添加大数模板

Author: taotao

Diff for: math/大数模板.md

@@ -0,0 +1,293 @@
+```c++
+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;
+	scanf("%s", 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;
+}
+```