大数(高精度)加减乘除取模

#include <iostream>

#include <string>

using namespace std;

inline int compare(string str1, string str2)

{

if(str1.size() > str2.size()) //长度长的整数大于长度小的整数

return 1;

else if(str1.size() < str2.size())

return -1;

else

return str1.compare(str2); //若长度相等，从头到尾按位比较，compare函数：相等返回0，大于返回1，小于返回－1

}

//高精度加法

string ADD_INT(string str1, string str2)

{

string MINUS_INT(string str1, string str2);

int sign = 1; //sign 为符号位

string str;

if(str1[0] == '-') {

if(str2[0] == '-') {

sign = -1;

str = ADD_INT(str1.erase(0, 1), str2.erase(0, 1));

}else {

str = MINUS_INT(str2, str1.erase(0, 1));

}

}else {

if(str2[0] == '-')

str = MINUS_INT(str1, str2.erase(0, 1));

else {

//把两个整数对齐，短整数前面加0补齐

string::size_type l1, l2;

int i;

l1 = str1.size(); l2 = str2.size();

if(l1 < l2) {

for(i = 1; i <= l2 - l1; i++)

str1 = "0" + str1;

}else {

for(i = 1; i <= l1 - l2; i++)

str2 = "0" + str2;

}

int int1 = 0, int2 = 0; //int2 记录进位

for(i = str1.size() - 1; i >= 0; i--) {

int1 = (int(str1[i]) - 48 + int(str2[i]) - 48 + int2) % 10; //48
为 '0' 的ASCII码

int2 = (int(str1[i]) - 48 + int(str2[i]) - 48 +int2) / 10;

str = char(int1 + 48) + str;

}

if(int2 != 0) str = char(int2 + 48) + str;

}

}

//运算后处理符号位

if((sign == -1) && (str[0] != '0'))

str = "-" + str;

return str;

}

//高精度减法

string MINUS_INT(string str1, string str2)

{

string MULTIPLY_INT(string str1, string str2);

int sign = 1; //sign 为符号位

string str;

if(str2[0] == '-')

str = ADD_INT(str1, str2.erase(0, 1));

else {

int res = compare(str1, str2);

if(res == 0) return "0";

if(res < 0) {

sign = -1;

string temp = str1;

str1 = str2;

str2 = temp;

}

string::size_type tempint;

tempint = str1.size() - str2.size();

for(int i = str2.size() - 1; i >= 0; i--) {

if(str1[i + tempint] < str2[i]) {

str1[i + tempint - 1] = char(int(str1[i + tempint - 1]) - 1);

str = char(str1[i + tempint] - str2[i] + 58) + str;

}

else

str = char(str1[i + tempint] - str2[i] + 48) + str;

}

for(i = tempint - 1; i >= 0; i--)

str = str1[i] + str;

}

//去除结果中多余的前导0

str.erase(0, str.find_first_not_of('0'));

if(str.empty()) str = "0";

if((sign == -1) && (str[0] != '0'))

str = "-" + str;

return str;

}

//高精度乘法

string MULTIPLY_INT(string str1, string str2)

{

int sign = 1; //sign 为符号位

string str;

if(str1[0] == '-') {

sign *= -1;

str1 = str1.erase(0, 1);

}

if(str2[0] == '-') {

sign *= -1;

str2 = str2.erase(0, 1);

}

int i, j;

string::size_type l1, l2;

l1 = str1.size(); l2 = str2.size();

for(i = l2 - 1; i >= 0; i --) { //实现手工乘法

string tempstr;

int int1 = 0, int2 = 0, int3 = int(str2[i]) - 48;

if(int3 != 0) {

for(j = 1; j <= (int)(l2 - 1 - i); j++)

tempstr = "0" + tempstr;

for(j = l1 - 1; j >= 0; j--) {

int1 = (int3 * (int(str1[j]) - 48) + int2) % 10;

int2 = (int3 * (int(str1[j]) - 48) + int2) / 10;

tempstr = char(int1 + 48) + tempstr;

}

if(int2 != 0) tempstr = char(int2 + 48) + tempstr;

}

str = ADD_INT(str, tempstr);

}

//去除结果中的前导0

str.erase(0, str.find_first_not_of('0'));

if(str.empty()) str = "0";

if((sign == -1) && (str[0] != '0'))

str = "-" + str;

return str;

}

//高精度除法

string DIVIDE_INT(string str1, string str2, int flag)

{

//flag = 1时,返回商; flag = 0时,返回余数

string quotient, residue; //定义商和余数

int sign1 = 1, sign2 = 1;

if(str2 == "0") { //判断除数是否为0

quotient = "ERROR!";

residue = "ERROR!";

if(flag == 1) return quotient;

else return residue;

}

if(str1 == "0") { //判断被除数是否为0

quotient = "0";

residue = "0";

}

if(str1[0] == '-') {

str1 = str1.erase(0, 1);

sign1 *= -1;

sign2 = -1;

}

if(str2[0] == '-') {

str2 = str2.erase(0, 1);

sign1 *= -1;

}

int res = compare(str1, str2);

if(res < 0) {

quotient = "0";

residue = str1;

}else if(res == 0) {

quotient = "1";

residue = "0";

}else {

string::size_type l1, l2;

l1 = str1.size(); l2 = str2.size();

string tempstr;

tempstr.append(str1, 0, l2 - 1);

//模拟手工除法

for(int i = l2 - 1; i < l1; i++) {

tempstr = tempstr + str1[i];

for(char ch = '9'; ch >= '0'; ch --) { //试商

string str;

str = str + ch;

if(compare(MULTIPLY_INT(str2, str), tempstr) <= 0) {

quotient = quotient + ch;

tempstr = MINUS_INT(tempstr, MULTIPLY_INT(str2, str));

break;

}

}

}

residue = tempstr;

}

//去除结果中的前导0

quotient.erase(0, quotient.find_first_not_of('0'));

if(quotient.empty()) quotient = "0";

if((sign1 == -1) && (quotient[0] != '0'))

quotient = "-" + quotient;

if((sign2 == -1) && (residue[0] != '0'))

residue = "-" + residue;

if(flag == 1) return quotient;

else return residue;

}

//高精度除法,返回商

string DIV_INT(string str1, string str2)

{

return DIVIDE_INT(str1, str2, 1);

}

//高精度除法,返回余数

string MOD_INT(string str1, string str2)

{

return DIVIDE_INT(str1, str2, 0);

}

int main()

{

char ch;

string s1, s2, res;

while(cin >> ch) {

cin >> s1 >> s2;

switch(ch) {

case '+': res = ADD_INT(s1, s2); break; //高精度加法

case '-': res = MINUS_INT(s1, s2); break; //高精度减法

case '*': res = MULTIPLY_INT(s1, s2); break; //高精度乘法

case '/': res = DIV_INT(s1, s2); break; //高精度除法,返回商

case 'm': res = MOD_INT(s1, s2); break; //高精度除法,返回余数

default : break;

}

cout << res << endl;

}

return(0);

}