//设计一个支持大数运算的计算器，其中乘法使用分治法求解。该计算器支持加减乘除还有开方根运算。
#include <iostream>
#include <list>
#include <string>
#include <cstdio>
#include <cctype>
#include <cmath>
using namespace std;
list<char> Add(list<char> s, list<char> t);
list<char> Sub(list<char> s, list<char> t);
list<char> Mul(list<char> s, list<char> t);
void Div(list<char> s, list<char> t);
void Root(list<char>);
void print(list<char> ans);
void printhelp() //打印帮助信息
{
cout << "请选择要进行的大数运算" << endl;
cout << "1:加法运算" << endl;
cout << "2:减法运算" << endl;
cout << "3:乘法运算" << endl;
cout << "4:除法运算" << endl;
cout << "5:开平方根运算" << endl;
cout << "6:退出" << endl;
}
list<char> Add(list<char> num1,list<char> num2) //加法运算
{
list<char> ans;
list<char>::iterator iter1,iter2;
iter1 = num1.begin();
iter2 = num2.begin();
int sign = 0; //标记结果符号
if((*iter1) == '-' && (*iter2) == '-') //如果两个数都是负数
{
num1.pop_front();
num2.pop_front();
sign = 1;
ans = Add(num1,num2);
ans.push_front('-');
}
else if((*iter1) == '-' && (*iter2) != '-') //如果一负一正
{
num1.pop_front();
ans = Sub(num2,num1);
}
else if((*iter1) != '-' && (*iter2) == '-') //如果一正一负
{
num2.pop_front();
ans = Sub(num1,num2);
}
else //如果都为正
{
int len1,len2,i,len,carry;
len1 = num1.size();
len2 = num2.size();
if(len1 >= len2) //补齐两个数的位数
{
len = len1;
for(i = 0; i < len1 - len2; i++)
num2.push_front('0');
}
else
{
len = len2;
for(i = 0; i < len2 - len1; i++)
num1.push_front('0');
}
//print(num1);
//print(num2);
carry = 0;
iter1 = num1.end();
iter2 = num2.end();
iter1--;
iter2--;
for(;(iter1 != num1.begin()) && (iter2 != num2.begin()); --iter1,--iter2) //进行运算
{
i = (*iter1 - '0') + (*iter2 - '0') + carry;
//cout << (*iter1 - '0') << " " << (*iter2 - '0') << " " << i << endl;
ans.push_front((i % 10) + '0');
carry = i / 10;
}
i = (*iter1 - '0') + (*iter2 - '0') + carry;
//cout << (*iter1 - '0') << " " << (*iter2 - '0') << " " << i << endl;
ans.push_front((i % 10) + '0');
carry = i / 10;
if(carry)
ans.push_front(carry+'0');
}
return ans; //返回结果
}
list<char> Sub(list<char> num1,list<char> num2) //减法运算
{
list<char> ans;
int sign = 0;
list<char>::iterator iter1,iter2;
int len1,len2,len;
iter1 = num1.begin();
iter2 = num2.begin();
if((*iter1) == '-' && (*iter2) == '-') //如果两个数都为负数
{
num2.pop_front();
num1.pop_front();
ans = Sub(num2,num1);
//ans.push_front('-');
}
else if( (*iter1) == '-' && (*iter2) != '-') //如果一负一正
{
num1.pop_front();
ans = Add(num1,num2);
ans.push_front('-');
}
else if( (*iter1) != '-' && (*iter2) == '-') //如果一正一负
{
num2.pop_front();
ans = Add(num1,num2);
}
else //如果都为正
{
len1 = num1.size();
len2 = num2.size();
if(len1 >= len2) //补齐位数
{
len = len1;
for(int i = 0; i < len1 - len2; i++)
num2.push_front('0');
}
else
{
len = len2;
for(int i = 0; i < len2 - len1; i++)
num1.push_front('0');
}
//print(num1);cout << endl;
//print(num2);cout << endl;
int carry = 0,i;
iter1 = num1.end();
iter2 = num2.end();
iter1--;
iter2--;
for(;(iter1 != num1.begin()) && (iter2 != num2.begin()); --iter1,--iter2) //进行运算
{
i = (*iter1 - '0' - carry) - (*iter2 - '0');
carry = 0;
if( i < 0)
{
i += 10;
carry = 1;
}
//cout << (*iter1 - '0') << " " << (*iter2 - '0') << " " << i << endl;
ans.push_front((i % 10) + '0');
}
i = (*iter1 - '0' - carry) - (*iter2 - '0');
if(i < 0)
{
i += 10;
sign = 1;
}
//cout << (*iter1 - '0') << " " << (*iter2 - '0') << " " << i << endl;
if(i) ans.push_front(i + '0');
if(sign)
ans.push_front('-');
}
return ans;
}
list<char> Mul(list<char> num1,list<char> num2) // 分治法求两大数的积
