multi.cpp

分治法实现大数乘法

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

list<char> long_sub(list<char> clist1, list<char> clist2);
/*******大整数加法*********/
list<char> long_add(list<char> clist1, list<char> clist2)
{
list<char> rs; //存放最后的结果
//如果一个正，一个负，做两数相减
if ( *(clist1.begin()) == '-' && *(clist2.begin()) != '-' )
{
   clist1.erase(clist1.begin()); //去掉符号位
   rs = long_sub(clist2, clist1);
   return rs;
}
//如果一个负，一个正，做两数相减
if ( *(clist1.begin()) != '-' && *(clist2.begin()) == '-' )
{
   clist2.erase(clist2.begin()); //去掉符号位
   rs = long_sub(clist1, clist2);
   return rs;
}
if ( *(clist1.begin()) == '-' && *(clist2.begin()) == '-' )
{
   clist1.erase(clist1.begin());
   clist2.erase(clist2.begin());
   rs = long_add(clist1,clist2);
   rs.push_front('-');
   return rs;
}
if ( *(clist1.begin()) != '-' && *(clist2.begin()) != '-' )
{
   //首先保证两数位数相同(填充0)
   int   length1 = clist1.size();
   int   length2 = clist2.size();
   if( length1 < length2 )
   {
    for(int i=0; i<(length2 -length1); ++i)
    {
     clist1.push_front('0');
    }
   }
   else if ( length1 > length2 )
   {
    for(int i=0; i<(length1 -length2); ++i)
    {
     clist2.push_front('0');
    }
   }
  
   //整数加法，从低位加起，最低位的进位初始为0
   int   c = 0; //低位借位初始为0
   int   low; //减完后本位的数值

   list<char>::iterator iter1 = clist1.end();
   --iter1;
   list<char>::iterator iter2 = clist2.end();
   --iter2;
   for(; iter1!=clist1.begin() && iter2!=clist2.begin();--iter1,--iter2)
   {
    int   num1 = *iter1 -'0';
    int   num2 = *iter2 -'0';
    low = (num1+num2+c)%10;
    c = (num1+num2+c)/10;
    rs.push_front(low+'0');
   }
   //双方最高位相加的处理
   int   num1 = *iter1 -'0';
   int   num2 = *iter2 -'0';
   low = (num1+num2+c)%10;
   c = (num1+num2+c)/10;
   rs.push_front(low+'0');
   if ( c != 0 )
   {
    rs.push_front(c+'0');
   }
   return rs;
}
return rs;
}

/*******大整数减法*********/
list<char> long_sub(list<char> clist1, list<char> clist2)
{
list<char> rs; //存放最后的结果
//如果一正一负相减，做相加
if (*(clist1.begin()) != '-' && *(clist2.begin()) == '-' )
{
   clist2.erase(clist2.begin()); //去掉符号位
   rs = long_add(clist1, clist2);
   return rs;
}
//如果一负一正相减，做相加(添符号)
if ( *(clist1.begin()) == '-' && *(clist2.begin()) != '-' )
{
   clist1.erase(clist1.begin()); //去掉符号位
   rs   = long_add(clist1, clist2);
   rs.push_front('-');
   return rs;
}
//如果两负相减，作相减
if ( *(clist1.begin()) == '-' && *(clist2.begin()) == '-' )
{
   clist1.erase(clist1.begin());
   clist2.erase(clist2.begin());   //去掉符号位
   rs = long_sub(clist2, clist1);
   return rs;
}
//如果两正相减，做相减
if ( *(clist1.begin()) != '-' && *(clist2.begin()) != '-' )
{
   int   sign = -1;   //代表两数相减结果的正负，如果最高位为'-'(ascii码为45)表示负，否则表示正
   //首先保证加数位数相同(填充0)
   int   length1 = clist1.size();
   int   length2 = clist2.size();
   if( length1 < length2 )
   {
    sign = '-';
    for(int i=0; i<(length2 -length1); ++i)
    {
     clist1.push_front('0');
    }
   }
   else if ( length1 > length2 )
   {
    for(int i=0; i<(length1 -length2); ++i)
    {
     clist2.push_front('0');
    }
   }
   else if ( *(clist1.begin()) < *(clist2.begin()) )
   {
    sign = '-';
   }
   //整数减法，从低位减起，最低位的借位初始为0
   int   c = 0; //低位借位初始为0
   int   low; //减完后本位的数值
  
