大数相乘（整数）

真言

思考真的很舒服。

引言

大数据的时代已经到来，大数据的操作还是需要的。很多面试题的根本就在于大数据的处理，大数据超出了整形的表示范围。

题目

想法实现大数的乘法。

思路

用字符串可以很长的特点，去模拟数字的乘法操作。

实验

代码

test.cpp

#include 
     
      
#include 
      
        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 MinusInt( a,b.substr( 1,b.size() ) ); else if(a[0] == '-'&& b[0] != '-') return MinusInt(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 MINUS_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 MinusInt(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 MinusInt( b.substr(1,b.size()) , a.substr(1,a.size()) ); } // make a*b mode int a * b; static string MULT_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); string::size_type i = a.size(),j = b.size(); string c = "0",d = ""; bool fushu = (a[0] == '-' && b[0] != '-')||(a[0] != '-' && b[0] == '-'); if(a[0] == '-') a = a.substr(1,a.size()); if(b[0] == '-') b = b.substr(1,b.size()); int jinwei = 0; for( j = b.size()-1 ; j < b.size() ;j--) { // each number of b to * a jinwei = 0; for( i = a.size()-1 ; i < a.size() ;i-- ) { d = IntToChar( ( CharToNumber(a[i]) * CharToNumber(b[j]) + jinwei ) % 10 )+ d ; jinwei = ( CharToNumber(a[i]) * CharToNumber(b[j]) + jinwei ) / 10 ; } // add all number result c = ADD_Int(c,d); d = ""; int zero = 0 ; while( zero < b.size() - j ) { d = d + '0'; zero ++; } } if( fushu ) return '-'+c; else return c; } private: // make a-b mode int a - b; static string MinusInt(string a,string b) { // exception of input if(!check_all_number(a) || !check_all_number(b)) return "exception of input MinusInt"; 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<
       
        = 0 && i <= 9 ) { return char(i+48); } else { cout<
        
          '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 input 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>>b; cout<<"a="<