{
list<char> ans;
int sign = 0;
int len1,len2,len;
list<char>::iterator iter1,iter2,iter;
list<char> high,low;
list<char> anshigh,anslow;
int th,tl;
int i,j,k;
//print(num1);cout << endl;
//print(num2);cout << endl;
if(num1.size() == 1 && num2.size() == 1) //如果两数都已是一位数，则进行运算
{
th = *(num1.begin()) - '0';
tl = *(num2.begin()) - '0';
th *= tl;
ans.push_front( th % 10 + '0');
ans.push_front( th / 10 + '0');
return ans;
}
else if(num1.size() == 1 && num2.size() > 1) //如果num1位数大于1，则对Num1分治求积
{
if(*(num2.begin()) == '-')
{
sign = 1;
num2.pop_front();
}
len2 = num2.size();
if(len2 == 1)
{
ans = Mul(num1,num2);
if(sign)
ans.push_front('-');
}
else
{
for(iter= num2.begin(),i = 0; i < len2 / 2; i++,iter++)
{
high.push_back(*iter);
}
for(;iter!=num2.end();iter++)
{
low.push_back(*iter);
}
len = low.size();
anshigh = Mul(num1,high); //num1分为两部分，high,low
anslow = Mul(num1,low);
for(i = 0; i < len; i++)
anshigh.push_back('0');
ans = Add(anshigh,anslow); //合并结果
if(sign)
ans.push_front('-');
}
return ans;
}
else if(num2.size() == 1 && num1.size() > 1) //如果num2位数大于1，则对Num2分治求积
{
if(*(num1.begin()) == '-')
{
sign = 1;
num1.pop_front();
}
len1 = num1.size();
if(len2 == 1)
{
ans = Mul(num1,num2);
if(sign)
ans.push_front('-');
}
else
{
for(iter= num1.begin(),i = 0; i < len1 / 2; i++,iter++)
{
high.push_back(*iter);
}
for(;iter!=num1.end();iter++)
{
low.push_back(*iter);
}
len = low.size();
anshigh = Mul(num2,high); //num2分为两部分，high,low
anslow = Mul(num2,low);
for(i = 0; i < len; i++)
anshigh.push_back('0');
ans = Add(anshigh,anslow); //合并结果
if(sign)
ans.push_front('-');
}
return ans;
} //如果两数位数都大于1，则都运用分治
else
{
list<char> num1high,num1low,num2high,num2low;
int flag1 = 0,flag2 = 0;
if(*(num1.begin()) == '-')
{
flag1 = 1;
num1.pop_front();
}
if(*(num2.begin()) == '-')
{
flag2 = 1;
num2.pop_front();
}
if((flag1 == 1 && flag2 == 0)||(flag1 == 0 && flag2 == 1)) //如果有一正一负，则标记结果为负
{
sign = 1;
}
len1 = num1.size();
len2 = num2.size();
if(len1 == 1 || len2 == 1) //如果有一个数是一位数，则直接递归调用
{
ans = Mul(num1,num2);
if(sign)
ans.push_front('-');
}
else
{ //否则分治法求
for(iter = num1.begin(),i = 0; i < len1 / 2; iter++,i++)
num1high.push_back(*iter); //被乘数高位部分
for( ; iter != num1.end(); iter++)
num1low.push_back(*iter); //被乘数低位部分
for(iter = num2.begin(),i = 0; i < len2 / 2; iter++,i++)
num2high.push_back(*iter); //乘数高位部分
for( ; iter != num2.end(); iter++)
num2low.push_back(*iter); //乘数低位部分
int a = (len1 + 1) / 2;
int b = (len2 + 1) / 2;
list<char> AC,AD,BC,BD;
//print(num2high);cout << endl;
//print(num2low);cout << endl;
AC = Mul(num1high,num2high); //运用X=A*10^a + B; Y= C*10^b + D;
AD = Mul(num1high,num2low); // X*Y = AC * 10 ^(a+b) + AD *10^a + BC * 10 ^b + BD公式求
BC = Mul(num1low,num2high);
BD = Mul(num1low,num2low);
for(i = 0; i < a + b; i++)
AC.push_back('0');
for(i = 0; i < a; i++)
AD.push_back('0');
for(i = 0; i < b; i++)
BC.push_back('0');
ans = Add(AC,AD);
ans = Add(ans,BC);
ans = Add(ans,BD); //累加结果
if(sign)
ans.push_front('-');
}
return ans;
}
}
void Div(list<char> num1,list<char> num2) //用辗转相除求结果
{
list<char> ans;
list<char> temp;
int len1,len2,len;
int i,j,k;
int sign = 0;
int flag1 = 0,flag2 = 0;
list<char>::iterator iter;
if(*(num1.begin()) == '-')
{
flag1 = 1;
num1.pop_front();
}
if(*(num2.begin()) == '-')
{
flag2 = 1;
num2.pop_front();
}
if((flag1 == 1 && flag2 != 1) || (flag1 == 0 && flag2 == 1))
sign = 1; //标记结果符号
len1 = num1.size();
len2 = num2.size();
if(len1 < len2) //如果被除数小于除法，除数为0