   list<char>::iterator iter1 = clist1.end();
   --iter1;
   list<char>::iterator iter2 = clist2.end();
   --iter2;
   if (sign != '-' )
   {
    for(; iter1!=clist1.begin() && iter2!=clist2.begin();--iter1,--iter2)
    {
     int   num1 = *iter1 -'0';
     int   num2 = *iter2 -'0';
     int   c_new = 0; //向高位的借位
     if ( num1 < num2+c )
     {
      c_new = 1;
      num1 = num1+10;
     }
     low = (num1-num2-c)%10;
     c = c_new;
     rs.push_front(low+'0');
    }
    //双方最高位相减的处理
    int   num1 = *iter1 -'0';
    int   num2 = *iter2 -'0';
    low = (num1-num2-c)%10;
    if ( low != 0 )
    {
     rs.push_front(low+'0');
    }
   }
   else if ( sign == '-' )
   {
    for(; iter1!=clist1.begin() && iter2!=clist2.begin();--iter1,--iter2)
    {
     int   num1 = *iter1 -'0';
     int   num2 = *iter2 -'0';
     int   c_new = 0; //向高位的借位
     if ( num2 < num1+c )
     {
      c_new = 1;
      num2 = num2+10;
     }
     low = (num2-num1-c)%10;
     c = c_new;
     rs.push_front(low+'0');
    }
    //双方最高位相减的处理
    int   num1 = *iter1 -'0';
    int   num2 = *iter2 -'0';
    low = (num2-num1-c)%10;
    if ( low != 0 )
    {
     rs.push_front(low+'0');
    }
    rs.push_front('-'); //最高位的'-'作为负数的标志
   }
   return rs;
}
return rs;
}

