面试题之自创 大数相加减

大数相加减

• 真言

做我自己，不要做别人眼中的自己。我就是这样，这样的一个疯子。。。

• 引言

这是我补前面大正整数相加减的博客，正数很常用，但是如果出现负数，我们肿么办？

• 题目

 大数相加减，大数已经超出了int，long，long long 的表示范围。

• 思路

用字符串可以很长的特点，去模拟大数加减操作

• 实验

• 代码

test.cpp

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

// extra the class of string
class String:public string
{
public:
	// mode the add of int
	static string ADD_Int(string a,string b)
	{
		// exception of input
		if( a.empty() )
			return b;
		else if( b.empty() )
			return "0";
		if(!check_all_number(a) || !check_all_number(b))
		{
			return "exception of input ADD_Int";
		}
		Standardization(a);
		Standardization(b);	

		if(a[0] != '-' && b[0] != '-')
			return AddInt(a,b);
		else if(a[0] != '-'&& b[0] == '-')		
			return MultipliesInt( a,b.substr( 1,b.size() ) );
		else if(a[0] == '-'&& b[0] != '-')
			return MultipliesInt(b,a.substr(1,a.size()));
		else return '-'+AddInt(a.substr(1,a.size()),b.substr( 1,b.size() ));
	}

	// make a-b mode int a - b;
	static string MUL_Int(string a,string b)
	{
		// exception of input
		if( a.empty() )
			return b;
		else if( b.empty() )
			return "0";
		if(!check_all_number(a) || !check_all_number(b))
		{
			return "exception of input Multiplies_Int";
		}
		Standardization(a);
		Standardization(b);	
		if(a[0] != '-' && b[0] != '-')
			return MultipliesInt(a,b);
		else if(a[0] != '-' && b[0] == '-')
			return AddInt(a,b.substr(1,b.size()));
		else if(a[0] == '-' && b[0] != '-')
			return "-"+AddInt(a.substr(1,a.size()),b);
		else return MultipliesInt( b.substr(1,b.size()) , a.substr(1,a.size()) );
	}


private:


	// make a-b mode int a - b;
	static string MultipliesInt(string a,string b)
	{
		// exception of input
		if(!check_all_number(a) || !check_all_number(b))
			return "exception of input Multiplies";
		Standardization(a);
		Standardization(b);
		// particular string of input
		if(a.empty())
		{
			if(b.empty())
				return "0";
			else
				return "-"+b;
		}
		else if(b.empty())
		{
			return a;
		}

		// normal number a < b
		string c = "";
		bool check = true ;
		if(Compare(a,b) == '=')
			return "0";
		else if(Compare(a,b) == '<')
		{
			c = a ;
			a = b ;
			b = c ;
			c = "";
			check = false ;
		}
		// normal number a >= b
		string::size_type i = a.size()-1, j = b.size()-1;
		int jiewei = 0,now;

		while(i < a.size() && j < b.size())
		{
			now = CharToNumber(a[i]) - CharToNumber(b[j]) - jiewei ;

			if( now < 0 )
			{
				jiewei = 1;
				now = 10 + now ;
			}
			else jiewei = 0;
			c = IntToChar(now)  + c ;
			i--;j--;
		}
		while(i < a.size())
		{
			now = CharToNumber(a[i]) - jiewei ;
			if( now < 0 )
			{
				jiewei = 1;
				now = 10 + now ;
			}
			else jiewei = 0;
			c = IntToChar( now )  + c ;
			i--;
		}
		Standardization(c);
		if(!check)
			c = '-' + c;		
		return c; 
	}


	// mode the add of int
	static string AddInt(string a,string b)
	{
		// exception of input
		if( a.empty() )
			return b;
		else if( b.empty() )
			return "0";
		if(!check_all_number(a) || !check_all_number(b))
		{
			return "exception of input AddInt";
		}
		Standardization(a);
		Standardization(b);
		string::size_type i = a.size()-1 ,j = b.size()-1 , k = 0 ;
		string c = "";
		int jinwei = 0;
		while( i < a.size() && j < b.size() )
		{
			c = IntToChar( ( CharToNumber(a[i]) + CharToNumber(b[j]) + jinwei ) % 10 ) + c;
			jinwei = ( CharToNumber(a[i]) + CharToNumber(b[j]) + jinwei ) / 10;
			j--;i--;
		}
		while( j < b.size()  )
		{
			c =  IntToChar( ( CharToNumber(b[j]) + jinwei ) % 10 ) + c;
			jinwei = ( jinwei + CharToNumber(b[j]) ) / 10;	
			j--;
		}
		while( i < a.size() )
		{
			c =  IntToChar( ( CharToNumber(a[i]) + jinwei ) % 10 ) + c;
			jinwei = ( jinwei + CharToNumber(a[i]) ) / 10;	
			i--;
		}
		if( jinwei )
			c = IntToChar(  jinwei  ) + c;
		return c;
	}

	// make char to the int number
	static int CharToNumber(char c)
	{
		if( c >= '0' && c <= '9' )
			return int(c - '0');
		else 
		{
			cout<<"exception of input CharToNumber "<<endl;
			system("pause");
			return 0;
		}
	}

	// make int to the model char
	static char IntToChar(int i)
	{
		if( i >= 0 && i <= 9 )
		{
			return char(i+48);
		}
		else
		{
			cout<<i<<" exception of input IntToChar"<<endl;
			system("pause");
		}
	}

	// check whether the string is legal 
	static bool check_all_number(string a)
	{
		if(a.empty())
			return true ;
		string::size_type L = a.size(),i = 0;
		if(a[0] == '-')
			i++;
		while( i < L )
		{
			if( a[i] < '0' || a[i] > '9')
				return false;
			i++; 
		}
		return true ;
	}



	// compare string a and b
	static char Compare(string a,string b)
	{
		if(a.empty() || b.empty())
		{
			cout<<"error of imput compare";
			return 'e';
		}
		else
		{
			if(a.size() > b.size())
				return '>' ;
			else if(a.size() == b.size())
			{
				for(string::size_type i = 0;i < a.size(); i++)
				{
					if(a[i] > b[i])
						return '>';
					if(a[i] < b[i])
						return '<';
				}
				return '=';
			}			
			return '<';
		}
	}

	// make string into standard number
	static void Standardization(string &a)
	{
		if(!check_all_number(a))
		{
			cout<<a<<" exception of input Standardization"<<endl;
		}
		string::size_type i = 0;
		bool fushu = false ;
		if( a[0] == '-' )
		{
			fushu = true;
			i = 1;
		}
		while(i < a.size())
		{
			if(a[i] != '0')
				break;
			i++;
		}
		if(i == a.size())
			i--;
		a = a.substr(i,a.size());
		if( fushu && a != "0")
			a = '-' + a;
	}
};


// main function
int main()
{
	string a ;
	string b ;
	cin>>a>>b;
	cout<<"a="<<a<<",b="<<b<<endl;
	cout<<"add = "<<String::ADD_Int(a,b)<<endl;
	cout<<"mul = "<<String::MUL_Int(a,b)<<endl;
	system("pause");
	return 0;
}