大整数类——C++实现

大整数类

题解：

要实现大整数类，我们首先要设置多个构造器，使之能识别字符串作为数字，因为使用字符串可以输入很大的数字且不越界。

• 同时由于拿到的是字符串不是直接的数字了，所以我们还需要通过运算符重载来实现加法和等于。

如何实现字符串形式的加法？

• 我们先计算一下要加的两个字符串形式的数字的位数，我们使用给位数小的数字进行补0操作，使之位数相同且多补一位0防止进位，接着在二者位数相同的情况下，我们逐位相加，一旦大于10进位即可，再把原先补的多余的0判断是否要去掉即可。

代码：

#include 
#include 
#include 
using namespace std;

class HugeInteger {
	private:
		string str;

	public:
		HugeInteger();
		
		HugeInteger(int i);
		
		HugeInteger(string s);

		friend ostream & operator<<( ostream & os,HugeInteger & c);

		string operator + (const HugeInteger & h) {
			char stand = '0'; 
			string b = h.str;
			string a = this->str;
			if(a.length()>b.length()){
				while(a.length()>b.length()) {
					b = stand + b;
				}
			}
			if(a.length()<b.length()){
				while(a.length()<b.length()) {
					a = stand + a;
				}
			}
			a = stand + a;
			b = stand + b;
		
			for(int i=a.length()-1; i>=0; i--) {
				char tempSum = a[i] + b[i] - stand;
				a[i] = tempSum;
				if(a[i]>57) {
					char temp = a[i] - 10;
					a[i] = temp;
					a[i-1] += 1;
				}
			}
			
			a = a[0]==stand ? a.replace(0,1,""): a;

			return a;
		}
		string operator + (string a) {
			char stand = '0';
			string b = this->str;
			if(a.length()>b.length()){
				while(a.length()>b.length()) {
					b = stand + b;
				}
			}
			if(a.length()<b.length()){
				while(a.length()<b.length()) {
					a = stand + a;
				}
			}
			a = stand + a;
			b = stand + b;
			for(int i=a.length()-1; i>=0; i--) {
				char tempSum = a[i] + b[i] - stand;
				a[i] = tempSum;
				if(a[i]>57) {
					a[i] -= 10;
					a[i-1] += 1;
				}
			}
			
			a = a[0]==stand ? a.replace(0,1,""): a;
			
			return a;
		}

		HugeInteger operator = (string & a) {
			HugeInteger h(a);
			return h;
		}
};

HugeInteger::HugeInteger(string s) {
	this->str = s;
}

ostream & operator<<( ostream & os,HugeInteger & c) {
	os<<c.str;
	return os;
}

HugeInteger::HugeInteger() {
	str = "0";
}


HugeInteger::HugeInteger(int i) {
	int k = i;

	while(i) {
		char tempchar = char( i%10 +48) ;
		str = tempchar + str;
		i/=10;
	}
	
	if(k==0){
		str="0";	
	} 
}

int main() {
	HugeInteger n1( 7654321 );
	HugeInteger n2( 7891234 );
	HugeInteger n3( "99999999999999999999999999999" );
	HugeInteger n4( "1" );
	HugeInteger n5;
	cout << "n1 is " << n1 << "\nn2 is " << n2
	     << "\nn3 is " << n3 << "\nn4 is " << n4
	     << "\nn5 is " << n5 << "\n\n";
	n5 = n1 + n2;
	cout << n1 << " + " << n2 << " = " << n5 << "\n\n";
	cout << n3 << " + " << n4 << "\n= " << ( n3 + n4 ) << "\n\n";
	n5 = n1 + 9;
	cout << n1 << " + " << 9 << " = " << n5 << "\n\n";
	n5 = n2 + "10000";
	cout << n2 << " + " << "10000" << " = " << n5 << endl;

	return 0;
}