//大数乘法
list<char> long_mul(list<char> clist1, list<char> clist2)
{
list<char> rs;   //保存最后的结果
//递归出口
if(clist1.size() == 1 && clist2.size() == 1)   //两个数都成1位了
{
   int num1 = *(clist1.begin())-'0';
   int num2 = *(clist2.begin())-'0';
   int   high = (num1*num2)/10;   //积的高位
   int   low   = (num1*num2)%10;   //积的低位
   if ( high != 0 )
   {
    rs.push_back(high+'0');
   }
   rs.push_back(low+'0');
   return rs;
}
if (clist1.size() == 1 && clist2.size() > 1)
{
   int sign = -1; //最后结果的正负标志，'-'(ascii码为45)表示负，其他表示正
   char high_bit2 = *(clist2.begin()); //clist2的最高位
   if ( high_bit2 == '-' )
   {
    sign = '-'; //相乘结果为负
    clist2.erase(clist2.begin()); //去掉高位的'-'
   }
   int length2 = clist2.size(); //clist2的有效长度(去除'-'号后)
   if ( length2 > 1 )
   {
    //对clist2进行拆分
    list<char>   clist2_1;   //高位部分
    list<char>   clist2_2;   //低位部分
    int i;
    list<char>::iterator iter;
    for (i=0,iter=clist2.begin(); i<length2/2; ++i,++iter)
    {
     clist2_1.push_back(*iter);
    }
    for(; iter != clist2.end(); ++iter)
    {
     clist2_2.push_back(*iter);
    }
    list<char> rs1; //高位部分和clist1的积
    list<char> rs2; //低位部分和clist1的积
    rs1 = long_mul(clist1, clist2_1);
    rs2 = long_mul(clist1, clist2_2);
    //对高位积进行移位(末尾添0)
    for( i=0; i<clist2_2.size(); ++i )
    {
     rs1.push_back('0');
    }
    rs = long_add(rs1,rs2); //两部分积相加
    if( sign == '-' )
    {
     rs.push_front('-');
    }
   }
   else
   {
    rs = long_mul(clist1, clist2);
    if ( sign == '-' )
    {
     rs.push_front('-'); //结果添上'-'号
    }
   }
   return rs;
}
if (clist1.size() >1 && clist2.size() == 1)
{
   int sign = -1; //最后结果的正负标志，'-'表示负，其他表示正
   char high_bit1 = *(clist1.begin()); //clist1的最高位
   if ( high_bit1 == '-' )
   {
    sign = '-'; //相乘结果为负
    clist1.erase(clist1.begin()); //去掉高位的'-'
   }
   int length1 = clist1.size(); //clist1的有效长度(去除'-'号后)
   if ( length1 > 1 )
   {
    //对clist1进行拆分
    list<char>   clist1_1;   //高位部分
    list<char>   clist1_2;   //低位部分
    int i;
    list<char>::iterator iter;
    for (i=0,iter=clist1.begin(); i<length1/2; ++i,++iter)
    {
     clist1_1.push_back(*iter);
    }
    for(; iter != clist1.end(); ++iter)
    {
     clist1_2.push_back(*iter);
    }
    list<char> rs1; //高位部分和clist2的积
    list<char> rs2; //低位部分和clist2的积
    rs1 = long_mul(clist1_1, clist2);
    rs2 = long_mul(clist1_2, clist2);
    //对高位积进行移位(末尾添0)
    for( i=0; i<clist1_2.size(); ++i )
    {
     rs1.push_back('0');
    }
    rs = long_add(rs1,rs2); //两部分积相加
    if( sign == '-' )
    {
     rs.push_front('-');
    }
   }
   else
   {
    rs = long_mul(clist1, clist2);
    if ( sign == '-' )
    {
     rs.push_front('-'); //结果添上'-'号
    }
   }
   return rs;
}
if (clist1.size() >1 && clist2.size() > 1 )
{
   int sign = -1; //最后结果的正负标志，'-'表示负，其他表示正
   char   high_bit1 = *(clist1.begin());   //clist1的最高位
   char   high_bit2 = *(clist2.begin());   //clist2的最高位
   if ( high_bit1 == '-'   && high_bit2 != '-' )
   {
    sign = '-';   //相乘结果为负
    clist1.erase(clist1.begin());   //去掉高位的'-'
   }
   if ( high_bit1 != '-' && high_bit2 == '-' )
   {
    sign = '-';   //相乘结果为负
    clist2.erase(clist2.begin());   //去掉高位的'-'
   }
   if ( high_bit1 =='-' && high_bit2 == '-' )
   {
    clist1.erase(clist1.begin());
    clist2.erase(clist2.begin());    //去掉高位的'-'
   }
   int length1 = clist1.size(); //clist1的有效长度
   int length2 = clist2.size(); //clist2的有效长度
   if ( length1 == 1 || length2 == 1 )
   {
    rs = long_mul(clist1, clist2);
    if ( sign == '-' )
    {
     rs.push_front('-');
    }
   }
   else if ( length1 > 1 && length2 > 1 )
   {
    //对clist1和clist2分别进行划分
    list<char> clist1_1;   //clist1的高位部分
    list<char> clist1_2;   //clist1的低位部分
    list<char> clist2_1;   //clist2的高位部分
    list<char> clist2_2;   //clist2的低位部分
    int i;
    list<char>::iterator iter;
    for(i=0,iter=clist1.begin(); i<length1/2; ++i,++iter)
    {
     clist1_1.push_back(*iter);
    }
    for(; iter!=clist1.end(); ++iter)
    {
     clist1_2.push_back(*iter);
    }
    for(i=0,iter=clist2.begin(); i<length2/2; ++i,++iter)
    {
     clist2_1.push_back(*iter);
    }
    for(; iter!=clist2.end(); ++iter)
    {
     clist2_2.push_back(*iter);
    }
    list<char> rs_hh;   //两个高位相乘的结果
    list<char> rs_ll;   //两个低位相乘的结果
    rs_hh = long_mul(clist1_1, clist2_1);
    //高位相乘结果移位(末尾添0)
    for(i=0; i<clist1_2.size()+clist2_2.size(); ++i)
    {
     rs_hh.push_back('0');
    }
    rs_ll = long_mul(clist1_2, clist2_2);
    list<char> sub1_hl;   //clist1的高位和低位部分的差
    list<char> sub2_lh;   //clist2的低位和高位部分的差
    //两个高位分别移位
    for(i=0; i<clist1_2.size(); ++i)
    {
     clist1_1.push_back('0');
    }
    for(i=0; i<clist2_2.size(); ++i)
    {
     clist2_1.push_back('0');
    }
    sub1_hl = long_sub(clist1_1, clist1_2);
    sub2_lh = long_sub(clist2_2, clist2_1);
    list<char> rs_sub1_sub2; //两个差的乘积
    rs_sub1_sub2 = long_mul(sub1_hl, sub2_lh);
    //把几个乘积的结果加起来
    list<char> tmp1 = long_add(rs_hh, rs_ll);
    list<char> tmp2 = long_add(tmp1, rs_sub1_sub2);
    list<char> tmp3 = long_add(tmp2, rs_hh);
    rs = long_add(tmp3, rs_ll);
    if ( sign == '-' )
    {
     rs.push_front('-');
    }
   }
   return rs;
}
return rs;
}

void main()
{
	while(true)
{
list<char> clist1;
list<char> clist2;
cout <<"请您输入2个乘数: "<<endl;
cout <<"被乘数: ";
int i;
string   str1;
cin >> str1;
for(i=0; i<str1.size(); ++i)
{
   if (str1[i] >= '0' && str1[i] <= '9' )
   {
    clist1.push_back(str1[i]);
   }
   else
   {
    cout <<"被乘数中的数字只能为0~9" <<endl;
    exit(1);
   }
}
cout <<"乘数: ";
string str2;
cin >> str2;
for(i=0; i<str2.size(); ++i)
{
   if ( str2[i] >= '0' && str2[i] <= '9' )
   {
    clist2.push_back(str2[i]);
   }
   else
   {
    cout <<"乘数中的数字只能为0~9" <<endl;
    exit(1);
   }
}
list<char> rs = long_mul(clist1,clist2);
cout << "2数相乘的积为: ";
for(list<char>::iterator iter=rs.begin(); iter!=rs.end(); ++iter)
{
   cout << *iter;
}
cout <<endl;
}
}