = 0 ; i < len ; i++)
		a[i] = T.a[i];
}
BigNum & BigNum::operator=(const BigNum & n)   //重載賦值運算符，大數之間進行賦值運算
{
	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)   //重載輸入運算符
{
	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)   //重載輸出運算符
{
	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   //兩個大數之間的相加運算
{
	BigNum t(*this);
	int i,big;      //位數
	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   //兩個大數之間的相減運算
{
	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   //兩個大數之間的相乘運算
{
	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   //大數對一個整數進行相除運算
{
	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    //大數對一個int類型的變量進行取模運算
{
	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    //大數的n次方運算
{
	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   //大數和另一個大數的大小比較
{
	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    //大數和一個int類型的變量的大小比較
{
	BigNum b(t);
	return *this>b;
}
void BigNum::print()    //輸出大數
{
	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()
{
  	int n,i;
	char a[1500], b[1500];
	BigNum sa,sb;
	scanf("%d",&n);
	for(i=1;i<=n;i++)
	{
		printf("Case %d:\n",i);
		scanf("%s %s",a,b);
		printf("%s + %s = ",a,b);
		sa=BigNum(a);
		sb=BigNum(b);
		BigNum sc=sa+sb;
		(sc).print();
		if(i!=n) printf("\n");
	}
	return 0;
}