大数加减乘除求根源码

//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; } } }