{
cout << "商是0；余数是" ;
print(num2);
cout << endl;
return ;
}
else //用辗转相除求结果
{
for(iter = num1.begin(),i = 0; i < len2 ;++i,++iter)
temp.push_back(*iter);
list<char> digit,res;
for(j = 0; j < 10; j++)
{
digit.clear();
digit.push_back(j + '0');
res = Mul(num2,digit);
res = Sub(temp,res);
if(*(res.begin()) == '-')
break;
}
//cout << endl;print(temp); cout << endl;
j -= 1;
if(j > 0)
{
digit.clear();
digit.push_back(j + '0');
temp = Sub(temp,num2);
ans.push_back(j + '0');
}
for(;iter != num1.end();++iter)
{
temp.push_back(*iter);
for(j = 0; j < 10; j++)
{
digit.clear();
digit.push_back(j + '0');
res = Mul(num2,digit);
res = Sub(temp,res);
if(*(res.begin()) == '-')
break;
}
//cout << endl;print(temp); cout << endl;
j -= 1;
digit.clear();
digit.push_back(j + '0');
res = Mul(num2,digit);
temp = Sub(temp,res);
ans.push_back(j + '0');
}
if(sign)
ans.push_front('-');
}
cout << "商是";
print(ans);
cout << "；余数是" ;
print(temp);
cout << endl;
return ;
}
void Root(list<char> num1) //求大数的平方根，用枚举算法暴力搜索算法求
{
list<char> ans;
int len1;
list<char> digit,temp;
len1 = num1.size();
int a = len1 / 2; //a是结果的最少位数
int i;
digit.push_back('1');
ans.push_back('1'); //从ans=10 ^ a 开始搜索
for(i = 0; i < a - 1; i++)
ans.push_back('0');
while(true) //搜到则结束
{
temp = Mul(ans,ans);
temp = Sub(num1,temp);
if(*(temp.begin()) == '-') //如果当前ans的平方大于num1，则得结果
break;
ans = Add(ans,digit);
}
ans = Sub(ans,digit);
print(ans);
cout << endl;
}
list<char> translate(string input)
{
list<char> res;
int len = input.length();
for(int i = 0; i < len; i++)
res.push_back(input[i]);
return res;
}
void print(list<char> ans)
{
list<char>::iterator iter;
int flag = 1;
iter = ans.begin();
if(*iter == '-')
{
cout << *iter;
iter++;
}
for(;iter != ans.end(); ++iter)
{
if(*iter == '0' && flag)
continue;
//cout << (*iter);
else
{
flag = 0;
cout << (*iter);
}
}
if( flag == 1)
cout << 0 ;;
//cout << endl;
}
int main()
{
char choice; //选择要进行的运算
list<char> num1;
list<char> num2;
list<char> res;
string input;
while(true)
{
cout << endl;
printhelp();
cin >> choice;
switch(choice)
{
case '1': //如果选择加法运算
cout << "请输入第一个数" << endl;
cin >> input;
num1 = translate(input);
cout << "请输入第二个数" << endl;
cin >> input;
num2 = translate(input);
res = Add(num1,num2);
print(num1);
cout << " + " ;
print(num2);
cout << " = ";
print(res);
cout << endl;
break;
case '2': //选择减法运算
cout << "请输入第一个数" << endl;
cin >> input;
num1 = translate(input);
cout << "请输入第二个数" << endl;
cin >> input;
num2 = translate(input);
res = Sub(num1,num2);
print(num1);
cout <<" - " ;
print(num2);
cout << " = ";
print(res);
cout << endl;
break;
case '3': //选择乘法运算
cout << "请输入第一个数" << endl;
cin >> input;
num1 = translate(input);
cout << "请输入第二个数" << endl;
cin >> input;
num2 = translate(input);
res = Mul(num1,num2);
print(num1);
cout <<" * " ;
print(num2);
cout << " = ";
print(res);
cout << endl;
break;
case '4': //选择除法运算
cout << "请输入第一个数" << endl;
cin >> input;
num1 = translate(input);
cout << "请输入第二个数" << endl;
cin >> input;
num2 = translate(input);
print(num1);
cout << " / " ;
print(num2);
cout << " = ";
if(num2.size() == 1 && (*(num2.begin()) == '0'))
{
cout << "divided zero error" << endl;
break;
}
Div(num1,num2);
//print(res);
cout << endl;
break;
case '5': //选择求根运算
cout << "请输入第一个数" << endl;
cin >> input;
num1 = translate(input);
if(*(num1.begin()) == '-')
{
cout << "负数没有实数平方根" << endl;
break;
}
Root(num1);
break;
case '6':
return 0;
default:
break;
}
}
}
