面试题之自创 实现两个整型大数（都是正数）的相减操作

非常大的正整数相减求差

真言

人生如此美好，世上如此多娇，可我只喜欢她，so beautiful。She is the power of mine,how about you?

引言

光大数的加法操作是满足不了我们的，在这里我给大家提供了减法的操作。

思路

被减数和减数对应位相减，如果不够，则向前借位，如果高位为0，继续向前借位。

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(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";
}
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;
while( i < L )
{
if( a[i] < '0' || a[i] > '9')
return false;
i++;
}
return true ;
}

// make a-b mode int a - b;
static string Multiplies(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;
}

// 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;
while(i < a.size())
{
if(a[i] != '0')
break;
i++;
}
a = a.substr(i,a.size());
}
};
// main function
int main()
{
string a ;
string b ;
cin>>a>>b;
cout<<"a="<<a<<",b="<<b<<endl;

cout<<String::Multiplies(a,b)<<endl;
system("pause");
return 0;
}