大数四则运算
// 大数的四则运算及求模。数字无位数限制，除法的商支持小数。
#include <iostream>
#include <string>
#include <time.h>
using namespace std;
class BIGINTEGEROPERATIONS
{
private:
static int COMPARE(string number1, string number2)
{
int j;
int length1 = number1.size();
int length2 = number2.size();
if(number1.size() == 0) number1 = "0";
if(number2.size() == 0) number2 = "0";
j = 0;
for(int i = 0; i < length1; ++i)
{
if(number1[i] == '0') ++j;
else break;
}
number1 = number1.substr(j);
j = 0;
for(int i = 0; i < length2; ++i)
{
if(number2[i] == '0') ++j;
else break;
}
number2 = number2.substr(j);
length1 = number1.size();
length2 = number2.size();
if(length1 > length2)
{
return 1;
}
else if(length1 == length2)
{
if(number1.compare(number2) > 0)
{
return 1;
}
else if(number1.compare(number2) == 0)
{
return 0;
}
else
{
return -1;
}
}
else
{
return -1;
}
return 0;
}
public:
static string PLUS(string number1,string number2)
{
int i;
int length1 = number1.size();
int length2 = number2.size();
string result="";
reverse(number1.begin(), number1.end());
reverse(number2.begin(), number2.end());
for(i = 0; i < length1 && i < length2; i++)
{
char c = (char)(number1[i] + number2[i] - 48);
result = result + c;
}
while(i < length1)
{
result = result + number1[i];
++i;
}
while(i < length2)
{
result = result + number2[i];
++i;
}
int carry = 0;
for(i = 0; i < (int)result.size(); ++i)
{
int value = result[i] - 48 + carry;
result[i] = (char)(value % 10 + 48);
carry = value / 10;
}
if(carry !=0 )
{
result = result + (char)(carry + 48);
}
for(i = result.size() - 1; i >= 0; i--)
{
if(result[i] != '0') break;
}
result = result.substr(0, i + 1);
reverse(result.begin(), result.end());
if(result.length() == 0) result = "0";
return result;
}
static string MINUS(string number1,string number2)
{
int i;
string result = "";
int length1 = number1.size();
int length2 = number2.size();
if(COMPARE(number2,number1) > 0)
{
return "-" + MINUS(number2, number1);
}
reverse(number1.begin(),number1.end());
reverse(number2.begin(),number2.end());
for(i = 0; i < length1 && i < length2; i++)
{
char c = number1[i] - number2[i] + 48;
result = result + c;
}
if(i < length1)
{
for(; i < length1; i++)
{
result = result + number1[i];
}
}
int carry = 0;
for(i = 0; i < (int)result.length(); i++)
{
int value = result[i] - 48 + carry;
if(value < 0)
{
value = value + 10;
carry = -1;
}
else carry = 0;
result[i]=(char)(value + 48);
}
for(i = result.size() - 1; i >= 0; i--)
{
if(result[i] != '0')break;
}
result = result.substr(0, i+1);
reverse(result.begin(), result.end());
if(result.length()==0) result = "0";
return result;
}
static string MULTIPLY(string number1, string number2)
{
int i, j;
int *iresult;
int length1 = number1.size();
int length2 = number2.size();
string result = "";
reverse(number1.begin(), number1.end());
reverse(number2.begin(), number2.end());
iresult = (int*)malloc(sizeof(int) * (length1 + length2 + 1));
memset(iresult, 0, sizeof(int) * (length1 + length2 + 1));
for(i = 0; i < length1; i++)
{
for(j = 0; j < length2; j++)
{
iresult[i+j] += ((number1[i] - 48) * (number2[j] - 48));
}
}
int carry = 0;
for(i = 0; i < length1 + length2; i++)
{
int value = iresult[i] + carry;
iresult[i] = value % 10;
carry = value / 10;
}
for(i = length1 + length2 - 1; i >= 0; i--)
{
if(iresult[i] != 0)break;
}
for(; i >= 0; i--)
{
result = result + (char)(iresult[i]+48);
}
free(iresult);
if(result == "") result = "0";
return result;
}
// 缺省地，商数向下取整，floatpoint用于指定保留小数点的位数
static string DIVIDE(string number1, string number2, int floatpoint = 0)
{
int i, j, pos;
string result = "";
string tempstr = "";
int length1 = number1.size();
int length2 = number2.size();
if((COMPARE(number2, number1) > 0) && (floatpoint == 0))
{
return "0";
}
tempstr = number1.substr(0, length2);
pos = length2 - 1;
while(pos < length1)
{
int quotient = 0;
while(COMPARE(tempstr, number2) >= 0)
{
quotient++;
tempstr = MINUS(tempstr, number2);
}
result = result + (char)(quotient + 48);
pos++;
if(pos < length1)
{
tempstr += number1[pos];
}
}
if(floatpoint > 0)
{
result += '.';
string stmp = "1";
int itmp = 0;
for(int k = 0; k < floatpoint; ++k)
{
stmp += '0';
if(COMPARE(MULTIPLY(MINUS(number1, MULTIPLY(DIVIDE(number1, number2), number2)), stmp), number2) < 0)
{
result += '0';
++itmp;
}
}
string temp = DIVIDE(MULTIPLY(MINUS(number1, MULTIPLY(DIVIDE(number1, number2), number2)), stmp), number2);
if(temp[0] != '0') result += temp;
}
j = result.size();
for(i = 0; i < j; i++)
{
if(result[i] != '0') break;
}
result = result.substr(i, j);
return result;
}
static string MOD(string number1, string number2)
{
if(COMPARE(number2, number1) > 0)
{
return number1;
}
else if(COMPARE(number2, number1) == 0)
{
return "0";
}
else
{
return MINUS(number1, MULTIPLY(DIVIDE(number1, number2), number2));
}
}
};
int main(int argc, char* argv[])
{
clock_t start, end;
// 两个操作数均为600位
string number1 = "99999999999999999999999999999999999999999999999999"
"99999999999999999999999999999999999999999999999999"
"99999999999999999999999999999999999999999999999999"
"99999999999999999999999999999999999999999999999999"
"99999999999999999999999999999999999999999999999999"
"99999999999999999999999999999999999999999999999999"
"99999999999999999999999999999999999999999999999999"
"99999999999999999999999999999999999999999999999999"
"99999999999999999999999999999999999999999999999999"
"99999999999999999999999999999999999999999999999999"
"99999999999999999999999999999999999999999999999999"
"99999999999999999999999999999999999999999999999999";
string number2 = "99989998999899989998999899989998999899989998999899"
"98999899989998999899989998999899989998999899989998"
"99989998999899989998999899989998999899989998999899"
"98999899989998999899989998999899989998999899989998"
"99989998999899989998999899989998999899989998999899"
"98999899989998999899989998999899989998999899989998"
"99989998999899989998999899989998999899989998999899"
"98999899989998999899989998999899989998999899989998"
"99989998999899989998999899989998999899989998999899"
"98999899989998999899989998999899989998999899989998"
"99989998999899989998999899989998999899989998999899"
"98999899989998999899989998999899989998999899989998";
string result;
int interval = 0;
start = clock();
result = BIGINTEGEROPERATIONS::PLUS(number1, number2);
end = clock();
interval = (end - start) * 1000 / CLOCKS_PER_SEC;
cout << "Result of PLUS operation:" << endl;
cout << result << endl;
cout << "It took " << interval << "ms" << endl;
cout << endl;
start = clock();
result = BIGINTEGEROPERATIONS::MINUS(number1, number2);
end = clock();
interval = (end - start) * 1000 / CLOCKS_PER_SEC;
cout << "Result of MINUS operation:" << endl;
cout << result << endl;
cout << "It took " << interval << "ms" << endl;
cout << endl;
start = clock();
result = BIGINTEGEROPERATIONS::MULTIPLY(number1, number2);
end = clock();
interval = (end - start) * 1000 / CLOCKS_PER_SEC;
cout << "Result of MULTIPLY operation:" << endl;
cout << result << endl;
cout << "It took " << interval << "ms" << endl;
cout << endl;
start = clock();
result = BIGINTEGEROPERATIONS::DIVIDE(number1, number2);
end = clock();
interval = (end - start) * 1000 / CLOCKS_PER_SEC;
cout << "Result of DIVIDE operation:" << endl;
cout << result << endl;
cout << "It took " << interval << "ms" << endl;
cout << endl;
start = clock();
result = BIGINTEGEROPERATIONS::MOD(number1, number2);
end = clock();
interval = (end - start) * 1000 / CLOCKS_PER_SEC;
cout << "Result of MOD operation:" << endl;
cout << result << endl;
cout << "It took " << interval << "ms" << endl;
cout << endl;
return 0;
}
/* 计算结果如下(Release 模式)：
Result of PLUS operation:
1999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989997
It took 0ms
Result of MINUS operation:
100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001
It took 0ms
Result of MULTIPLY operation:
999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989998999899989997000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010002
It took 15ms
Result of DIVIDE operation:
1.0001
It took 0ms
Result of MOD operation:
100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001000100010001
It took 0ms
Debug模式下，加、减、乘、除以及取模的执行时间分别为：
0ms
0ms
63ms
78ms
0ms
*/
